Academia.edu no longer supports Internet Explorer.
To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to upgrade your browser.
Science Data Booklet
Manjunath RScience is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the nature. This booklet is designed to place less emphasis on factual material and greater emphasis on the understanding and application of scientific concepts and principles. This booklet has been designed in recognition of the need for students to develop skills that will be of long term value in an increasingly technological world rather than focusing on large quantities of factual material which may have only short term relevance.
Related papers
Data-Texts in the Sciences
2021
Grounded within current reform recommendations and built upon Giere’s views (1986, 1999) on model-based science, we propose an alternative approach to science education which we refer to as the Evidence-Explanation (EE) Continuum. The approach addresses conceptual, epistemological, and social domains of knowledge, and places emphasis on the epistemological conversations about data acquisitions and transformations in the sciences. The steps of data transformation, which we refer to as data-texts, we argue, unfold the processes of using evidence during knowledge building and reveal the dynamics of scientific practices. Data-texts involve (a) obtaining observations/measurements to become data; (b) selecting and interpreting data to become evidence; (c) using evidence to ascertain patterns and develop models; and (d) utilizing the patterns and models to propose and refine explanations. Throughout the transformations of the EE continuum, there are stages of transition that foster the eng...
Exploring Data to Learn about the Nature of Science
The American Biology Teacher, 2016
Biology is often taught as disconnected facts, even though the subject itself provides a holistic approach to the study of life, particularly through the overarching frame of evolution. The Framework for K–12 Science Education and Next Generation Science Standards promote a coherent approach to science that uses a developmental approach to learning. This is consistent with the use of data, reflective strategies, and a research inquiry approach that encourages students to confront their own thinking and reasoning, and thus encourages the engagement of argumentation in the classroom. This article presents narratives and classroom scenarios that might provide insights into learning strategies, with implications for a more cohesive approach to learning both biology concepts and the practices of science.
Teaching children the structure of science
2009
abstract Maps of the world are common in classroom settings. They are used to teach the juxtaposition of natural and political functions, mineral resources, political, cultural and geographical boundaries; occurrences of processes such as tectonic drift; spreading of epidemics; and weather forecasts, among others. Recent work in scientometrics aims to create a map of science encompassing our collective scholarly knowledge.
What Is Science?
Alan F. Chalmers introduces his 1982 book What Is This Thing Called Science? with the smilingly discouraging words:
Guidance document #3 - Collection of experiences on Science Education
2019
This is the 3rd document of the series, devoted to the experiences related to science education. Its aim is helping GRACE partners reflect on possible GAs to develop in this area during the project implementation period or in the framework of the 8-year Roadmap towards RRI.<br> The overall aim of Science Education is to enhance education processes to attract and better equip future researchers and other societal actors with the necessary knowledge to fully responsibly join research and innovation processes. This also includes initiatives aimed at boosting science literacy in society and sparking the interest of children in science and technology.<br> This short document also considers education initiatives aimed at supporting the diffusion of RRI in higher education settings. The document is organised in four sections, respectively devoted to: Science education with and for schools Science education outreach Internal skills in science education and RRI Governance structu...
<title>Teaching children the structure of science</title>
Visualization and Data Analysis 2009, 2009
1. I What is science?
2003
I have found Ms… has had to deal with another problem: the history of science is almost entirely the history of Western science, and Ms… has almost no knowledge of European history since classical times. This is obviously a considerable drawback in coming to a general view or coming to grips with many broader problems in the development of science…
Data, Phenomena, and Theory: How Clarifying the Concepts Can Illuminate the Nature of Science
Philosophy of Education Archive, 2003
Science Data Booklet
"The only true wisdom is in knowing you know nothing."
― Socrates
Manjunath.R
#16/1, 8th Main Road, Shivanagar, Rajajinagar, Bangalore560010, Karnataka, India
*Corresponding Author Email: manjunath5496@gmail.com
*Website: http://www.myw3schools.com/
Science is a systematic enterprise that builds and organizes knowledge in the form of
testable explanations and predictions about the nature. This booklet is designed to place
less emphasis on factual material and greater emphasis on the understanding and
application of scientific concepts and principles. This booklet has been designed in
recognition of the need for students to develop skills that will be of long term value in an
increasingly technological world rather than focusing on large quantities of factual
material which may have only short term relevance.
My brain is only a receiver, in the
Universe there is a core from which we
obtain knowledge, strength and
inspiration. I have not penetrated into
the secrets of this core, but I know that
it exists.
― Nikola Tesla
Laws of Exponents
1n = 1
0n = 0, for n > 0
x1 = x
x0 = 1
x ½ = √𝑥
n
x 1/n = √𝑥
x−1 =
1
𝑥
x m x n = xm+n
𝑥m
= x m – n , if m > n
𝑥m
= 1 , if m = n
𝑥m
=
𝑥n
𝑥n
𝑥
n
1
𝑥n–m
, if m < n; x ∈ R, x ≠ 0
(x m) n = x mn
(x y) n = x n y n
𝑥n
(x / y) n = 𝑦 n
1
x −n = 𝑥 n
x m / n = n√𝑥 m
(x m y n) p = x mp y np
1
(x m / y n) p =
𝑥 mp
𝑦 np
If n is even, (−1) n = 1
If n is odd, (−1) n = −1
Important Formulas in Algebra
(a + b) 2 = a2 + 2ab + b2
a2 + b2 = (a + b)2 − 2ab
(a − b)2 = a2 − 2ab + b2
a2 + b2 = (a − b)2 + 2ab
(a + b + c) 2 = a2 + b2 + c2 + 2(ab + bc + ca)
(a + b) 3 = a3 + b3 + 3ab (a + b)
a3 + b3 = (a + b) 3 − 3ab (a + b)
(a − b)3 = a3 − b3 − 3ab (a − b)
a3 − b3 = (a − b) 3 + 3ab (a − b)
a2 − b2 = (a + b) (a − b)
a3 − b3 = (a − b) (a2 + ab + b2)
a3 + b3 = (a + b) (a2 − ab + b2)
a4 – b4 = (a2 – b2) (a2 + b2) = (a + b) (a + b) (a2 + b2)
a4 + b4 = (a2 + b2) 2 – 2a2 b2 = (a2 + √2ab + b2) (a2 – √2ab + b2)
a5 + b5 = (a + b) (a4 – a3b + a2b2 – ab3 + b4 )
a5 – b5 = (a – b) (a4 + a3b + a2b2 + ab3 + b4)
an − bn = (a − b) (an−1 + an−2 b + an−3 b2 + ··· + bn−1n−1)
2
(a + b + c) 2 = a2 + b2 + c2 + 2 (ab + bc + ca)
a3 + b3 + c3 – 3abc = (a + b + c) (a2 + b2 + c2 – ab – bc – ca)
If a + b + c = 0, then the above identity reduces to a3 + b3 + c3 = 3abc
Roots of Quadratic Equation
For a quadratic equation ax2 + bx + c where a ≠ 0, the roots will be given by the equation as:
𝑥=
−b ± √b 2 − 4ac
2a
Δ = b2 − 4ac is called the discrimination
For real and distinct roots, Δ > 0
For real and coincident roots, Δ = 0
For non-real roots, Δ < 0
If α and β are the two roots of the equation ax2 + bx + c then,
α+β=
α×β=
−b
𝑎
c
a
If the roots of a quadratic equation are α and β, the equation will be (x − α) (x − β) = 0
TRIGONOMETRY FORMULAS
cos 2 ( x) sin 2 ( x) 1
1 tan 2 ( x) sec 2 ( x)
cos( x y ) cos( x) cos( y ) sin( x) sin( y )
sin( x y ) sin( x) cos( y ) cos( x) sin( y )
cot 2 ( x) 1 csc 2 ( x)
tan( x y )
3
tan( x) tan( y)
1 tan( x) tan( y)
sin( 2 x) 2 sin( x) cos( x)
c 2 a 2 b 2 2ab cos(C )
sin( A) sin( B) sin(C )
a
b
c
cos 2 ( x) sin 2 ( x)
cos( 2 x) 2 cos 2 ( x) 1
1 2 sin 2 ( x)
tan( 2 x)
2 tan( x)
1 tan 2 ( x)
1 cos( x)
x
cos
2
2
1 cos( 2 x)
2
1
cos(
2 x)
cos 2 ( x)
2
1 cos( 2 x)
tan 2 ( x)
1 cos( 2 x)
sin 2 ( x)
1 cos( x)
x
sin
2
2
1 cos( x)
x
tan
1 cos( x)
2
sin( x) sin( y ) 12 [cosx y cos( x y )]
cos( x) cos( y ) 12 [cosx y cos( x y )]
sin( x) cos( y ) 12 [sin x y sin( x y )]
cos( x) sin( y ) 12 [sin x y sin( x y )]
x y x y
sin( x) sin( y ) 2 sin
cos
2 2
x y x y
sin( x) sin( y ) 2 sin
cos
2 2
x y x y
cos( x) cos( y ) 2 cos
cos
2 2
x y x y
cos( x) cos( y ) 2 sin
sin
2 2
sin(−x) = −sin(x)
csc(−x) = −csc(x)
cos(−x) = cos(x)
4
sec(−x) = sec(x)
tan(−x) = −tan(x)
cot(−x) = −cot(x)
Pythagorean Theorem
c
a
α
b
a2 + b2 = c2
c = √a2 + b 2
a
sin α = =
c
hypotenuse
c
hypotenuse
b
cos α = =
a
tan α = =
cot α =
opposite
b
adjacent
opposite
1
adjacent
tan α
1
sec α =
cosec α =
The length of the longest side can never be greater than the sum of the two other sides.
cos α
1
sin α
5
The length of the shortest side can never be less than the positive difference of the other
two sides.
A "Pythagorean Triple" is a set of positive integers, a, b and c that fits the rule:
a2 + b2 = c2
The smallest Pythagorean Triple is 3, 4 and 5.
Hyperbolic Functions
sinh x = −sinh(−x)
sech x = sech(−x)
cosh x = cosh(−x)
cosech x = −cosech(−x)
tanh x = −tanh(−x)
coth x = −coth(−x)
cosh ix = cos x
cos ix = cosh x
sinh ix = i sin x
sin ix = i sinh x
tanh x =
coth x =
sech x =
cosech x =
cosh2 x − sinh2 x =1
cosh x = (ex + e−x) = 1 +
sinh 𝑥
cosh 𝑥
cosh 𝑥
sinh 𝑥
1
cosh 𝑥
1
2
1
sinh 𝑥
𝑥2
2!
+
𝑥4
4!
+ ….
6
valid for all x
1
sinh x = (ex − e−x) = x +
2
𝑥3
For large positive x:
3!
cosh x ≈ sinh x →
tanh x →1
+
𝑥5
5!
+ …. valid for all x
𝑒𝑥
2
For large negative x:
𝑒−𝑥
cosh x ≈ −sinh x → 2
tanh x → −1
Inverse functions
𝑥
= ln (
𝑥 + √𝑥 2 + 𝑎2
) for −∞ < x < ∞
𝑥
= ln (
𝑥 + √𝑥 2 − 𝑎2
) for x ≥ a
sinh −1
cosh −1
tanh −1
coth −1
sech −1
cosech −1
𝑎
𝑎
𝑥
𝑎
𝑥
𝑎
𝑥
𝑎
=
=
1
2
1
2
𝑎
ln (
ln (
𝑎
𝑎
𝑎+𝑥
𝑎−𝑥
𝑥+𝑎
𝑥−𝑎
) for x2 < a2
) for x2 > a2
𝑎2
= ln ( + √ 𝑥 2 − 1 ) for 0 < x ≤ a
𝑥
𝑎
𝑥
𝑎
𝑎2
= ln ( + √ 𝑥 2 + 1 ) for x ≠ 0
𝑥
Natural Number s
{1, 2, 3, 4 ...................}
Whole numbers
7
{0, 1, 2, 3 .................... }
0 is neither positive nor negative
Integers
{.....–3, –2, –1, 0, 1, 2, 3….}
Type of Integers
Non negative integers
{ 0, 1, 2, 3, ......... }
Negative integers
{. .......... –3, –2, –1}
Non positive integers
{. .......... –3, –2 –1, 0}
Positive integers
{1, 2, 3 .......... }
Rational Numbers
A number is called rational if it can be expressed in the form
Example:
4
3
p
q
where p and q are integers (q>0).
= 1.3̅ = 1.333.........
Irrational numbers
A number is called irrational if it cannot be expressed in the form
(q> 0).
Example:
√2 = 1.414..............
Real Numbers
8
p
q
where p and q are integers
Real → Rational + Irrational
Prime Numbers
Numbers which are divisible by 1 or itself
{2, 3, 5, 7, 11, 13 ..........}
1 is not a prime. 2 is the smallest prime and the only even prime.
Composite Numbers
Numbers which are multiples of prime are called composite numbers
{4, 6, 8, 9 ...........}
Coprime
21 and 22 are coprime:
The factors of 21 are 1, 3, 7 and 21
The factors of 22 are 1, 2, 11 and 22
(The only common factor is 1)
But 21 and 24 are NOT coprime:
•
•
The factors of 21 are 1, 3, 7 and 21
The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24
(The common factors are 1 and 3)
Twin primes
The prime numbers which having the difference of 2
e.g. (5, 3), (7, 5), (13, 11)............
1 is neither a prime nor a composite number
Order of Operations: PEMDAS
(Parentheses / Exponents / Multiply / Divide / Add / Subtract)
9
Euclid's Division Lemma: If two positive integers a and b, then there exists unique integers q
and r such that which satisfies the condition a = bq + r where 0 ≤ r ≤ b. If r = 0, then b is divisor
of a.
Coordinate Geometry
Any line can be represented by y = mx + b, where m is the slope and b is the y-intercept. This is
called slope-intercept form.
Distance between two points ( x1 , y1 ), ( x2 , y2 )
x1 x2 y1 y2
2
x x y y
Midpoint of two points ( x1 , y1 ), ( x2 , y2 ) 1 2 , 1 2
2
2
y
(x2, y2)
(x1, y1)
x
The slope of the line passing through the points (x1, y1) and (x2, y2) is
Differentiation Formulas
1.
d n
( x ) nx n 1
dx
2.
d
(sin x) cos x
dx
10
𝑦2 −𝑦1
𝑥2 −𝑥1
2
3.
d
(cos x) sin x
dx
4.
d
(tan x) sec 2 x
dx
5.
d
(cot x) csc 2 x
dx
6.
d
(sec x) sec x tan x
dx
7.
d
(csc x) csc x cot x
dx
8.
d x
(e ) e x
dx
9.
d x
(a ) a x ln a
dx
10.
d
1
(ln x )
dx
x
11.
d
1
( Arc sin x)
dx
1 x2
12.
1
d
( Arc tan x)
dx
1 x2
13.
d
1
( Arc sec x)
dx
| x | x2 1
14.
dy dy du
dx dx dx
15.
d
c 0
dx
16.
d
cu c du
dx
dx
11
17.
d
u v du dv
dx
dx dx
18.
d
uv u dv v du
dx
dx
dx
dv
du
u
d u
dx 2 dx
19.
dx v
v
v
20.
d
x 1
dx
Integration Formulas
1.
a dx ax C
2.
n
x dx
3.
x dx ln
4.
e
5.
x
a dx
6.
ln x dx x ln x x C
7.
sin x dx cos x C
8.
cos x dx sin x C
9.
tan x dx ln sec x C
1
x
x n 1
C , n 1
n 1
x C
dx e x C
ax
C
ln a
or ln cos x C
10. cot x dx ln sin x C
12
11. sec x dx ln sec x tan x C
12. csc x dx ln csc x cot x C ln csc x cot x C
13. sec 2 x d x tan x C
14. sec x tan x dx sec x C
15. csc 2 x dx cot x C
16. csc x cot x dx csc x C
17.
tan
18.
a
2
19.
x
Arc sin C
a
a2 x2
20.
x
2
x dx tan x x C
1
dx
x
Arc tan C
2
a
x
a
dx
dx
x2 a2
x
a
1
1
Arc sec C Arc cos C
x
a
a
a
21. u dv uv v du
HCF (Highest common factor)
HCF (a, b) =1. Then a and b are co primes
HCF (a, b) × LCM (a, b) = a × b
Vector Algebra
If i, j, k are orthonormal vectors and A = Axi + Ay j + Azk then |A|2 = Ax2 + Ay2 + Az2.
13
Scalar product
A ∙ B = |A| |B| cosθ where θ is the angle between the vectors.
Scalar multiplication is commutative: A ∙ B = B ∙ A.
Vector product
A × B = n |A| |B| sinθ, where θ is the angle between the vectors and n is a unit vector
normal to the plane containing A and B in the direction for which A, B, n form a righthanded set of axes.
Vector multiplication is not commutative: A×B = −B×A.
Scalar triple product
A × B ∙ C = A ∙B × C
Vector triple product
A × (B × C) = (A ∙ C) B − (A ∙ B) C
(A×B) × C = (A ∙ C) B − (B ∙ C) A
Angles on the inside of any triangle add up to 180◦
The length of one side of any triangle is always less than the sum
and more than the difference of the lengths of the other two sides.
If two lines intersect, the sum of the resulting four angles equals
360.
Average formula:
14
Let a1, a2, a3... an be a set of numbers, average =
𝑎1 + 𝑎2 + 𝑎3 + ….+ 𝑎n
Fractions formulas:
a
+
a
−
a
×
b
b
b
a
b
a
b
=
c
d
=
ad+bc
c
d
=
ad−bc
c
=
ac
d
c
c
d
d
bd
bd
bd
=
a
b
×
d
c
=
→ ad = bc
ad
bc
Geometry formulas:
Perimeter:
Perimeter of a square: s + s + s + s
s: length of one side
Perimeter of a rectangle: l + w + l + w
l: length
w: width
Perimeter of a triangle: a + b + c
a, b, and c: lengths of the 3 sides
Area:
15
n
Area of a square: s × s
s: length of one side
Area of a rectangle: l × w
l: length
w: width
Area of a triangle:
b: length of base
b×h
2
h: length of height
Area of a trapezoid: (b1 + b2) ×
h
2
b1 and b2: parallel sides or the bases
h: length of height
Volume:
Volume of a cube: s × s × s
s: length of one side
Volume of a box: l × w × h
l: length
w: width
h: height
4
Volume of a sphere: × π × r3
3
π: 3.14159265359
r: radius of sphere
16
Volume of a triangular prism: area of triangle × height of the triangular prism
Volume of a cylinder: π × r2 × h
r: radius of the circle of the base
h: height of the cylinder
Quadrilaterals
The diagonals of a square bisect one another, forming four 90 degree angles
The diagonals of a rhombus bisect one another, forming four 90 degree angles
The perimeter of a rectangle is twice its height plus twice its length (or, the sum of all its
sides).
The area of a parallelogram can be found multiplying base × height (the base always
forms a right angle with the height).
Circles:
Area = πr2
Circumference = 2πr
A circle has 360 degrees. An arc is the portion of the circumference of a circle in x degrees of the
circle.
Arc length =
𝑥
360
Area of sector =
× 2πr
𝑥
360
× πr2
Basic Identities
17
a+0=a
a + (−a) = 0
(a + b) + c = a + (b + c)
a+b=b+a
a − b = a + (−b)
a*1=a
a*
a*0=0
(a * b) * c = a * (b * c)
a*b=b*a
a (b + c) = ab + ac
a
b
1
a
=1
(a ≠ 0)
1
=a(b)
Negative exponents:
x −2 =
1
𝑥2
Negative bases:
(−2) 4 = −2 × −2 × −2 × −2 = 16
(−2) 5 = −2 × −2 × −2 × −2 × −2 = 32
Perfect Squares:
Perfect Square
Factors
18
1
1 * 1
4
2 * 2
9
3 * 3
16
4 * 4
25
5 * 5
36
6 * 6
49
7 * 7
64
8 * 8
81
9 * 9
100
10 * 10
121
11 * 11
144
12 * 12
169
13 * 13
196
14 * 14
225
15 * 15
256
16 * 16
289
17 * 17
324
18 * 18
361
19 * 19
19
400
20 * 20
Inequalities:
If w < x and x < y, then w < y.
If a < b and c < d, then a + c < b + d. However, this does not hold for subtracting, multiplying, or
dividing.
Probabilities
Probability is a representation of the odds of something happening. A probability of 1 is
guaranteed to happen. A probability of 0 will never happen. 0.5 = there is a 50/50 chance the
event will occur.
Probability of an outcome happening =
number of desired outcomes
total number of possible outcomes
Probability of two independent outcomes both happening is
Probability of event A * probability of event B
e.g., Event A has a probability of
events happening is:
happening.
1
4
*
1
8
=
1
1
4
and event B has a probability of
1
. The probability of both
8
. There is a 1 in 32 chance of both events A and event B
32
Combinations
20
Possible combinations = number of element A * number of element B * number of
element C….
e.g., In a cafeteria, there are 3 different dessert options, 2 different entree options, and 4 drink
options. How many different lunch combinations are possible, using one drink, one, dessert, and
one entree?
The total combinations possible = 3 * 2 * 4 = 24
Fundamental Counting Principle:
If an event can happen in N ways, and another, independent event can happen in M ways, and
then both events together can happen in N × M ways.
Combinations:
n
5
Cr =
C3 =
𝑛!
𝑟!(𝑛−𝑟)!
5!
3! (2!)
= 10
Permutations:
n
Pr =
𝑛!
(𝑛−𝑟)!
Probability that event A will happen:
P (A) =
Number of outcomes where A occurs
Total number of outcomes
P (event happens) + P (event does not happen) = 1
21
Mutually exclusive events:
Two events are mutually exclusive if they can't happen together: P (A and B) = 0
Events A and B (if they are independent events):
P (A and B) = P (A) × P (B)
Events A or B:
A happens, B happens, or both A and B happen.
P (A or B) = P (A) + P (B) – P (A and B)
Events A and B (if A and B are dependent events):
P (A and B) = P (A) × P (B | A)
P (B | A) is the probability that B occurs given that A occurs.
Number of ways to follow a rule = number of ways to ignore the rule – number of ways to break the rule.
Percents:
part =
percent
100
× whole
mode = value in the list that appears most often
median = middle value in the list
median of {3, 9, 10, 27, 50} = 10
median of {3, 9, 10, 27} =
9 + 10
2
= 9.5
Range = Greatest value – least value
Polygons
22
Total degrees = 180 (n −2) where n = number of sides
Average degrees per side =
180 (𝑛−2)
𝑛
Distance, Rate, and Time
Distance = Rate × Time
Rate =
Time =
Average speed =
Distance
Time
Distance
Rate
Total Distance Traveled
Total Time
Standard deviation:
If you're given a set of n numbers a, b, c … with a mean m:
(a−m)2 + (b−m)2 + (c−m)2 + …
SD = √
n
Variance = SD2
Integer series
𝑛 (𝑛+1)
1 + 2 + 3 + ….. + n =
12 + 22 + 32 + ….. + n2 =
1 + 2 + 3 + ….. + n =
3
3
3
3
2
𝑛 (𝑛+1) (2𝑛+1)
6
𝑛2 (𝑛+1)2
4
23
𝑛(𝑛+1)(2𝑛+1)(3𝑛2 + 3𝑛−1)
14+ 24 + 34 + ….. + n4 =
1−
1
+ −
1
1
+ ….. = ln2
1−
1
+ −
1
1
+ ….. =
1−
1
+ −
1
1
1.2.3 + 2.3.4+ … + n (n+1) (n+2) =
2
3
4
3
5
9
4
7
16
30
𝜋
4
+ ….. =
𝜋2
6
𝑛 (𝑛+1) (𝑛+2) (𝑛+3)
4
Arithmetic and Geometric progressions
A.P. Sn = a + (a + d) + (a + 2d) + … + [a + (n − 1) d] =
G.P. Sn = a + ar + ar2 + … + ar n −1 = a
1−𝑟 𝑛
1−𝑟
𝑛
2
[2𝑎 + (𝑛 − 1)𝑑]
𝑎
, (S∞ = 1− 𝑟 for |r| < 1)
Convergence of series: the ratio test
Sn = u1 + u2 + u3 + …..+ un converges as n → ∞ if lim |
𝑛→∞
𝑢𝑛+1
𝑢𝑛
|<1
Convergence of series: the comparison test
If each term in a series of positive terms is less than the corresponding term in a series known
to be convergent, then the given series is also convergent.
Power series with real variables
ex = 1 + x +
𝑥2
2!
+ ….. +
𝑥𝑛
𝑛!
+ …… valid for all x
24
𝑥2
𝑥3
ln(1+x) =x −
cosx =
𝑒 𝑖𝑥 + 𝑒 −𝑖𝑥
= 1−
sinx =
𝑒 𝑖𝑥 − 𝑒 −𝑖𝑥
= x−
tanx = x +
2
2
2𝑖
1
3
tan −1x = x −
sin −1x = x +
+
𝑥3 +
𝑥3
3
+
1 𝑥3
2 3
3
2
15
𝑥5
5
+
+ …. + (−1) n+1
𝑥2
2!
𝑥3
3!
+
+
𝑥4
4!
𝑥5
5!
𝑥 5 + ….
− ….
1.3 𝑥 5
2.4 5
𝑥6
𝑥𝑛
𝑛!
+ …. valid for −1 < x ≤ 1
− 6! + …… valid for all values of x
+ …… valid for all values of x
valid for −
π
2
<x<
valid for −1 ≤ x ≤ 1
+ ….
π
2
valid for −1 < x < 1
Complex numbers
The complex number z = x + iy = r (cosθ + i sinθ) = r e
arbitrary integer.
, where i2 = −1 and n is an
i (θ+2nπ)
The complex conjugate of z is z* = x − iy = r (cosθ − i sinθ) = re−iθ; zz* = |z|2 = x2 + y2
De Moivre's theorem
(cosθ + i sinθ) n = einθ = cos nθ + i sin nθ
Power series for complex variables
ez = 1 + z +
sin z = z −
𝑧2
2!
𝑧3
cos z = 1 −
3!
𝑧2
2!
+ …… +
+
𝑧5
+
ln (1 + z) = z −
5!
𝑧4
4!
𝑧2
2
𝑧𝑛
𝑛!
+…
convergent for all finite z
− ……
convergent for all finite z
− ……
convergent for all finite z
+
𝑧3
3
− ……
principal value of ln(1 + z)
25
Sum of first n odd numbers = n²
Sum of first n even numbers = n (n + 1)
Profit, Loss and Discount
Profit or Gain = Selling Price – Cost Price
Profit % =
Selling Price =
Cost Price =
Loss = Cost Price – Selling Price
Loss % =
Selling Price =
Cost Price =
Discount % =
Effective Discount after successive discount of a% and b% is (a + b −
Profit
Cost Price
×100
100 + Profit %
100
100
100 + Profit %
Loss
Cost Price
× Cost Price
× Selling Price
× 100
100− loss %
100
100
100− loss %
× Cost Price
× Selling Price
Marked Price−Selling Price
Marked Price
× 100
y
buy x goods and get y goods free is x + y × 100
LCM and HCF
Product of two numbers = Their H. C. F. × Their L. C. M.
LCM of Co-prime Numbers = Product of the Numbers
HCF of Fractions =
LCM of Fractions =
HCF of Numerator
LCM of denominator
LCM of Numerator
HCF of denominator
26
ab
100
). Effective Discount when you
Percentages
To find what percentage of x is y:
Increase N by S % = N( 1+
Decrease N by S % = N (1−
S
100
S
)
100
y
x
× 100
)
Time and Work
If A can do a piece of work in n days, then A's 1 day's work =
1
If A's 1 day's work = 𝑛, then A can finish the work in n days.
1
𝑛
If A is thrice as good a workman as B, then:
Ratio of work done by A and B = 3 : 1
Ratio of times taken by A & B to finish a work = 1 : 3
Pipes and Cisterns
If a pipe can fill a tank in 'x' hours and another pipe can empty the full tank in 'y' hours (where y > x), then
1
1
on opening both the pipes, the net part of the tank filled in 1 hour is ( x − y )
Time and Distance
Suppose a man covers a distance at 'x' kmph and an equal distance at 'y' kmph, then average speed during
his whole journey is [
2xy
x+y
] kmph
Trains
Lengths of trains are 'x' km and 'y' km, moving at 'u' kmph and 'v' kmph (where u > v) in the same
direction, then the time taken y the over-taker train to cross the slower train is [
27
x+y
u−v
] hrs
x+y
Time taken to cross each other is [
If two trains start at the same time from two points A and B towards each other and after crossing they take
u+ v
] hrs
a and b hours in reaching B and A respectively. Then, A's speed : B's speed = (√b : √a).
Boats and Streams
If the speed of a boat in still water is u km/hr and the speed of the stream is v km/hr, then:
Speed downstream = (u + v) km/hr.
Speed upstream = (u − v) km/hr.
If the speed downstream is a km/hr and the speed upstream is b km/hr, then:
1
Speed in still water = (a + b) km/hr.
1
2
Rate of stream = 2 (a −b) km/hr.
Mixtures and Alligations
Alligation: It is the rule that enables us to find the ratio in which two or more ingredients at the given price
must be mixed to produce a mixture of desired price.
Mean Price: The cost of a unit quantity of the mixture is called the mean price.
Rule of Alligation:
If two ingredients are mixed, then
Quantity of cheaper
Quantity of dearer
Cost Price of dearer – Mean Price
= Mean
price – Cost Price of cheaper
Where a is the original quantity, b is the quantity that is replaced and n is the number of times the
replacement process is carried out, then
Quantity of original entity after n operation
Quantity of mixture
Inequalities
If a > b and c > 0,
28
=(
a−b
a
)n
a+c>b+c
a−c>b−c
ac > bc
a
c
>
b
c
If a, b ≥ 0, then an > bn and
1
an
<
a < b and x > 0, then
a > b and x > 0, then
1
n, where n is positive.
b
a+x
b+x
a+x
b+x
>
<
a
b
a
b
1. n (n+l)(2n+1) is always divisible by 6.
2. 32n leaves remainder = 1 when divided by 8
3. n3 + (n+1)3 + (n+2)3 is always divisible by 9
4. 102n+1 + 1 is always divisible by 11
5. n(n2-1) is always divisible by 6
6. n2+ n is always even
7. 23n-1 is always divisible by 7
8. 152n-1 +l is always divisible by 16
9. n3 + 2n is always divisible by 3
10. 34n – 43n is always divisible by 17
11. Product of n consecutive numbers is always divisible by n!
12. If n is a positive integer and p is a prime, then n p – n is divisible by p.
13. |x| = x if x ≥ 0 and |x| = – x if x ≤ 0.
14. Dividend = Quotient × Divisor + Remainder
15. A number is divisible by 2, if its unit’s place digit is 0, 2, 4, or 8
16. A number is divisible by 3, if the sum of its digits is divisible by 3
17. A number is divisible by 4, if the number formed by its last two digits is
29
divisible by 4
18. A number is divisible by 8, if the number formed by its last three digits is
divisible by 8
19. A number is divisible by 9, if the sum of its digits is divisible by 9
20. If the population of a town is 'P' in a year, then its population after 'N'
years is P(1+
R
100
)N
21. If the population of a town is 'P' in a year, then its population 'N' years ago
is
P /[(1+
R
100
)N]
22. The equality of two ratios is called a proportion. If a : b = c : d, we write
a : b :: c : d and we say that a, b, c, d are in proportion. In a proportion,
the first and fourth terms are known as extremes, while the second and third are
known as means.
23. Product of extremes = Product of means
24. Mean proportion between a and b is √ab
25. The compounded ratio of the ratios (a : b), (c : d), (e : f) is (ace : bdf)
26. a2 : b2 is a duplicate ratio of a : b
27. √a : √b is a sub-duplicate ration of a : b
28. a3 : b3 is a triplicate ratio of a : b
29. a1/3 : b1/3 is a sub-triplicate ratio of a : b
30. If
31. If
32. If
a
=
a
=
a
=
b
b
b
c
, then,
(a + b)
=
(c + d)
c
, then,
(a− b)
=
(c− d)
d
d
c
d
, then,
b
b
(a + b)
(a − b)
=
d
d
(c + d)
(c − d)
, which is called the componendo.
, which is called the dividendo.
, which is called the componendo and dividendo.
33. Variation: We say that x is directly proportional to y if x = ky for some
constant k and we write, x α y. Also, we say that x is inversely proportional to
y if x =
k
y
for some constant k and we write x α
1
y
34. The cost of articles is directly proportional to the number of articles.
35. The work done is directly proportional to the number of men working at it.
30
n = m × 10P
If n = 12345:
12345 = 1.2345 × 104
Any single digit number written (P −1) times is divisible by P, where P is a prime number >5.
If log x = y, then antilog y = x.
Logarithms to the base 10 are known as common logarithms.
Characteristic and Mantissa in Logarithms:
log10 15 = 1.176 = 1 + 0.176
Characteristic
Mantissa
(Integral part)
When the number is greater than 1
(Decimal part)
When the number is less than 1
log10 x = y
log10 15 = 1.176 = 1 + 0.176
log10 250 = 2.397 = 2 + 0.397
log10 4000 = 3.602 = 3 + 0.602
log10 50000 = 4.698 = 4 + 0.698
log10 x = y
log10 0.5 = − 0.301 = −1 + 0.699
log10 0. 08 = − 1.096 = −2 + 0.904
log10 0.005 = − 2.3010 = −3 + 0.699
31
Fermat's Last Theorem:
No 3 positive integers a, b and c satisfy the equation:
an + bn = cn for any integer value of n > 2.
Fermat's little theorem:
If p is a prime number and a is any integer not divisible by p, then p divides ap−1 −1.
Fraction
Percentage
Fraction
Percentage
1
2
1
3
50%
1
9
1
10
11.11%
1
4
1
5
1
6
1
7
1
8
33.33%
1
11
1
12
1
13
1
14
1
15
25%
20%
16.66%
14.28%
12.5%
10%
9.09%
8.33%
7.69%
7.14%
6.66%
If N = (2) a (y) b (z) c where x, y, z are prime factors
Number of even factors of N = (a) (b+1) (c+1)
Number of odd factors of N = (b+1) (c+1)
Triangle inequality:
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
32
c
b
a
Properties of inequalities:
a+b>c
Let x, y, and z be real numbers
a+c>b
Addition property:
b+c>a
If x < y, then x + z < y + z
Subtraction property:
If x < y, then x − z < y – z
For a triangle with the side lengths:
Multiplication property:
7, 9, 13
If x < y and z > 0, then xz < yz
If x < y and z < 0, then xz > yz
The sum of 7 and 9 is 16 and 16 is greater than 13
The sum of 9 and 13 is 21 and 21 is greater than 7
The sum of 7 and 13 is 20 and 20 is greater than 9
Division property:
If x < y and z > 0, then
x
<
If x < y and z < 0, then
x
>
Modulus inequalities or Absolute value inequalities:
Transitive property:
z
z
x
y
x
y
If x < y and y < z, then x < z
If |x| < a, then – a < x < a
If |x| > a, then either x > a or x <−a
If |x – l| < a, then l – a < x < l + a
If |x – l| > a, then either x > l + a or x < l – a.
Comparison property:
If x = y + z and z > 0, then x > y
33
Segment Addition Postulate:
AB
A
BC
B
C
AC
If AB + BC = AC, then B is between A and C
Ceva's theorem:
If
AF BD CE
×
×
= 1, then the line AD, CF, BE forms a concurrent point at O.
FB DC EA
Decimal (Base 10) — Represent any number using 10 digits [0–9]
Binary (Base 2) — Represent any number using 2 digits [0–1]
Octal (Base 8) — Represent any number using 8 digits [0–7]
Hexadecimal (Base 16) — Represent any number using 10 digits and 6 characters [0–9, A, B, C,
D, E, F]
34
Decimal, hexadecimal, octal, and binary values
Decimal
Hexadecimal
Octal
Binary
0
0
0
0
1
1
1
1
2
2
2
10
3
3
3
11
4
4
4
100
5
5
5
101
6
6
6
110
7
7
7
111
8
8
10
1000
9
9
11
1001
10
A
12
1010
11
B
13
1011
12
C
14
1100
13
D
15
1101
14
E
16
1110
15
F
17
1111
16
10
20
10000
17
11
21
10001
18
12
22
10010
19
13
23
10011
20
14
24
10100
21
15
25
10101
22
16
26
10110
23
17
27
10111
24
18
30
11000
25
19
31
11001
26
1A
32
11010
27
1B
33
11011
28
1C
34
11100
29
1D
35
11101
30
1E
36
11110
31
1F
37
11111
32
20
40
100000
33
21
41
100001
34
22
42
100010
35
23
43
100011
36
24
44
100100
35
33
37
25
45
100101
38
26
46
100110
39
27
47
100111
40
28
50
101000
41
29
51
101001
42
2A
52
101010
43
2B
53
101011
44
2C
54
101100
45
2D
55
101101
46
2E
56
101110
47
2F
57
101111
48
30
60
110000
49
31
61
110001
50
32
62
110010
51
33
63
110011
52
34
64
110100
53
35
65
110101
54
36
66
110110
55
37
67
110111
56
38
70
111000
57
39
71
111001
58
3A
72
111010
59
3B
73
111011
60
3C
74
111100
61
3D
75
111101
62
3E
76
111110
63
3F
77
111111
64
40
100
1000000
65
41
101
1000001
66
42
102
1000010
67
43
103
1000011
68
44
104
1000100
69
45
105
1000101
70
46
106
1000110
71
47
107
1000111
72
48
110
1001000
73
49
111
1001001
74
4A
112
1001010
75
4B
113
1001011
76
4C
114
1001100
36
34
77
4D
115
1001101
78
4E
116
1001110
79
4F
117
1001111
80
50
120
1010000
81
51
121
1010001
82
52
122
1010010
83
53
123
1010011
84
54
124
1010100
85
55
125
1010101
86
56
126
1010110
87
57
127
1010111
88
58
130
1011000
89
59
131
1011001
90
5A
132
1011010
91
5B
133
1011011
92
5C
134
1011100
93
5D
135
1011101
94
5E
136
1011110
95
5F
137
1011111
96
60
140
1100000
97
61
141
1100001
98
62
142
1100010
99
63
143
1100011
100
64
144
1100100
101
65
145
1100101
102
66
146
1100110
103
67
147
1100111
104
68
150
1101000
105
69
151
1101001
106
6A
152
1101010
107
6B
153
1101011
108
6C
154
1101100
109
6D
155
1101101
110
6E
156
1101110
111
6F
157
1101111
112
70
160
1110000
113
71
161
1110001
114
72
162
1110010
115
73
163
1110011
116
74
164
1110100
37
35
117
75
165
1110101
118
76
166
1110110
119
77
167
1110111
120
78
170
1111000
121
79
171
1111001
122
7A
172
1111010
123
7B
173
1111011
124
7C
174
1111100
125
7D
175
1111101
126
7E
176
1111110
127
7F
177
1111111
128
80
200
10000000
129
81
201
10000001
130
82
202
10000010
131
83
203
10000011
132
84
204
10000100
133
85
205
10000101
134
86
206
10000110
135
87
207
10000111
136
88
210
10001000
137
89
211
10001001
138
8A
212
10001010
139
8B
213
10001011
140
8C
214
10001100
141
8D
215
10001101
142
8E
216
10001110
143
8F
217
10001111
144
90
220
10010000
145
91
221
10010001
146
92
222
10010010
147
93
223
10010011
148
94
224
10010100
149
95
225
10010101
150
96
226
10010110
151
97
227
10010111
152
98
230
10011000
153
99
231
10011001
154
9A
232
10011010
155
9B
233
10011011
156
9C
234
10011100
38
36
157
9D
235
10011101
158
9E
236
10011110
159
9F
237
10011111
160
A0
240
10100000
161
A1
241
10100001
162
A2
242
10100010
163
A3
243
10100011
164
A4
244
10100100
165
A5
245
10100101
166
A6
246
10100110
167
A7
247
10100111
168
A8
250
10101000
169
A9
251
10101001
170
AA
252
10101010
171
AB
253
10101011
172
AC
254
10101100
173
AD
255
10101101
174
AE
256
10101110
175
AF
257
10101111
176
B0
260
10110000
177
B1
261
10110001
178
B2
262
10110010
179
B3
263
10110011
180
B4
264
10110100
181
B5
265
10110101
182
B6
266
10110110
183
B7
267
10110111
184
B8
270
10111000
185
B9
271
10111001
186
BA
272
10111010
187
BB
273
10111011
188
BC
274
10111100
189
BD
275
10111101
190
BE
276
10111110
191
BF
277
10111111
192
C0
300
11000000
193
C1
301
11000001
194
C2
302
11000010
195
C3
303
11000011
196
C4
304
11000100
39
37
197
C5
305
11000101
198
C6
306
11000110
199
C7
307
11000111
200
C8
310
11001000
201
C9
311
11001001
202
CA
312
11001010
203
CB
313
11001011
204
CC
314
11001100
205
CD
315
11001101
206
CE
316
11001110
207
CF
317
11001111
208
D0
320
11010000
209
D1
321
11010001
210
D2
322
11010010
211
D3
323
11010011
212
D4
324
11010100
213
D5
325
11010101
214
D6
326
11010110
215
D7
327
11010111
216
D8
330
11011000
217
D9
331
11011001
218
DA
332
11011010
219
DB
333
11011011
220
DC
334
11011100
221
DD
335
11011101
222
DE
336
11011110
223
DF
337
11011111
224
E0
340
11100000
225
E1
341
11100001
226
E2
342
11100010
227
E3
343
11100011
228
E4
344
11100100
229
E5
345
11100101
230
E6
346
11100110
231
E7
347
11100111
232
E8
350
11101000
233
E9
351
11101001
234
EA
352
11101010
235
EB
353
11101011
236
EC
354
11101100
40
38
237
ED
355
11101101
238
EE
356
11101110
239
EF
357
11101111
240
F0
360
11110000
241
F1
361
11110001
242
F2
362
11110010
243
F3
363
11110011
244
F4
364
11110100
245
F5
365
11110101
246
F6
366
11110110
247
F7
367
11110111
248
F8
370
11111000
249
F9
371
11111001
250
FA
372
11111010
251
FB
373
11111011
252
FC
374
11111100
253
FD
375
11111101
254
FE
376
11111110
255
FF
377
11111111
Any prime number greater than 3 can be written as 6k±1.
The product of 'n' consecutive natural numbers is always divisible by
n!
Square of any natural number can be written in the form of 3n or 3n+1.
Also, square of any natural number can be written in the form of 4n or
4n+1.
Any two digit number 'pq' can effectively be written as 10p + q and a
three digit number 'pqr' can effectively be written as 100p + 10q + r.
Number of ways N can be written as product of two factors =
P is even or odd respectively
P
2
or
(P+1)
2
if
The number of ways in which a composite number can be resolved into two
co-prime factors is 2m-1, where m is the number of different prime
factors of the number.
41
39
(x + a)(x + b) (x + c) = x3 + (a + b + c) x2 + (ab + bc + ac)x + abc
(x – a)(x – b) (x – c) = x3 – (a + b + c) x2 + (ab + bc + ac)x – abc
Arithmetic Mean = (a1 + a2 + a3 ….an) / n
Geometric Mean =
Harmonic Mean = n / (
For two numbers a and b
n
√a1 a2 … . . an
1
x1
+
1
+ ...+
x2
AM =
1
xn
)
(a + b)
2
GM = √ab
HM =
2ab
a+b
AM ≥ GM ≥ HM is always true. They will be equal if all elements are equal to
each other. If there are just two values then GM2 = AM × HM
Absolute Growth = Final Value – Initial Value
Growth rate for one year period =
Compound Annual Growth Rate =
Average Annual Growth Rate =
Linear Races
(
Final Value – Initial Value
Initial Value
Final Value
Initial Value
)
1
𝑛𝑜. 𝑜𝑓 𝑦𝑒𝑎𝑟𝑠
Final Value – Initial Value
Number of years
× 100
− 1
× 100
Winner's distance = Length of race
Loser's distance = Winner's distance – (beat distance + start distance)
Winner's time = Loser's time – (beat time + start time)
Circular Races
42
40
Two people are running on a circular track of length L with speeds a and b in
the same direction
L
Time for 1st meeting =
a−b
They meet at a – b distinct points (reduced ratio)
L
L
Time for 1st meeting at the starting point = LCM ( a , b )
Two people are running on a circular track of length L with speeds a and b in
the opposite direction
Time for 1st meeting =
L
a+b
They meet at a + b distinct points (reduced ratio)
L
L
Time for 1st meeting at the starting point = LCM ( a , b )
Three people are running on a circular track of length L with speeds a, b and c
in the same direction
Time for 1st meeting = LCM (
L
a−b
,
L
a−c
)
Time for 1st meeting at the starting point = LCM (
If a and b are positive quantities, then
a+b
2
L L
,
a b
≥ √ab
If a, b, c, d are positive quantities, then
a
b
+
b
c
+
c
d
+
d
a
≥ 4
a4 + b4 + c4 +d4 ≥ 4abcd
43
41
,
L
)
c
For any positive integer n, 2 ≤
(n!)2 ≥ nn
am + bm
2
> (
Simple Interest Formula
2
n
≤ 3
a+b m
) [m ≤ 0 or m ≥ 1]
2
am + bm
< (
1
(1+ )n
a+b m
) [0 < m
2
< 1]
Simple interest = P × i × n
where:
P = principal amount
i = interest rate
n = term of the loan
Compound Interest Formula
The formula for calculating compound interest in a year is:
Compound interest = [P (1 + i) n] − P
where:
P = principal amount
i = interest rate in percentage terms
n = number of compounding periods for a year
44
42
Total value with compound interest = [P (
where:
1+ 𝑖
n
) nt] − P
P = principal amount
i = interest rate in percentage terms
n = number of compounding periods per year
t = total number of years for the investment or loan
The formulas for obtaining the future value (FV) and present value (PV) are as follows:
FV = PV × (
PV =
(
1+ 𝑖
n
) nt
FV
1+ 𝑖 nt
)
n
Theorems
Mid Point Theorem: The line joining the midpoint of any two sides is parallel to the third side and is half
the length of the third side.
Apollonius' Theorem:
A
B
C
D
AB2 + AC2 = 2 (AD2 + BD2)
Basic Proportionality Theorem:
45
43
A
D
E
B
If DE || BC, then
AD
DB
=
C
AE
EC
Interior Angle Bisector Theorem:
A
E
D
B
AE
ED
=
BA
BD
Right Angled Triangle:
A
∆ABC ≈ ∆ADB ≈ ∆BDC
BD2 = AD × DC
AB × BC = BD × AC
D
C
B
46
44
Fundamental Theorem of Arithmetic:
Every integer greater than 1 can be factored uniquely into a product of prime numbers
For example:
4312 = 2 × 2 × 2 × 7 × 7 × 11
Euclid's lemma: If a prime number divides a product of two numbers, it must divide at least one
of the numbers.
Stewart's Theorem:
If a, b and c are the lengths of the sides of a triangle. If d is the length of the cevian of the side of
the length a. Suppose this cevian divides the side 'a' into 2 segments of the length m and n, where
m is adjacent to the side c and whereas n is adjacent to the side b, then
b2m + c2 n = a (d2 + mn)
47
The Square Root of 2 is Called "Pythagoras' Constant."
0 is the Only Number That Can't Be Represented In
Roman Numerals
0 is an Even Number
6 is the Smallest Perfect Number
The Number Pi (the ratio of the circumference to the diameter
of a circle) is Irrational
If we multiply a number by 9 and add all the digits of the new number together, the sum will always add
up to 9. For example:
8 × 9 = 72
7+2=9
4 × 9 = 36
3+6=9
48
Number
Square
Cube
Square Root
Cubic Root
1
1
1
1.000
1.000
2
4
8
1.414
1.260
3
9
27
1.732
1.442
4
16
64
2.000
1.587
5
25
125
2.236
1.710
6
36
216
2.449
1.817
7
49
343
2.646
1.913
8
64
512
2.828
2.000
9
81
729
3.000
2.080
10
100
1000
3.162
2.154
11
121
1331
3.317
2.224
12
144
1728
3.464
2.289
13
169
2197
3.606
2.351
14
196
2744
3.742
2.410
15
225
3375
3.873
2.466
16
256
4096
4.000
2.520
17
289
4913
4.123
2.571
18
324
5832
4.243
2.621
19
361
6859
4.359
2.668
20
400
8000
4.472
2.714
21
441
9261
4.583
2.759
22
484
10648
4.690
2.802
23
529
12167
4.796
2.844
24
576
13824
4.899
2.884
25
625
15625
5.000
2.924
26
676
17576
5.099
2.962
49
27
729
19683
5.196
3.000
28
784
21952
5.292
3.037
29
841
24389
5.385
3.072
30
900
27000
5.477
3.107
31
961
29791
5.568
3.141
32
1024
32768
5.657
3.175
33
1089
35937
5.745
3.208
34
1156
39304
5.831
3.240
35
1225
42875
5.916
3.271
36
1296
46656
6.000
3.302
37
1369
50653
6.083
3.332
38
1444
54872
6.164
3.362
39
1521
59319
6.245
3.391
40
1600
64000
6.325
3.420
41
1681
68921
6.403
3.448
42
1764
74088
6.481
3.476
43
1849
79507
6.557
3.503
44
1936
85184
6.633
3.530
45
2025
91125
6.708
3.557
46
2116
97336
6.782
3.583
47
2209
103823
6.856
3.609
48
2304
110592
6.928
3.634
49
2401
117649
7.000
3.659
50
2500
125000
7.071
3.684
51
2601
132651
7.141
3.708
52
2704
140608
7.211
3.733
53
2809
148877
7.280
3.756
50
54
2916
157464
7.348
3.780
55
3025
166375
7.416
3.803
56
3136
175616
7.483
3.826
57
3249
185193
7.550
3.849
58
3364
195112
7.616
3.871
59
3481
205379
7.681
3.893
60
3600
216000
7.746
3.915
61
3721
226981
7.810
3.936
62
3844
238328
7.874
3.958
63
3969
250047
7.937
3.979
64
4096
262144
8.000
4.000
65
4225
274625
8.062
4.021
66
4356
287496
8.124
4.041
67
4489
300763
8.185
4.062
68
4624
314432
8.246
4.082
69
4761
328509
8.307
4.102
70
4900
343000
8.367
4.121
71
5041
357911
8.426
4.141
72
5184
373248
8.485
4.160
73
5329
389017
8.544
4.179
74
5476
405224
8.602
4.198
75
5625
421875
8.660
4.217
76
5776
438976
8.718
4.236
77
5929
456533
8.775
4.254
78
6084
474552
8.832
4.273
79
6241
493039
8.888
4.291
80
6400
512000
8.944
4.309
51
81
6561
531441
9.000
4.327
82
6724
551368
9.055
4.344
83
6889
571787
9.110
4.362
84
7056
592704
9.165
4.380
85
7225
614125
9.220
4.397
86
7396
636056
9.274
4.414
87
7569
658503
9.327
4.431
88
7744
681472
9.381
4.448
89
7921
704969
9.434
4.465
90
8100
729000
9.487
4.481
91
8281
753571
9.539
4.498
92
8464
778688
9.592
4.514
93
8649
804357
9.644
4.531
94
8836
830584
9.695
4.547
95
9025
857375
9.747
4.563
96
9216
884736
9.798
4.579
97
9409
912673
9.849
4.595
98
9604
941192
9.899
4.610
99
9801
970299
9.950
4.626
100
10000
1000000
10.000
4.642
Logarithm Table
x
log10 x
log2 x
loge x
0
undefined
undefined
undefined
52
0.0001
−4
−13.287712
−9.210340
0.001
−3
−9.965784
−6.907755
0.01
−2
−6.643856
−4.605170
0.1
−1
−3.321928
−2.302585
1
0
0
0
2
0.301030
1
0.693147
3
0.477121
4
0.602060
5
0.698970
2.321928
1.609438
6
0.778151
2.584963
1.791759
7
0.845098
2.807355
1.945910
8
0.903090
9
0.954243
3.169925
2.197225
10
1
3.321928
2.302585
20
1.301030
4.321928
2.995732
30
1.477121
4.906891
3.401197
40
1.602060
5.321928
3.688879
50
1.698970
5.643856
3.912023
1.584963
2
3
53
1.098612
1.386294
2.079442
60
1.778151
5.906991
4.094345
70
1.845098
6.129283
4.248495
80
1.903090
6.321928
4.382027
90
1.954243
6.491853
4.499810
100
2
6.643856
4.605170
200
2.301030
7.643856
5.298317
300
2.477121
8.228819
5.703782
400
2.602060
8.643856
5.991465
500
2.698970
8.965784
6.214608
600
2.778151
9.228819
6.396930
700
2.845098
9.451211
6.551080
800
2.903090
9.643856
6.684612
900
2.954243
9.813781
6.802395
1000
3
9.965784
6.907755
10000
4
13.287712
9.210340
1 is Not a Prime Number
Six Weeks = 10! Seconds
10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3,628,800 seconds = 60,480 minutes = 1,008 hours = 42 days = 6 weeks
54
Multiplication Table
× 0
1
2
3
4
5
6
7
8
9
10
11
12
0 0
0
0
0
0
0
0
0
0
0
0
0
0
1 0
1
2
3
4
5
6
7
8
9
10
11
12
2 0
2
4
6
8 10 12 14 16
18
20
22
24
3 0
3
6
9 12 15 18 21 24
27
30
33
36
4 0
4
8 12 16 20 24 28 32
36
40
44
48
5 0
5 10 15 20 25 30 35 40
45
50
55
60
6 0
6 12 18 24 30 36 42 48
54
60
66
72
7 0
7 14 21 28 35 42 49 56
63
70
77
84
8 0
8 16 24 32 40 48 56 64
72
80
88
96
9 0
9 18 27 36 45 54 63 72
81
90
99
108
10 0
10 20 30 40 50 60 70 80
90
100
110
120
11 0
11 22 33 44 55 66 77 88
99
110
121
132
12 0
12 24 36 48 60 72 84 96
108
120
132
144
13 + 53 +33 = 153
163 + 503 +333 = 165033
1663 + 5003 +3333 = 166500333
16663 + 50003 +33333 = 166650003333
55
1×8+1=9
12 × 8 + 2 = 98
123 × 8 + 3 = 987
1234 × 8 + 4 = 9876
12345 × 8 + 5 = 98765
123456 × 8 + 6 = 987654
1234567 × 8 + 7 = 9876543
12345678 × 8 + 8 = 98765432
123456789 × 8 + 9 = 987654321
Metric Units of Measurement
Prefix Name
Prefix Symbol
Value
yotta
Y
1024
Septillion
zetta
Z
1021
Sextillion
exa
E
1018
Quintillion
peta
P
1015
Quadrillion
tera
T
1012
Trillion
giga
G
109
Billion
mega
M
106
Million
kilo
k
103
Thousand
hecto
h
102
Hundred
deka
da
101
Ten
100
One
deci
d
10−1
Tenth
centi
c
10−2
Hundredth
milli
m
10−3
Thousandth
micro
μ
10−6
Millionth
56
nano
n
10−9
Billionth
pico
p
10−12
Trillionth
femto
f
10−15
Quadrillionth
atto
a
10−18
Quintillionth
zepto
z
10−21
Sextillionth
yocto
y
10−24
Septillionth
From 0 to 1000, the only number that has the letter "a" in it is "one thousand".
Units of Length
10 millimeter (mm)
1 centimeter (cm)
10 centimeter
1 decimeter (dm) = 100 millimeters
10 decimeter
1 meter (m) = 1000 millimeters
10 meter
1 decameter (dam)
10 decameter
1 hectometer (hm) = 100 meters
10 hectometer
1 kilometer (km) = 1000 meters
The numbers on opposite sides of a dice always add up to seven
Units of Area
100 square millimeter (mm2)
1 square centimeter (cm2)
100 square centimeter
1 square decimeter (dm2)
100 square decimeter
1 square meter (m2)
100 square meter
1 square decameter (dam2) = 1 are
100 square decameter
1 square hectometer (hm2) = 1 hectare (ha)
100 square hectometer
1 square kilometer (km2)
57
Units of Liquid Volume
10 milliliters (mL)
1 centiliter (cL)
10 centiliters
1 deciliter (dL) = 100 milliliters
10 deciliters
1 liter = 1000 milliliters
10 liters
1 decaliter (daL)
10 decaliter
1 hectoliter (hL) = 100 liters
10 hectoliters
1 kiloliter (kL) = 1000 liters
The number 0.999999….. is exactly equal to 1
Units of Volume
1000 cubic millimeter (mm3)
1 cubic centimeter (cm3)
1000 cubic centimeter
1 cubic decimeter (dm3)
1 000 000 cubic millimeter
1000 cubic decimeter
1 cubic meter (m3)
1 000 000 cubic centimeter
1 000 000 000 cubic millimeter
Dividing by zero once put a US Navy Warship out of action
Units of Mass
10 milligrams (mg)
1 centigram (cg)
10 centigrams
1 decigram (dg) = 100 milligrams
10 decigrams
1 gram (g) = 1000 milligrams
10 grams
1 dekagram (dag)
10 decagrams
1 hectogram (hg) = 100 grams
10 hectograms
1 kilogram
1000 kilograms
1 megagram (Mg) or 1 metric ton (t)
(kg) = 1000 grams
58
Physical constants
Symbol
Quantity
Value
c
speed of light in vacuum
299792458 m⋅s−1
h
Planck constant
6.62607015×10−34 J⋅Hz−1
ℏ
reduced Planck constant
1.054571817...×10−34 J⋅s
Newtonian constant of gravitation
6.67430(15)×10−11 m3⋅kg−1⋅s−2
G
vacuum electric permittivity
8.8541878128(13)×10−12 F⋅m−1
μ0
vacuum magnetic permeability
1.25663706212(19)×10−6 N⋅A−2
Z0 = μ0c
characteristic impedance of vacuum
376.730313668(57) Ω
e
elementary charge
1.602176634×10−19 C
ΔυCs
hyperfine transition frequency
of 133Cs
9192631770 Hz
NA
Avogadro constant
6.02214076×1023 mol−1
kB
Boltzmann constant
1.380649×10−23 J⋅K−1
conductance quantum
7.748091729...×10−5 S
ε0 =
1
μ0 c2
G0 =
2e2
h
59
Josephson constant
483597.8484...×109 Hz⋅V−1
Coulomb constant
8.9875517923(14)×109 kg⋅m3⋅s−2⋅C−2
h
von Klitzing constant
25812.80745... Ω
h
magnetic flux quantum
2.067833848...×10−15 Wb
inverse conductance quantum
12906.40372... Ω
eℏ
Bohr magneton
9.2740100783(28)×10−24 J⋅T−1
eℏ
nuclear magneton
5.0507837461(15)×10−27 J⋅T−1
e2
fine-structure constant
7.2973525693(11)×10−3
α−1
inverse fine-structure constant
137.035999084(21)
me
electron mass
9.1093837015(28)×10−31 kg
mp
proton mass
1.67262192369(51)×10−27 kg
mn
neutron mass
1.67492749804(95)×10−27 kg
Bohr radius
5.29177210903(80)×10−11 m
2e
KJ =
h
1
4πε0
RK =
e2
Φ0 =
2e
1
G0
μB =
μN =
α=
2me
2mp
4πε0 ℏc
a0 =
ℏ
αme c
60
classical electron radius
2.8179403262(13)×10−15 m
ge
electron g-factor
−2.00231930436256(35)
GF / (ℏc)3
Fermi coupling constant
1.1663787(6)×10−5 GeV−2
Eh = 2R∞ hc
Hartree energy
4.3597447222071(85)×10−18 J
h
quantum of circulation
3.6369475516(11)×10−4 m2⋅s−1
α2 me c
Rydberg constant
10973731.568160(21) m−1
8πr2e
Thomson cross section
6.6524587321(60)×10−29 m2
W-to-Z mass ratio
0.88153(17)
weak mixing angle
0.22290(30)
mu = 1Da
atomic mass constant
1.66053906660(50)×10−27 kg
F=NAe
Faraday constant
96485.33212... C⋅mol−1
R = NAkB
molar gas constant
Mu = M (12C) /12
molar mass constant
8.314462618... J⋅mol−1⋅K−1
0.99999999965(30)×10−3 kg⋅mol−1
Stefan–Boltzmann constant
5.670374419...×10−8 W⋅m−2⋅K−4
re =
e2
4πε0 me c2
2me
R∞=
2h
σe =
3
mW
mZ
sin2θW = 1 – (
σ=
mW 2
)
mZ
π2 k4B
60ℏ3 c2
61
c1 = 2πhc2
first radiation constant
3.741771852...×10−16 W⋅m2
first radiation constant for spectral
radiance
1.191042972...×10−16 W⋅m2⋅sr−1
M (12C) = NA m (12C)
molar mass of carbon-12
11.9999999958(36)×10−3 kg⋅mol−1
NAh
molar Planck constant
3.990312712...×10−10 J⋅Hz−1⋅mol−1
c1L =
c2 =
c1
π
hc
kB
second radiation constant
1.438776877...×10−2 m⋅K
Wien wavelength displacement law
constant
2.897771955...×10−3 m⋅K
b'
Wien frequency displacement law
constant
5.878925757...×1010 Hz⋅K−1
bentropy
Wien entropy displacement law
constant
3.002916077...×10−3 m⋅K
b
111111111 × 111111111 = 12345678987654321
Euler's identity:
eiπ +1 = 0
i = √−1
Euler's number − the base of natural logarithms
62
Planetary Fact Sheet
Data about the planets of our solar system (Planetary facts taken from NASA's Planetary Fact Sheet−Metric).
Distance
Name
Mercury
Terrestrial planets
Gas
Mass
Diameter
Density
Gravity
(1024 kg)
(km)
(kg/m3 )
(m/s2 )
Length
from
Mean
of day
Sun
te mp e ra t ure
of
(hours)
(106 km)
(°C)
moons
0.330
4,879
5427
3.7
4222.6
57.9
167
0
Venus
4.87
12,104
5243
8.9
2802.0
108.2
464
0
Earth
5.97
12,756
5514
9.8
24.0
149.6
15
1
Mars
0.642
6,792
3933
3.7
24.7
227.9
−65
2
Jupiter
1898
142,984
1326
23.1
9.9
778.6
−110
67
568
120,536
687
9.0
10.7
1433.5
−140
62
Uranus
86.8
51,118
1271
8.7
17.2
2872.5
−195
27
Neptune
102
49,528
1638
11.0
16.1
4495.1
−200
14
0.0146
2,370
2095
0.7
153.3
5906.4
−225
5
Saturn
giants
Jovian
planets
Ice
giants
Dwarf
planets
Number
Pluto
Sun Reference Data
Diameter:
1.4 million km
Age:
4.5 billion years
(870,000 miles)
Mass:
330,000 × Earth
Distance from Earth:
149.6 million km (93 million miles)
Density:
1.41 (water =1)
Distance to Nearest Star:
4.3 light years
Solar Wind Speed:
3 million km/hr.
Luminosity:
390 billion billion megawatts
Solar Cycle:
8 - 11 years
Temperature at surface:
5,500 oC (9,932 oF)
Temperature at Core:
14 million oC
Temperature of Sunspots:
4,000 oC (7,232 oF)
Rotation Period at Poles:
35 Earth days
(22.5 million oF)
Rotation Period at Equator:
25 Earth days
63
Mercury and Venus are the only 2 planets in our solar system that have no moons.
The hottest planet in our solar system is Venus.
Enceladus − one of Saturn's smaller moons, reflects 90% of the Solar radiation.
A light-year is the distance covered by light in a single year.
The Milky Way galaxy is 105,700 light-years wide.
The Sun weighs about 330,000 times more than Earth.
Footprints left on the Moon won't disappear as there is no wind.
The Sun makes a full rotation once every 25 – 35 days.
Earth is the only planet not named after a God.
Pluto is smaller than the United States.
64
He is like the fox, who effaces his tracks in the sand with his tail.
{Describing the writing style of famous mathematician Carl Friedrich Gauss}
― Niels Henrik Abel
There are more volcanoes on Venus than any other
planet in our solar system.
Neptune's moon [Triton] orbits the planet backwards.
65
There are more stars in space than there are grains of sand in the world.
Neptune takes nearly 165 Earth years to make one orbit of the Sun.
Pluto's largest moon [Charon] is half the size of Pluto.
A day on Pluto is lasts for 153.6 hours long.
Any free-moving liquid in outer space will shape itself into a sphere.
Only 5% of the universe is visible from Earth.
Light travels from the Sun to the Earth in less than 10 minutes.
The Earth's rotation is slowing slightly as time goes on.
There are three main types of galaxies:
elliptical
spiral
irregular
There are approximately 100 thousand
million stars in the Milky Way.
66
Essential Amino Acids
Nonessential Amino Acids
These cannot be synthesized or produced by
These are produced or synthesized by our
the body and are required from food
bodies and are not taken up as food
supplements
supplements
Leucine
Arginine
Isoleucine
Alanine
Histidine
Aspartic acid
Lysine
Asparagine
Methionine
Cysteine
Threonine
Glutamine
Phenylalanine
Glutamic acid
Tryptophan
Proline
Valine
Glycine
Serine
Tyrosine
Conditional Amino Acids
These are usually not essential but in times of illness and stress − may become essential
Cysteine
Arginine
Tyrosine
Glutamine
Ornithine
Glycine
Serine
Proline
67
Common Amino Acids
Name
Abbr.
Molecular Weight
Molecular Formula
Alanine
Ala
A
89.10
C3H7NO2
Arginine
Arg
R
174.20
C6H14N4O2
Asparagine
Asn
N
132.12
C4H8N2O3
Aspartic acid
Asp
D
133.11
C4H7NO4
Cysteine
Cys
C
121.16
C3H7NO2S
Glutamic acid
Glu
E
147.13
C5H9NO4
Glutamine
Gln
Q
146.15
C5H10N2O3
Glycine
Gly
G
75.07
C2H5NO2
Histidine
His
H
155.16
C6H9N3O2
Hydroxyproline
Hyp
O
131.13
C5H9NO3
Isoleucine
Ile
I
131.18
C6H13NO2
Leucine
Leu
L
131.18
C6H13NO2
Lysine
Lys
K
146.19
C6H14N2O2
Methionine
Met
M
149.21
C5H11NO2S
Phenylalanine
Phe
F
165.19
C9H11NO2
Proline
Pro
P
115.13
C5H9NO2
Pyroglutamatic
Glp
U
139.11
C5H7NO3
Serine
Ser
S
105.09
C3H7NO3
Threonine
Thr
T
119.12
C4H9NO3
Tryptophan
Trp
W
204.23
C11H12N2O2
Tyrosine
Tyr
Y
181.19
C9H11NO3
Valine
Val
V
117.15
C5H11NO2
68
82
With our naked eye, we can see 3 – 7 different galaxies from Earth.
The closest galaxy to us is the Andromeda Galaxy – it's estimated
at 2.5 million light-years away.
The distance between the Sun and Earth is defined as an Astronomical Unit.
On Venus, it snows metal and rains sulfuric acid.
Space is completely silent.
Astronauts can grow approximately two inches in height when in space.
The first artificial satellite in space was called Sputnik
Exoplanets are planets that orbit around other stars.
The center of the Milky Way smells like rum and
tastes like raspberries.
69
Particles and their Properties
Particle name
Mass (MeV/c2)
Average lifetime (s)
Leptons
Electron
0.511
Stable
Electron neutrino
≈0
Stable
Muon
105.7
2.20×10−6
Muon neutrino
≈0
Stable
Tau
1784
<4×10−13
Tau neutrino
≈0
Stable
Proton
938.3
Stable
Neutron
939.6
920
Lambda
1115.6
2.6×10−10
Sigma
1189.4
0.80×10−10
Xi
1315
2.9×10−10
Omega
1672
0.82×10−10
Pion
139.6
2.60×10−8
π-Zero
135.0
0.83×10−16
Kaon
493.7
1.24×10−8
k-Short
497.6
0.89×10−10
k-Long
497.6
5.2×10−8
J/ψ
3100
7.1×10−21
Upsilon
9460
1.2×10−20
Hadrons
70
83
Composition of Earth's Atmosphere
Nitrogen
78.1%
Oxygen
20.9%
Argon
0.9%
Carbon dioxide, Methane, Rare (inert) gases
0.1%
Base Planck units
Name
Planck length
Planck mass
Dimension
Expression
Length (L)
𝑙𝑃 = √
1.616255(18)×10−35 m
ћ𝐺
𝑐3
Mass (M)
ћ𝑐
𝑚𝑃 = √
Planck time
Planck temperature
Time (T)
𝑡𝑃 = √
Temperature (θ)
Value (SI units)
2.176435(24)×10−8 kg
𝐺
5.391247(60)×10−44 s
ћ𝐺
𝑐5
ћ𝑐 5
1.416785(16)×1032 K
𝑇𝑃 = √ 2
𝐺𝑘
𝐵
Planck charge
Electric charge (Q)
71
84
−18
𝑞𝑃 = √4𝜋𝜀0 ћ𝑐 1.875545956(41)×10 C
Abundances of the Elements in the Earth's Crust
Element
Appro×imate % by weight
O×ygen
46.6
Silicon
27.7
Aluminum
8.1
Iron
5.0
Calcium
3.6
Sodium
2.8
Potassium
2.6
Magnesium
2.1
All others
1.5
Element Abundance in the Solar System
Element
Symbol
Mass Number A
Mass fraction in
Atom fraction in
parts per million
parts per million
Hydrogen-1
H
1
705700
909964
Helium-4
He
4
275200
88714
O×ygen-16
O
16
5920
477
Carbon-12
C
12
3032
326
Nitrogen-14
N
14
1105
102
Neon-20
Ne
20
1548
100
Silicon-28
Si
28
653
30
Magnesium-24
Mg
24
513
28
Iron-56
Fe
56
1169
27
Sulfur-32
S
32
396
16
72
85
Helium-3
He
3
35
15
Hydrogen-2
H
2
23
15
Neon-22
Ne
22
208
12
Magnesium-26
Mg
26
79
4
Carbon-13
C
13
37
4
Magnesium-25
Mg
25
69
4
Aluminum-27
Al
27
58
3
Argon-36
Ar
36
77
3
Calcium-40
Ca
40
60
2
Sodium-23
Na
23
33
2
Iron-54
Fe
54
72
2
Silicon-29
Si
29
34
2
Nickel-58
Ni
58
49
1
Silicon-30
Si
30
23
1
Iron-57
Fe
57
28
1
Composition of the Sun
Element
Abundance
Abundance
(percentage of total number of atoms)
(percentage of total mass)
Hydrogen
91.2
71.0
Helium
8.7
27.1
O×ygen
0.078
0.97
Carbon
0.043
0.40
Nitrogen
0.0088
0.096
Silicon
0.0045
0.099
Magnesium
0.0038
0.076
Neon
0.0035
0.058
73
86
Iron
0.0030
0.14
Sulfur
0.0015
0.040
Speed of Sound
Gases
Material
v (m/s)
Hydrogen (0°C)
1286
Helium (0°C)
972
Air (20°C)
343
Air (0°C)
331
Liquids at 25°C
Material
v (m/s)
Glycerol
1904
Sea water
1533
Water
1493
Mercury
1450
Kerosene
1324
Methyl alcohol
1143
Carbon tetrachloride
926
Solids
Material
v (m/s)
Diamond
12000
Pyre× glass
5640
Iron
5130
Aluminum
5100
Brass
4700
Copper
3560
Gold
3240
Lucite
2680
Lead
1322
Rubber
1600
74
87
Our moon is moving away from Earth at a rate of 4 cm per year.
Pluto is named after the Roman god of the underworld.
The first living mammal to go into space was a dog named "Laika" from Russia.
Saturn is the only planet that could float in water.
A sunset on Mars is blue.
Astronauts can grow approximately two inches in height when in space.
The Earth weighs about 81 times more than the Moon
Asteroids are the byproducts of formations in the solar
system, more than 4 billion years ago.
75
Molecule
Bond Energy (kJ/mol)
H—H
432
H—F
565
H—Cl
427
H—Br
363
H—I
295
C—H
413
C—C
347
C—N
305
C—O
358
C—F
485
C—Cl
339
C—Br
276
C—I
240.
C—S
259
N—H
391
N—N
160.
N—F
272
N—Cl
200.
N—Br
243
N—O
201
O—H
467
O—O
146
O—F
190.
O—Cl
203
76
88
O—I
234
F—F
154
F—Cl
253
F—Br
237
Cl—Cl
239
Cl—Br
218
Br—Br
193
I—I
149
I—Cl
208
I—Br
175
S—H
347
S—F
327
S—Cl
253
S—Br
218
S—S
266
Si—Si
340
Si—H
393
Si—C
360
Si—O
452
C=C
614
C≡C
839
O=O
495
C=O
799
C≡O
1072
N=O
607
77
89
N=N
418
N≡N
941
C≡N
891
C=N
615
Electron Affinities of the Main-Group Elements
Electron Affinities in kJ/mole
IA
Period 1
IIIA
IVA
VA
VIA
VIIA
Li
B
C
N
O
F
-60
-27
-122
0
-141
-328
Na
Al
Si
P
S
Cl
-53
-44
-134
-72
-200
-349
K
Ga
Ge
As
Se
Br
-48
-30
-120
-77
-195
-325
Rb
In
Sn
Sb
Te
I
-47
-30
-121
-101
-190
-295
Cs
Tl
Pb
Bi
Po
At
-45
-30
-110
-110
-180
-270
H
-73
Period 2
Period 3
Period 4
Period 5
Period 6
Work function of elements (eV)
Ag
4.26 – 4.74
Al
4.06 – 4.26
78
90
As
3.75
Au
5.10 – 5.47
B
~4.45
Ba
2.52 – 2.70
Be
4.98
Bi
4.31
C
~5
Ca
2.87
Cd
4.08
Ce
2.9
Co
5
Cr
4.5
Cs
1.95
Cu
4.53 – 5.10
Eu
2.5
Fe:
4.67 – 4.81
Ga
4.32
Gd
2.90
Hf
3.90
Hg
4.475
In
4.09
Ir
5.00 – 5.67
K
2.29
La
3.5
Li
2.9
Lu
~3.3
Mg
3.66
Mn
4.1
Mo
4.36 – 4.95
Na
2.36
Nb
3.95 – 4.87
Nd
3.2
Ni
5.04 – 5.35
Os
5.93
Pb
4.25
Pd
5.22 – 5.60
Pt
5.12 – 5.93
Rb
2.261
Re
4.72
Rh
4.98
79
91
Ru
4.71
Sb
4.55 – 4.70
Sc
3.5
Se
5.9
Si
4.60 – 4.85
Sm
2.7
Sn
4.42
Sr
~2.59
Ta
4.00 – 4.80
Tb
3.00
Te
4.95
Th
3.4
Ti
4.33
Tl
~3.84
U
3.63 – 3.90
W
4.32 – 5.22
Y
3.1
Zn
3.63 – 4.9
Zr
4.05
V
Yb
4.3
2.60
Fermi Energies, Fermi Temperatures, and Fermi Velocities
Element Fermi Energy Fermi Temperature Fermi Velocity
eV
104 K
106 m/s
Li
4.74
5.51
1.29
Na
3.24
3.77
1.07
K
2.12
2.46
0.86
Rb
1.85
2.15
0.81
Cs
1.59
1.84
0.75
Cu
7.00
8.16
1.57
Ag
5.49
6.38
1.39
Au
5.53
6.42
1.40
Be
14.3
16.6
2.25
Mg
7.08
8.23
1.58
80
92
Ca
4.69
5.44
1.28
Sr
3.93
4.57
1.18
Ba
3.64
4.23
1.13
Nb
5.32
6.18
1.37
Fe
11.1
13.0
1.98
Mn
10.9
12.7
1.96
Zn
9.47
11.0
1.83
Cd
7.47
8.68
1.62
Hg
7.13
8.29
1.58
Al
11.7
13.6
2.03
Ga
10.4
12.1
1.92
In
8.63
10.0
1.74
Tl
8.15
9.46
1.69
Sn
10.2
11.8
1.90
Pb
9.47
11.0
1.83
Bi
9.90
11.5
1.87
Sb
10.9
12.7
1.96
Radioactive Nuclide
Half-Life (years)
V
6.0×1015
Nd
2.4×1015
Hf
2.0×1015
Pt
1×1015
In
6.0×1014
Gd
1.08×1014
Te
1.2×1013
Pt
6.9×1011
50
144
174
192
115
152
123
190
81
93
La
1.12×1011
Sm
1.06×1011
Rb
4.88×1010
Re
4.3×1010
Lu
3.5×1010
Th
1.40×1010
U
4.47×109
K
1.25×109
U
7.04×810
Pu
8.2×107
Sm
7.0×107
Pb
3.0×107
U
2.39×107
I
1.7×107
Cm
1.60×107
Hf
9.0×106
Pd
7×106
Mn
3.7×106
Cs
3.0×106
Tc
2.6×106
Np
2.14×106
Gd
2.1×106
Be
1.6×106
Zr
1.5.0×106
Tc
1.5×106
138
147
87
187
176
232
238
40
235
244
146
205
236
129
247
182
107
53
135
97
237
150
10
93
98
82
94
1×106
153Dy
Standard Electrode Potentials in Aqueous Solution at 25°C
Cathode (Reduction)
Standard Potential
Half-Reaction
E° (volts)
Li+(aq) + e- → Li(s)
-3.04
K+(aq) + e- → K(s)
-2.92
Ca2+(aq) + 2e- → Ca(s)
-2.76
Na+(aq) + e- → Na(s)
-2.71
Mg2+(aq) + 2e- → Mg(s)
-2.38
Al3+(aq) + 3e- → Al(s)
-1.66
2H2O(l) + 2e- → H2(g) + 2OH-(aq)
-0.83
Zn2+(aq) + 2e- → Zn(s)
-0.76
Cr3+(aq) + 3e- → Cr(s)
-0.74
Fe2+(aq) + 2e- → Fe(s)
-0.41
Cd2+(aq) + 2e- → Cd(s)
-0.40
Ni2+(aq) + 2e- → Ni(s)
-0.23
Sn2+(aq) + 2e- → Sn(s)
-0.14
Pb2+(aq) + 2e- → Pb(s)
-0.13
Fe3+(aq) + 3e- → Fe(s)
-0.04
2H+(aq) + 2e- → H2(g)
0.00
Sn4+(aq) + 2e- → Sn2+(aq)
0.15
Cu2+(aq) + e- → Cu+(aq)
0.16
ClO4-(aq) + H2O(l) + 2e- → ClO3-(aq) + 2OH-(aq)
0.17
AgCl(s) + e- → Ag(s) + Cl-(aq)
0.22
Cu2+(aq) + 2e- → Cu(s)
0.34
ClO3-(aq) + H2O(l) + 2e- → ClO2-(aq) + 2OH-(aq)
0.35
IO-(aq) + H2O(l) + 2e- → I-(aq) + 2OH-(aq)
0.49
83
95
Cu+(aq) + e- → Cu(s)
0.52
I2(s) + 2e- → 2I-(aq)
0.54
ClO2-(aq) + H2O(l) + 2e- → ClO-(aq) + 2OH-(aq)
0.59
Fe3+(aq) + e- → Fe2+(aq)
0.77
Hg22+(aq) + 2e- → 2Hg(l)
0.80
Ag+(aq) + e- → Ag(s)
0.80
Hg2+(aq) + 2e- → Hg(l)
0.85
ClO-(aq) + H2O(l) + 2e- → Cl-(aq) + 2OH-(aq)
0.90
2Hg2+(aq) + 2e- → Hg22+(aq)
0.90
NO3-(aq) + 4H+(aq) + 3e- → NO(g) + 2H2O(l)
0.96
Br2(l) + 2e- → 2Br-(aq)
1.07
O2(g) + 4H+(aq) + 4e- → 2H2O(l)
1.23
Cr2O72-(aq) + 14H+(aq) + 6e- → 2Cr3+(aq) + 7H2O(l)
1.33
Cl2(g) + 2e- → 2Cl-(aq)
1.36
Ce4+(aq) + e- → Ce3+(aq)
1.44
MnO4-(aq) + 8H+(aq) + 5e- → Mn2+(aq) + 4H2O(l)
1.49
H2O2(aq) + 2H+(aq) + 2e- → 2H2O(l)
1.78
Co3+(aq) + e- → Co2+(aq)
1.82
S2O82-(aq) + 2e- → 2SO42-(aq)
2.01
O3(g) + 2H+(aq) + 2e- → O2(g) + H2O(l)
2.07
F2(g) + 2e- → 2F-(aq)
2.87
Astronomy Data
1 light-year = 9.47 × 1015 m
1 AU (astronomical unit) = 1.50 × 1011 m
84
96
Distilled Water at Room Temperature (25°C) and Standard Pressure (101.325 kPa)
Volume
Mass
Density
1.0 mL or 1.0 cm3
1.0 g
1.0 g/cm3
1.0 L or 1.0 dm3
1.0 kg
1.0 kg/dm3
Melting and Boiling points of Selected Compounds
Compound
Formula
Boiling Point
Melting Point
pentane
CH3(CH2)3CH3
36ºC
–130ºC
hexane
CH3(CH2)4CH3
69ºC
–95ºC
heptane
CH3(CH2)5CH3
98ºC
–91ºC
octane
CH3(CH2)6CH3
126ºC
–57ºC
nonane
CH3(CH2)7CH3
151ºC
–54ºC
decane
CH3(CH2)8CH3
174ºC
–30ºC
tetramethylbutane
(CH3)3C-C(CH3)3
106ºC
+100ºC
Flame Colour of Elements
Element
Symbol
Colour
barium
Ba
yellowish-green
calcium
Ca
yellowish red
cesium
Cs
violet
copper
Cu
blue to green
lead
Pb
blue-white
lithium
Li
red
potassium
K
violet
rubidium
Rb
violet
sodium
Na
yellow
85
97
strontium
Sr
scarlet red
Prefixes for Molecular Compounds
1 = mono-
6 = hexa-
2 = di-
7 = hepta-
3 = tri-
8 = octa-
4 = tetra-
9 = ennea- (nona-)
5 = penta-
10 = deca-
Properties of alkanes
Alkane
Formula
Boiling point [°C]
Melting point [°C]
Density [kg/m3]
(at 20 °C)
Methane
CH4
-162
−182
0.656 (gas)
Ethane
C2H6
−89
−183
1.26 (gas)
Propane
C3H8
−42
−188
2.01 (gas)
Butane
C4H10
0
−138
2.48 (gas)
Pentane
C5H12
36
−130
626 (liquid)
Hexane
C6H14
69
−95
659 (liquid)
Heptane
C7H16
98
−91
684 (liquid)
Octane
C8H18
126
−57
703 (liquid)
86
98
Nonane
C9H20
151
−54
718 (liquid)
Decane
C10H22
174
−30
730 (liquid)
Undecane
C11H24
196
−26
740 (liquid)
Dodecane
C12H26
216
−10
749 (liquid)
Tridecane
C13H28
235
-5.4
756 (liquid)
Tetradecane
C14H30
253
5.9
763 (liquid)
Pentadecane
C15H32
270
10
769 (liquid)
Hexadecane
C16H34
287
18
773 (liquid)
Heptadecane
C17H36
303
22
777 (solid)
Octadecane
C18H38
317
28
781 (solid)
Nonadecane
C19H40
330
32
785 (solid)
Icosane
C20H42
343
37
789 (solid)
Triacontane
C30H62
450
66
810 (solid)
Tetracontane
C40H82
525
82
817 (solid)
Pentacontane
C50H102
575
91
824 (solid)
Hexacontane
C60H122
625
100
829 (solid)
Heptacontane
C70H142
653
109
869 (solid)
87
99
Quantity
Time
Unit Name
Symbol
minute
min
1min = 60s
hour
h
1h = 3,600s
day
d
1d = 86,400s
year (annum)
a
1a = 31,557,600s
Area
hectare
ha
1ha = 10,000 m2
Volume
litre
L
1L = 1,000 cm3
Mass
metric ton or tonne
t
1t = 1,000 kg = 1 Mg
Pressure
standard atmosphere
atm
1atm = 101.325 kPa
Color of Transition Metal Ions in Aqueous Solution
Transition Metal Ion
Definition
Color
Co2+
pink
Cu2+
blue-green
Fe2+
olive green
Ni2+
bright green
Fe3+
brown to yellow
CrO42-
orange
Cr2O72-
yellow
Ti3+
purple
Cr3+
violet
Mn2+
pale pink
Zn2+
colorless
DNA Nitrogen Bases
Nitrogen Base
Abbreviation
adenine
A
100
88
cytosine
C
guanine
G
thymine
T
Acid–Base Indicators at 25°C
Colour Change as
Indicator
pH Range
methyl violet
0.0 – 1.6
yellow to blue
thymol blue
1.2 – 2.8
red to yellow
thymol blue
8.0 – 9.6
yellow to blue
orange IV
1.4 – 2.8
red to yellow
methyl orange
3.2 – 4.4
red to yellow
bromocresol green
3.8 – 5.4
yellow to blue
litmus
4.5 – 8.3
red to blue
methyl red
4.8 – 6.0
red to yellow
chlorophenol red
5.2 – 6.8
yellow to red
bromothymol blue
6.0 – 7.6
yellow to blue
phenol red
6.6 – 8.0
yellow to red
phenolphthalein
8.2 – 10.0
colourless to pink
thymolphthalein
9.4 – 10.6
colourless to blue
pH Increases
alizarin yellow R
10.1 – 12.0
yellow to red
indigo carmine
11.4 – 13.0
blue to yellow
1,3,5–trinitrobenzene
12.0 – 14.0
colourless to orange
101
89
Activity Series for 1.0 mol/L Solution at 25 °C and 101.325 kPa
Reduction Half-Reaction
Au (aq) + 3 e– Au(s)
3+
Hg2+(aq) + 2 e– Hg(l)
Ag+(aq)
+
e–
Ag(s)
–
Cu (aq) + 2 e Cu(s)
2+
2 H+(aq) + 2 e– H2(g)
Pb2+(aq) + 2 e– Pb(s)
Increasing strength of
reactant as an oxidizing
agent
Sn2+(aq) + 2 e– Sn(s)
Ni2+(aq) + 2 e–
Ni(s)
Cd2+(aq) + 2 e– Cd(s)
Fe2+(aq) + 2 e–
2+
Zn (aq) + 2 e
–
Cr2+(aq) + 2 e–
Fe(s)
Mg (aq) + 2 e
Na+(aq)
+
2+
e–
Ca (aq) + 2 e
–
–
Zn(s)
Cr(s)
Al3+(aq) + 3 e–
2+
Increasing strength of
reactant as a reducing
agent
Al(s)
Mg(s)
Na(s)
Ca(s)
–
Li (aq) + e Li(s)
+
Symbol
Symbols in Chemical Equations
Meaning
+
used to separate one reactant or product from another
→
used to separate the reactants from the products - it is pronounced
"yields" or "produces" when the equation is read
↔
used when the reaction can proceed in both directions - this is
called an equilibrium arrow and will be used later in the course
(g)
↑
(s)
indicates that the substance is in a gaseous state
an alternative way of representing a substance in a gaseous state
indicates that the substance is in a solid state
102
90
↓
an alternative way of representing a substance in a solid state
(aq)
indicates that the substance is dissolved in water - the aq comes
from aqueous
∆
→
indicates that heat is applied to make the reaction proceed
ℎ𝑣
The reaction undergoes photolysis (catalyzed with light/radiation)
indicates that the substance is in a liquid state
(l)
→
𝐹𝑒(𝑠)
Catalyzed by iron (solid).
4𝑜 𝐶
The reaction occurs at 4°C
→
→
Geological time scale
Era
Period
Epoch
Plant and Animal
Development
Cenozoic
Quaternary
Holocene (.01)
Humans develop
Pleistocene (1.8)
Tertiary
Pliocene (5.3)
Miocene (23.8)
Oligocene (33.7)
"Age of mammals"
Eocene (54.8)
Paleocene (65.0)
Extinction of dinosaurs and
many other species.
Mesozoic
Cretaceous (144)
"Age of Reptiles"
First flowering plants
Jurassic (206)
Triassic (248)
First birds
Dinosaurs dominant.
Paleozoic
Permian (290)
"Age of
Extinction of trilobites and many
Carboniferous:
Amphibians"
other marine animals
Pennyslvanian (323)
Carboniferous:
103
91
Mississippian (354)
First reptiles
Large coal swamps
Large Amphibians abundant.
Devonian (417)
"Age of Fishes"
First insect fossils
Silurian (443)
Fishes dominant
First land plants
Ordovician (490)
"Age of
Cambrian (540)
Invertebrates"
First fishes
Trilobites dominant
First organisms with shells
Precambrian - comprises about 88% of geologic time (4500)
First multicelled organisms
First one-celled organisms
Origin of Earth
prefix
number of carbons
alkyl group
meth-
1
methyl
eth-
2
ethyl
104
92
prop-
3
propyl
but-
4
butyl
pent-
5
pentyl
hex-
6
hexyl
hept-
7
heptyl
oct-
8
octyl
non-
9
nonyl
dec-
10
decyl
The suffix associated with various functional groups
Functional group
suffix
alkane
-ane
alkene
-ene
alkyne
-yne
alcohol
-ol
aldehyde
-al
ketone
-one
105
93
carboxylic acid
-oic acid
ester
-oate
Heat Capacities of Selected Substances at 1 atm and 25°C
Specific Heat Capacity
(J/g°C)
Substance
air
1.012
aluminum
0.89
argon
0.5203
copper
0.385
granite
0.790
graphite
0.710
helium
5.1932
iron
0.450
lead
0.129
lithium
3.58
mercury
0.14
methanol
2.14
sodium
1.228
steel
0.466
titanium
0.523
water (ice, O°C)
2.09
water
4.184
water (steam, 100°C)
2.03
106
94
Thermodynamic Properties of Selected Compounds
Compound
Melting Point
Boiling Point
Heat of Fusion
Heat of
(°C)
(°C)
(kJ/mol)
Vaporization
(kJ/mol)
water
0.00
100.00
6.01
40.66
hexane
–95.35
68.73
13.08
28.85
ethanol
–114.14
78.29
4.93
38.56
methanol
–97.53
64.6
3.22
35.21
toluene
–94.95
110.63
6.64
33.18
Standard Heats of Formation of Selected Compounds at 25°C
Compound
Standard heat of formation
(kJ/mol)
ammonia
–45.9
benzene
+49.1
butane
–125.7
calcium carbonate
–1207.6
calcium hydroxide
–985.2
carbon dioxide
–393.5
carbon monoxide
–110.5
ethane
–84.0
ethanoic acid (acetic acid)
–484.3
ethanol
–277.6
ethene (ethylene)
+52.4
ethyne (acetylene)
+227.4
glucose
–1273.3
hydrogen sulfide
–20.6
methane
–74.6
107
95
methanol
–239.2
nitrogen dioxide
+33.2
nitrogen monoxide
+91.3
octane
–250.1
pentane
–173.5
propane
–103.8
sucrose
–2226.1
sulfur dioxide
–296.8
sulfur trioxide
–395.7
water (liquid)
–285.8
water (gas)
–241.8
Note:
Negative sign (–) denotes exothermic change.
Positive sign (+) denotes endothermic change.
1.00 kilowatt hour = 1.00 kW.h = 3.60 × 106 J
Elements for Radioactive Dating
Radioisotope
Final Decay Nuclide
Approximate Half-Life
(annum—a)
(Parent Nuclide)
carbon-14
nitrogen-14
5.73 × 103
potassium-40
argon-40
1.26 × 109
rubidium-87
strontium-87
4.88 × 1010
uranium-235
lead-207
7.04 × 108
uranium-238
lead-206
4.47 × 109
108
96
Types of Reactions
Formation (Synthesis)
element + element → compound
Decomposition
compound → element + element
Single Replacement
compound + element → new compound + new element
Double Replacement
compound + compound → new compound + new compound
Complete Hydrocarbon Combustion
hydrocarbon + oxygen → carbon dioxide + water
Addition
alkene or alkyne + excess hydrogen → alkane
alkene or alkyne + halogen → halogenated hydrocarbon
Cracking
large hydrocarbon → small hydrocarbons
Polymerization
monomer + monomer → polymer
Esterification
alcohol + carboxylic acid → ester + water
109
97
Table of Polyatomic Ions
Name
Formula
ammonium
NH4+
nitrite
NO2−
nitrate
NO3−
sulfite
SO32−
sulfate
SO42−
hydrogen sulfate
HSO4−
(bisulfate)
thiosulfate
S2O32−
oxalate
C2O42−
hydroxide
OH−
phosphite
PO33−
phosphate
PO43−
hydrogen phosphate
HPO42−
dihydrogen
H2PO4−
phosphate
perchlorate
ClO4−
chlorate
ClO3−
110
98
chlorite
ClO2−
hypochlorite
ClO−
bromate
BrO3−
iodate
IO3−
acetate
CH3COO−
acetate
C2H3O2−
carbonate
CO32−
hydrogen carbonate
HCO3−
(bicarbonate)
chromate
CrO42−
dichromate
Cr2O72−
permanganate
MnO4−
peroxide
O22−
cyanide
CN−
cyanate
OCN−
thiocyanate
SCN−
Standard index of refraction measurements taken at the "yellow doublet" sodium D line with a
wavelength of 589 nm
111
99
MATERIAL
INDEX OF REFRACTION
STATE
Vacuum
1
(by definition)
Helium
1.000036
Gas
(0°C and 1 atm)
Hydrogen
1.000132
Gas
(0°C and 1 atm)
Air
1.000277
Gas
(at STP*)
Air
1.000293
Gas
(0°C and 1 atm)
Carbon Dioxide
1.001
Gas
(0°C and 1 atm)
Liquid Helium
1.025
Liquid
(at -270°C)
Water Ice
1.31
Solid
(at 0°C)
Water
1.330
Liquid
(at 20°C)
Acetone
1.36
Liquid
(at 20°C)
Ethanol
1.361
Liquid
(at 20°C)
Kerosene
1.39
Liquid
(at 20°C)
Corn Oil
1.47
Liquid
(at 20°C)
Glycerol
1.4729
Liquid
(at 20°C)
Acrylic Glass
1.490–1.492
Solid
(at 20°C)
Benzene
1.501
Liquid
(at 20°C)
Crown Glass (pure)
1.50–1.54
Solid
(at 20°C)
Plate Glass (window glass)
1.52
Solid
(at 20°C)
Sodium Chloride (table salt)
1.544
Solid
(at 20°C)
Amber
1.55
Solid
(at 20°C)
Polycabonate
1.60
Solid
(at 20°C)
Flint Glass (pure)
1.60–1.62
Solid
(at 20°C)
Bromine
1.661
Liquid
(at 20°C)
Sapphire
1.762–1.778
Solid
(at 20°C)
Cubic Zirconia
2.15–2.18
Solid
(at 20°C)
Diamond
2.417
Solid
(at 20°C)
Silicon
3.42–3.48
Solid
(at 20°C)
Germanium
4.05–4.01
Solid
(at 20°C)
100
112
STP is defined as a temperature of 273.15 K (0 °C, 32 °F) and an absolute pressure of
exactly 105 Pa (100 kPa, 1 bar).
Solubility Products for Selected Ionic Substances at 25°C
Solid
Color
Ksp
Solid
Acetates
Ca(O2CCH3)2·3H2O
white
Hg2Br2
4 × 10−3
Hg2I2
yellow 5.2 × 10−29
PbI2
yellow
off-white 5.35 × 10−13
yellow
Ksp
Iodides
Bromides
AgBr
Color
6.40 × 10−23
Carbonates
Oxalates
Ag2C2O4
white 5.40 × 10−12
MgC2O4·2H2O white
CaCO3
white
3.36 × 10−9
PbCO3
white
7.40 × 10−14
Chlorides
PbC2O4
4.83 × 10−6
4.8 × 10−10
white
Phosphates
Ag3PO4
AgCl
white
1.77 × 10−10
Hg2Cl2
white
1.43 × 10−18 FePO4·2H2O
PbCl2
white
1.70 × 10−5
Chromates
9.8 × 10−9
Sr3(PO4)2
white 8.89 × 10−17
white
4.0 × 10−28
pink
9.91 × 10−16
Sulfates
Ag2SO4
white
1.20 × 10−5
CaCrO4
yellow
7.1 × 10−4
BaSO4
white 1.08 × 10−10
PbCrO4
yellow
2.8 × 10−13
PbSO4
white
Fluorides
2.53 × 10−8
Sulfides
BaF2
white
1.84 × 10−7
Ag2S
black
PbF2
white
3.3 × 10−8
CdS
yellow 8.0 × 10−27
PbS
black
8.0 × 10−28
ZnS
white
1.6 × 10−24
Hydroxides
Ca(OH)2
white
5.02 × 10−6
Cu(OH)2
pale blue
1 × 10−14
Mn(OH)2
light pink 1.9 × 10−13
Cr(OH)3
gray-green 6.3 × 10−31
Fe(OH)3
rust red
2.79 × 10−39
101
113
6.3 × 10−50
20 Amino Acids In Human Protein:
Table of DNA Base Triplets, RNA Codons and Anticodons
Amino Acid
DNA Base Triplets
M-RNA Codons
T-RNA Anticodons
alanine
CGA, CGG, CGT, CGC
GCU, GCC, GCA, GCG
CGA, CGG, CGU, CGC
arginine
GCA, GCG, GCT, GCC
CGU, CGC, CGA, CGG
GCA, GCG, GCU, GCC
TCT, TCC
AGA, AGG
UCU, UCC
asparagine
TTA, TTG
AAU, AAC
UUA, UUG
aspartate
CTA, CTG
GAU, GAC
CUA, CUG
cysteine
ACA, ACG
UGU, UGC
ACA, ACG
glutamate
CTT, CTC
GAA, GAG
CUU, CUC
glutamine
GTT, GTC
CAA, CAG
GUU, GUC
glycine
CCA, CCG, CCT, CCC
GGU, GGC, GGA, GGG
CCA, CCG, CCU, CCC
histidine
GTA, GTG
CAU, CAC
GUA, GUG
isoleucine
TAA, TAG, TAT
AUU, AUC, AUA
UAA, UAG, UAU
leucine
AAT, AAC, GAA, GAG
UUA, UUG, CUU, CUC
AAU, AAC, GAA, GAG
GAT, GAC
CUA, CUG
GAU, GAC
lysine
TTT, TTC
AAA, AAG
UUU, UUC
methionine
TAC
AUG
UAC
phenylalanine
AAA, AAG
UUU, UUC
AAA, AAG
proline
GGA, GGG, GGT, GGC
CCU, CCC, CCA, CCG
GGA, GGG, GGU, GGC
serine
AGA, AGG, AGT, AGC
UCU, UCC, UCA, UCG
AGA, AGG, AGU, AGC
TCA, TCG
AGU, AGC
UCA, UCG
Stop
ATG, ATT, ACT
UAA, UAG, UGA
AUG, AUU, ACU
threonine
TGA, TGG, TGT, TGC
ACU, ACC, ACA, ACG
UGA, UGG, UGU, UGC
tryptophan
ACC
UGG
ACC
tyrosine
ATA, ATG
UAU, UAC
AUA, AUG
valine
CAA, CAG, CAT, CAC
GUU, GUC, GUA, GUG
CAA, CAG, CAU, CAC
102
114
Element
Symbol
Relative atomic mass
Density (g / cm3)
Date of Discovery
Actinium
Ac
227
10·1
1899
Aluminium
Al
27
2·70
1825
Americium
Am
243
13·7
1944
Antimony
Sb
122
6·68
Ancient
Argon
Ar
40
0·0018
1894
Arsenic
As
75
5·78
~1250
Astatine
At
210
unknown
1940
Barium
Ba
137·5
3·62
1808
Berkelium
Bk
247
14·8
1949
Beryllium
Be
9
1·85
1798
Bismuth
Bi
209
9·79
1753
Boron
B
11
2·47
1808
Bromine
Br
80
3·12
1826
Cadmium
Cd
112·5
8·69
1817
Calcium
Ca
40
1·54
1808
Californium
Cf
251
unknown
1950
Carbon
C
12
*
Prehistoric
Cerium
Ce
140
6·77
1803
Caesium
Cs
133
1·93
1860
Chlorine
Cl
35·5
0·0032
1774
Chromium
Cr
52
7·15
1797
Cobalt
Co
59
8·86
1739
Copper
Cu
63·5
8·96
Ancient
Curium
Cm
247
13·3
1944
Dysprosium
Dy
162·5
8·55
1886
Einsteinium
Es
252
unknown
1952
Erbium
Er
167·5
9·07
1843
Europium
Eu
152
5·24
1896
Fluorine
F
19
0·0017
1886
Francium
Fr
223
unknown
1939
Gadolinium
Gd
157
7·90
1880
Gallium
Ga
69·5
5·91
1875
Germanium
Ge
72·5
5·32
1886
Gold
Au
197
19·3
Ancient
Hafnium
Hf
178·5
13·3
1923
Helium
He
4
0·0002
1868
Holmium
Ho
165
8·80
1879
Hydrogen
H
1
0·00009
1766
Indium
In
115
7·31
1863
Iodine
I
127
4·95
1811
Iridium
Ir
192
22·5
1803
Iron
Fe
56
7·87
Ancient
Krypton
Kr
84
0·0037
1898
Lanthanum
La
139
6·15
1839
Lead
Pb
207
11·3
Ancient
Lithium
Li
7
0·53
1817
103
115
Lutetium
Lu
175
9·84
1907
Magnesium
Mg
24·5
1·74
1808
Manganese
Mn
55
7·47
1774
Mercury
Hg
200·5
13·5
Ancient
Molybdenum
Mo
96
10·2
1778
Neodymium
Nd
144
7·01
1885
Neon
Ne
20
0·0009
1898
Neptunium
Np
237
20·2
1940
Nickel
Ni
58·5
8·90
1751
Niobium
Nb
93
8·57
1801
Nitrogen
N
14
0.0013
1772
Osmium
Os
190
22·6
1803
Oxygen
O
16
0·0014
1774
Palladium
Pd
106·5
12·0
1803
Phosphorus
P
31
1·82
1669
Platinum
Pt
195
21·5
1735
Plutonium
Pu
244
19·7
1941
Polonium
Po
209
9·20
1898
Potassium
K
39
0·89
1807
Praseodymium
Pr
141
6·77
1885
Promethium
Pm
145
7·26
1944
Protactinium
Pa
231
15·4
1913
Radium
Ra
226
5·00
1898
Radon
Rn
222
0·0097
1900
Rhenium
Re
186
20·8
1925
Rhodium
Rh
103
12·4
1803
Rubidium
Rb
85·5
1·53
1861
Ruthenium
Ru
101
12·1
1844
Samarium
Sm
150·5
7·52
1853
Scandium
Sc
45
2·99
1879
Selenium
Se
79
4·81
1817
Silicon
Si
28
2·33
1824
Silver
Ag
108
10·5
Ancient
Sodium
Na
23
0·97
1807
Strontium
Sr
87·5
2·64
1790
Sulfur
S
32
2·09
Ancient
Tantalum
Ta
181
16·4
1802
Technetium
Tc
98
11
1937
Tellurium
Te
127·5
6·25
1782
Terbium
Tb
159
8·23
1843
Thallium
Tl
204·5
11·8
1861
Thorium
Th
232
11·7
1828
Thulium
Tm
169
9·32
1879
Tin
Sn
118·5
7·26
Ancient
Titanium
Ti
48
4·51
1791
Tungsten
W
184
19·3
1783
Uranium
U
238
19·1
1789
Vanadium
V
51
6·00
1801
104
116
Xenon
Xe
131·5
0·0059
1898
Ytterbium
Yb
173
6·90
1878
Yttrium
Y
89
4·47
1789
Zinc
Zn
65·5
7·14
Ancient
Zirconium
Zr
91
6·52
1789
Solubilities of Selected Compounds in Water
vs
means very
soluble
(a solubility greater than 10 gl−1)
s
means soluble
(a solubility of between 1 and 10 gl−1)
i
means insoluble
(a solubility of less than 1 gl−1)
−
no data
bromide
carbonate
chloride
iodide
nitrate
phosphate
sulfate
oxide
hydroxide
aluminium
vs
−
vs
vs
vs
i
vs
i
i
ammonium
vs
vs
vs
vs
vs
vs
vs
−
−
barium
vs
i
vs
vs
vs
i
i
vs
vs
calcium
vs
i
vs
vs
vs
i
s
s
s
copper(II)
vs
i
vs
−
vs
i
vs
i
i
iron(II)
vs
i
vs
vs
vs
i
vs
i
i
iron(III)
vs
−
vs
−
vs
i
vs
i
i
lead(II)
s
i
s
i
vs
i
i
i
i
lithium
vs
vs
vs
vs
vs
i
vs
vs
vs
magnesium
vs
i
vs
vs
vs
i
vs
i
i
nickel
vs
i
vs
vs
vs
i
vs
i
i
potassium
vs
vs
vs
vs
vs
vs
vs
vs
vs
i
i
i
i
vs
i
s
i
−
sodium
vs
vs
vs
vs
vs
vs
vs
vs
vs
tin(II)
vs
i
vs
s
−
i
vs
i
i
zinc
vs
i
vs
vs
vs
i
vs
i
i
silver
105
117
Bond
Bond length (pm)
Bond energy (kJ/mol)
H−H
74
436
C−C
154
348
N−N
145
170
O−O
148
145
F−F
142
158
Cl−Cl
199
243
Br−Br
228
193
I−I
267
151
C−C
154
348
C−N
147
308
C−O
143
360
C−S
182
272
C−F
135
488
C−Cl
177
330
C−Br
194
288
C−I
214
216
H−C
109
413
H−N
101
391
H−O
96
366
H−F
92
568
H−Cl
127
432
H−Br
141
366
H−I
161
298
C−C
154
348
C=C
134
614
C≡C
120
839
O−O
148
145
O=O
121
498
N−N
145
170
N≡N
110
945
106
118
We cannot taste anything without saliva.
Blue is the color of liquid oxygen.
Every hydrogen atom in our body is likely 13.5 billion years old because they
were created at the birth of the universe.
Gallium has a melting point of 29.76 degrees centigrade and can
melt on the palm of our hand.
If we pour a handful of salt into a glass of
water, the water level will go down
When we freeze seawater or saltwater, we get freshwater ice.
More than 78% of human brain consists of water.
The rarest naturally-occurring element in the Earth's crust is astatine
107
Spectrochemical series
Ligands can be arranged in a spectrochemical series according to the energy difference they produce between
the two sets of d-orbitals in an octahedral complex.
2−
I − < Br− < S < Cl− < F− < OH− < H2O < SCN− < NH3 < CN− ≈ CO
Values of the ionization constant of water
Temperature (oC)
Kw value
0
0.113 × 10−14
5
0.185 × 10−14
10
0.292 × 10−14
15
0.453 × 10−14
20
0.684 × 10−14
25
1.00 × 10−14
30
1.47 × 10−14
35
2.09 × 10−14
40
2.92 × 10−14
45
4.02 × 10−14
50
5.43 × 10−14
55
7.24 × 10−14
60
9.55 × 10−14
65
12.4 × 10−14
70
15.9 × 10−14
75
20.1 × 10−14
80
25.2 × 10−14
85
31.3 × 10−14
90
38.3 × 10−14
95
46.6 × 10−14
100
56.0 × 10−14
108
119
Specific Gravity of Liquids
Liquid
Temperature
kg/m3
1,1,2-Trichlorotrifluoroethane
25 °C
1564.00
1,2,4-Trichlorobenzene
20 °C
1454.00
1,4-Dioxane
20 °C
1033.60
2-Methoxyethanol
20 °C
964.60
Acetic Acid
25 °C
1049.10
Acetone
25 °C
784.58
Acetonitrile
20 °C
782.20
Alcohol, ethyl
25 °C
785.06
Alcohol, methyl
25 °C
786.51
Alcohol, propyl
25 °C
799.96
Ammonia (aqua)
25 °C
823.35
Analine
25 °C
1018.93
Automobile oils
15 °C
880 - 940
Beer (varies)
10 °C
1010
Benzene
25 °C
873.81
Benzil
25 °C
1079.64
Brine
15 °C
1230
Bromine
25 °C
3120.40
Butyric Acid
20 °C
959
Butane
25 °C
599.09
n-Butyl Acetate
20 °C
879.60
n-Butyl Alcohol
20 °C
809.70
n-Butyl Chloride
20 °C
886.20
Caproic acid
25 °C
921.06
Carbolic acid
15 °C
956.30
Carbon disulfide
25 °C
1260.97
Carbon tetrachloride
25 °C
1584.39
Carene
25 °C
856.99
Castor oil
25 °C
956.14
Chloride
25 °C
1559.88
Chlorobenzene
20 °C
1105.80
Chloroform
20 °C
1489.20
Chloroform
25 °C
1464.73
Citric acid
25 °C
1659.51
Coconut oil
15 °C
924.27
Cotton seed oil
15 °C
925.87
Cresol
25 °C
1023.58
Creosote
15 °C
1066.83
109
120
Crude oil, 48° API
60 °F
790
Crude oil, 40° API
60 °F
825
Crude oil, 35.6° API
60 °F
847
Crude oil, 32.6° API
60 °F
862
Crude oil, California
60 °F
915
Crude oil, Mexican
60 °F
973
Crude oil, Texas
60 °F
873
Cumene
25 °C
860.19
Cyclohexane
20 °C
778.50
Cyclopentane
20 °C
745.40
Decane
25 °C
726.28
Diesel fuel oil 20 to 60
15 °C
820 - 950
Diethyl ether
20 °C
714
o-Dichlorobenzene
20 °C
1305.80
Dichloromethane
20 °C
1326.00
Diethylene glycol
15 °C
1120
Dichloromethane
20 °C
1326.00
Dimethyl Acetamide
20 °C
941.50
N,N-Dimethylformamide
20 °C
948.70
Dimethyl Sulfoxide
20 °C
1100.40
Dodecane
25 °C
754.63
Ethane
-89 °C
570.26
Ether
25 °C
72.72
Ethylamine
16 °C
680.78
Ethyl Acetate
20 °C
900.60
Ethyl Alcohol
20 °C
789.20
Ethyl Ether
20 °C
713.30
Ethylene Dichloride
20 °C
1253.00
Ethylene glycol
25 °C
1096.78
Fluorine refrigerant R-12
25 °C
1310.95
Formaldehyde
45 °C
812.14
Formic acid 10% concentration
20 °C
1025
Formic acid 80% concentration
20 °C
1221
Freon - 11
21 °C
1490
Freon - 21
21 °C
1370
Fuel oil
60 °F
890.13
Furan
25 °C
1416.03
Furforol
25 °C
1154.93
Gasoline, natural
60 °F
711.22
Gasoline, Vehicle
60 °F
737.22
110
121
Gas oils
60 °F
890
Glucose
60 °F
1350 - 1440
Glycerin
25 °C
1259.37
Glyme
20 °C
869.10
Glycerol
25 °C
1126.10
Heptane
25 °C
679.50
Hexane
25 °C
654.83
Hexanol
25 °C
810.53
Hexene
25 °C
671.17
Hydrazine
25 °C
794.52
Iodine
25 °C
4927.28
Ionene
25 °C
932.27
Isobutyl Alcohol
20 °C
801.60
Iso-Octane
20 °C
691.90
Isopropyl Alcohol
20 °C
785.40
Isopropyl Myristate
20 °C
853.20
Kerosene
60 °F
817.15
Linolenic Acid
25 °C
898.64
Linseed oil
25 °C
929.07
Methane
-164 °C
464.54
Methanol
20 °C
791.30
Methyl Isoamyl Ketone
20 °C
888.00
Methyl Isobutyl Ketone
20 °C
800.80
Methyl n-Propyl Ketone
20 °C
808.20
Methyl t-Butyl Ether
20 °C
740.50
N-Methylpyrrolidone
20 °C
1030.40
Methyl Ethyl Ketone (MEK)
20 °C
804.90
MEK
25 °C
802.52
Milk
15 °C
1020 - 1050
Naphtha
15 °C
664.77
Naphtha, wood
25 °C
959.51
Napthalene
25 °C
820.15
Ocimene
25 °C
797.72
Octane
15 °C
917.86
Olive oil
20 °C
800 - 920
Oxygen (liquid)
-183 °C
1140
Palmitic Acid
25 °C
850.58
Pentane
20 °C
626.20
Pentane
25 °C
624.82
Petroleum Ether
20 °C
640.00
111
122
Petrol, natural
60 °F
711.22
Petrol, Vehicle
60 °F
737.22
Phenol
25 °C
1072.28
Phosgene
0 °C
1377.59
Phytadiene
25 °C
823.35
Pinene
25 °C
856.99
Propane
-40 °C
583.07
Propane, R-290
25 °C
493.53
Propanol
25 °C
804.13
Propylene Carbonate
20 °C
1200.60
Propylene
25 °C
514.35
n-Propyl Alcohol
20 °C
803.70
Propylene glycol
25 °C
965.27
Pyridine
25 °C
978.73
Pyrrole
25 °C
965.91
Rape seed oil
20 °C
920
Resorcinol
25 °C
1268.66
Rosin oil
15 °C
980
Sabiname
25 °C
812.14
Sea water
25 °C
1025.18
Silane
25 °C
717.63
Sodium Hydroxide (caustic soda)
15 °C
1250
Sorbaldehyde
25 °C
895.43
Soya bean oil
15 °C
924 - 928
Stearic Acid
25 °C
890.63
Sulphuric Acid 95% conc.
20 °C
1839
Sugar solution 68 brix
15 °C
1338
Sunflower oil
20 °C
920
Styrene
25 °C
903.44
Terpinene
25 °C
847.38
Tetrahydrofuran
20 °C
888.00
Toluene
20 °C
866.90
Toluene
25 °C
862.27
Triethylamine
20 °C
727.60
Trifluoroacetic Acid
20 °C
1489.00
Turpentine
25 °C
868.20
Water, pure
4 °C
1000.00
Water, sea
77 °F
1021.98
Whale oil
15 °C
925
o-Xylene
20 °C
880.20
112
123
Bromine and mercury are the only elements that can stay liquid at room
temperature.
DNA is a flame retardant
There is about 250 g of table salt (NaCl) in an average adult human body.
Air becomes liquid at −190°C
Frogs don't drink water because they can
absorb it through their skin
Helium and Hydrogen account for 98% of all matter.
The chemical elements are organized in order of their
increasing atomic numbers.
Mars is red because of iron oxide
113
Molecular formula
Compound name
Ac2O3
Actinium(III) oxide
AgBF4
Silver tetrafluoroborate
AgBr
silver bromide
AgBrO
silver hypobromite
AgBrO2
silver bromite
AgBrO3
silver bromate
AgBrO4
silver perbromate
AgCl
silver chloride
AgCl3Cu2
dicopper silver trichloride
AgClO3
silver chlorate
AgClO4
silver perchlorate
AgCN
silver cyanide
AgCNO
silver fulminate
AgF
silver fluoride
AgF2
silver(II) fluoride
AgI
silver iodide
AgIO
silver hypoiodite
AgIO2
silver iodite
AgIO3
silver iodate
AgIO4
silver periodate
AgMnO4
silver permanganate
AgN3
silver azide
AgNO3
silver nitrate
AgO
silver monoxide
AgONC
silver cyanate
AgPF6
silver hexafluorophosphate
AgSNC
silver thiocyanate
Ag2C2
silver acetylide
Ag2CO3
silver(I) carbonate
Ag2C2O4
silver oxalate
Ag2Cl2
silver(II) dichloride
Ag2CrO4
silver chromate
Ag2Cr2O7
silver dichromate
Ag2F
silver subfluoride
Ag2MoO4
silver molybdate
Ag2O
silver(I) oxide
Ag2S
silver sulfide
Ag2SO4
silver sulfate
Ag2Se
silver selenide
114
124
Ag2SeO3
silver selenite
Ag2SeO4
silver selenate
Ag2Te
silver(I) telluride
Ag3Br2
silver dibromide
Ag3Br3
silver tribromide
Ag3Cl3
silver(III) trichloride
Ag3I3
silver(III) triiodide
Ag3PO4
silver phosphate
AlBO
aluminium boron oxide
AlBO3
aluminium borate
AlBr
aluminium monobromide
AlBr3
aluminium tribromide
AlCl
aluminium monochloride
AlClF
aluminium chloride fluoride
AlCl2<F
aluminium chloride fluoride
AlClO
aluminium chloride oxide
AlCl2H
Dichloroalumane
AlCl3
aluminium chloride
AlCl2F
aluminium chloride fluoride
AlCl3
aluminium trichloride
AlCl4Cs
aluminium caesium tetrachloride
AlCl4K
potassium tetrachloroaluminate
AlCl4Na
sodium tetrachloroaluminate
AlCl4Rb
aluminium rubidium tetrachloride
AlCl6K3
potassium hexachloroaluminate
AlCl6Na3
sodium hexachloroaluminate
AlF
aluminium monofluoride
AlFO
aluminium monofluoride monoxide
AlF2
aluminium difluoride
AlF2O
aluminium difluoride oxide
AlF3
aluminium trifluoride
AlF4K
potassium tetrafluoroaluminate
AlF4Li
lithium tetrafluoroaluminate
AlF6K3
potassium hexafluoraluminate
AlF6Li3
lithium hexafluoroaluminate
AlF6Na3
cryolite
AlGaInP
aluminium-gallium-indium phosphide
Al(OH)3
aluminium hydroxide
AlI
aluminium monoiodide
AlI3
aluminium triiodide
115
125
AlLiO2
lithium aluminate
AlN
aluminium nitride
Al(NO2)3
aluminium nitrite
Al(NO3)3
aluminium nitrate
AlNaO2
sodium aluminate
AlO
aluminium monoxide
AlOSi
aluminium silicon monoxide
AlO2
Aluminium(IV) oxide
AlP
aluminium monophosphide
AlPO4
aluminium phosphate
AlTe
aluminium monotelluride
AlTe2
monoaluminium ditelluride
Al2BeO4
beryllium aluminium oxide
Al2Br6
dialuminium hexabromide
Al2(CO3)3
aluminium carbonate
Al2Cl9K3
potassium aluminium chloride
Al2CoO4
cobalt blue
Al2F6
aluminium fluoride
Al2I6
aluminium iodide
Al2MgO4
magnesium aluminium oxide
Al2O
dialuminium monoxide
Al2O2
dialuminium dioxide
Al2O3
aluminium oxide
Al2O5Si
aluminium silicate
Al2O5Si
aluminium silicate
Al2O5Si
andalusite
Al2O7Si2
aluminium silicate
Al2S
dialuminium monosulfide
Al2S3
aluminium sulfide
Al2(SO4)3
aluminium sulphate
Al2Se
dialuminium selenide
Al2Si2O5(OH)4
kaolin
Al2Te
dialuminium telluride
Al3F14Na5
chiolite
Al4C3
aluminium carbide
Al6BeO10
beryllium aluminium oxide
Al6O13Si2
mullite
ArClF
argon chloride fluoride
ArClH
argon chloride hydride
ArFH
argon fluoride hydride
116
126
AsBrO
arsenic oxybromide
AsBr3
arsenic tribromide
AsClO
arsenic monoxide monochloride
AsCl3
arsenic trichloride
AsCl3O
arsenic oxychloride
AsCl4F
arsenic tetrachloride fluoride
AsF3
arsenic trifluoride
AsF5
arsenic pentafluoride
AsH3
arsine
AsI3
arsenic triiodide
AsO
arsenic monoxide
AsO2
arsenic dioxide
AsP
arsenic monophosphide
AsP3
arsenic triphosphide
AsTl
thallium arsenide
As2I4
arsenic diiodide
As2O3
arsenic trioxide
As2P2
arsenic diphosphide
As2O5
arsenic pentoxide
As2S4
arsenic tetrasulfide
As2S5
arsenic pentasulfide
As2Se
arsenic hemiselenide
As2Se3
arsenic triselenide
As2Se5
arsenic pentaselenide
As3O4
arsenic tetraoxide
As3P
arsenic(III) phosphide
As4O3
tetraarsenic trioxide
As4O5
tetraarsenic pentaoxide
As4S3
tetraarsenic trisulfide
As4S4
tetraarsenic tetrasulfide
AuBO
gold monoboride monoxide
AuBr
gold bromide
AuBr3
gold tribromide
AuCN
gold cyanide
AuCl
gold chloride
AuCl3
gold trichloride
AuF3
gold trifluoride
AuI
gold iodide
AuI3
gold(III) iodide
Au(OH)3
gold hydroxide
117
127
AuTe
gold telluride
Au2O3
gold trioxide
Au2S
gold sulfide
Au2S3
gold trisulfide
Au2(SeO4)3
gold triselenate
Au2Se3
gold triselenide
BAs
boron arsenide
BAsO4
boron(III) arsenate
BBr3
boron tribromide
BCl3
boron trichloride
BF3
boron trifluoride
BI3
boron iodide
BN
boron nitride
c(NO2)3
boron nitrite
B(NO3)3
boron nitrate
B(OH)3
boric acid
BP
boron(III) phosphide
BPO4
boron(III) orthophosphate
B2Cl4
boron chloride
B 2F 4
Diboron tetrafluoride
B 2H 6
boron hydride
B 2O 3
boron(III) oxide
B 2S 3
boron sulfide
B2Se3
boron selenide
B3N3H6
borazine
B 4C
boron carbide
Ba(AlO2)2
barium aluminate
Ba(AsO3)2
barium arsenite
Ba(AsO4)2
barium arsenate
BaB6
barium hexaboride
Ba(BrO3)2·H2O
barium bromate monohydrate
Ba(BrO3)2·2H2O
barium bromate dihydrate
BaBr2
barium bromide
Ba(BrO)2
barium hypobromite
Ba(BrO2)2
barium bromite
Ba(BrO3)2
barium bromate
Ba(BrO4)2
barium perbromate
Ba(CHO2)2
barium formate
Ba(C2H3O2)2
barium acetate
Ba(CN)2
barium cyanide
118
128
BaHfO3
barium hafnate
BaHgI4
barium tetraiodomercurate(II)
Ba(HS)2
barium hydrosulfide
BaI2
barium iodide
Ba(IO)2
barium hypoiodite
Ba(IO2)2
barium iodite
Ba(IO3)2
barium iodate
Ba(IO4)2
barium periodate
BaK2(CrO4)2
barium potassium chromate
BaMnO4
barium manganate
Ba(MnO4)2
barium permanganate
BaMoO4
barium molybdate
BaN6
barium azide
Ba(NO2)2
barium nitrite
Ba(NO3)2
barium nitrate
Ba(NbO3)2
barium niobate
BaNb2O6
barium metaniobate
BaO
barium oxide
Ba(OH)2
barium hydroxide
baryta
BaO2
barium peroxide
Ba(PO3)2
barium metaphosphate
BaS
barium sulfide
Ba(SCN)2
barium thiocyanate
BaS2O3
barium thiosulfate
BaSiF6
barium hexafluorosilicate
BaSO3
barium sulfite
BaSO4
barium sulfate
barite
BaSe
barium selenide
Ba(SeCN)2
barium selenocyanate
BaSeO3
barium selenite
BaSeO4
barium selenate
BaSiO3
barium metasilicate
BaSi2
barium silicide
BaSi2O5
barium disilicate
BaSnO3
barium stannate
BaTeO3
barium tellurite
BaTeO4·3H2O
barium tellurate trihydrate
BaTiO3
barium titanate
barium metatitanate
119
129
BaU2O7
barium uranium oxide
BaWO4
barium tungstate
BaZrO3
barium zirconate
Ba2Na(NbO3)5
barium sodium niobate
Ba2P2O7
barium pyrophosphate
Ba2V2O7
barium pyrovanadate
Ba2XeO6
barium perxenate
Ba3(CrO4)2
barium chromate(V)
Ba3N2
barium nitride
Ba3(PO4)2
barium orthophosphate
Ba3(VO4)2
barium orthovandate
BeB2
beryllium boride
Be(BH4)2
beryllium borohydride
BeBr2
beryllium bromide
Be(CHO2)2
beryllium formate
BeCO3
beryllium carbonate
Be(C2H3O2)2
beryllium acetate
Be(C5H7O2)2
beryllium acetylacetonate
BeCl2
beryllium chloride
Be(ClO)2
beryllium hypochlorite
Be(ClO3)2
beryllium chlorate
Be(ClO4)2
beryllium perchlorate
BeF2
beryllium fluoride
BeI2
beryllium iodide
Be(NO2)2
beryllium nitrite
Be(NO3)2
beryllium nitrate
BeO
beryllium oxide
bromellite
Be(OH)2
beryllium hydroxide
BeS
beryllium sulfide
BeSO3
beryllium sulfite
BeSO4
beryllium sulfate
Be2C
beryllium carbide
Be3Al2(SiO3)6
beryl
Be3N2
beryllium nitride
BiBO3
bismuth(III) orthoborate
BiBr3
bismuth(III) bromide
Bi(C2H3O2)3
bismuth(III) acetate
BiC6H5O7
bismuth(III) citrate
BiCl3
bismuth(III) chloride
BiF3
bismuth(III) fluoride
120
130
BiI3
bismuth(III) iodide
Bi(NO3)3·5H2O
bismuth(III) nitrate pentahydrate
BiOCl
bismuth(III) oxychloride
BiOI
bismuth(III) oxyiodide
(BiO)2CO3
bismuth oxycarbonate
BiPO4
bismuth(III) orthophosphate
Bi(VO3)5
bismuth(III) metavanadate
Bi2Se3
bismuth(III) selenide
bismuth selenide
Bi2(MoO4)3
bismuth(III) molybdate
Bi2O3
bismuth(III) oxide
Bi2S3
bismuth(III) sulfide
bismuthinite
Bi2Se3
bismuth(III) selenide
BrCl
bromine chloride
BrCl3
bromine trichloride
BrCl5
bromine pentachloride
BrF
bromine monofluoride
bromine fluoride
BrF3
bromine trifluoride
BrF5
bromine pentafluoride
BrO3−
bromate ion
Br2
bromine
Br2O5
dibromine pentoxide
CCl2F2
dichlorodifluoromethane
freon-12
CCl4
carbon tetrachloride
tetrachloromethane
C(CN)4
tetracyanomethane
CFCl3
freon-11
CFCl2CF2Cl
freon-13
CHCl3
chloroform
trichloromethane
methyl trichloride
CHClF2
chlorodifluoromethane
CH(CN)3
cyanoform
CHO2−
formate ion
CH2CHCHCH2
1,3-butadiene
CH2CO
ketene
CH2CHOH
ethenol
CH2ClCOOH
chloroacetic acid
121
131
CH2Cl2
dichloromethane
CH2ClF
chlorofluoromethane
CH2(CN)2
malononitrile
CH2O
formaldehyde
CH2(OH)2
methanediol
CH2OHCH2OH
ethylene glycol
CH3CCH
propyne
CH3CdCH3
dimethylcadmium
CH3CHCHCH3
2-butene
CH3CHCH2
propene
CH3CHO
acetaldehyde
CH3CH2Br
bromoethane
CH3CH2CH2CH2OH
butan-1-ol
CH3CH2CH2OH
1-propanol
propan-1-ol
CH3CH2CONH2
propanamide
CH3CH2COOH
propionic acid
CH3CH2OCH2CH3
diethyl ether
ethoxyethane
CH3CH2OH
ethanol
CH3(CH2)16COOH
stearic acid
CH3CN
acetonitrile
CH3COCH3
acetone
CH3COOCH3
methyl acetate
CH3COCl
acetyl chloride
CH3CONH2
acetamide
ethanamide
CH3COO−
acetate ion
CH3COOCHCH2
vinyl acetate
CH3COOCH2C6H5
benzyl acetate
CH3COO(CH2)2CH(CH3)2
isoamyl acetate
CH3COOH
acetic acid
ethanoic acid
CH3COONa
sodium acetate
CH3COOK
potassium acetate
CH3COORb
rubidium acetate
CH3COOCs
caesium acetate
(CH3CO)2O
acetic anhydride
CH3Cl
chloromethane
methyl chloride
CH3HgCH3
dimethylmercury
122
132
CH3I
iodomethane
methyl iodide
CH3OCH3
dimethyl ether
CH3NH2
methylamine
CH3NO
oxaziridine
CH3OCs
caesium methoxide
CH3OH
methanol
CH3OK
potassium methoxide
CH3OLi
lithium methoxide
CH3ONa
sodium methoxide
CH3ORb
rubidium methoxide
CH3SCH3
dimethyl sulfide
DMS
CH3SH
methanethiol
(CH3)2CHOH
isopropyl alcohol
2-propanol
propan-2-ol
isopropanol
(CH3)2CO
acetone
(CH3)2C2O4
dimethyl oxalate
(CH3)2NNH2
dimethyl hydrazine
(CH3)2NH
dimethylamine
(CH3)2S+CH2CH2COO−
dimethylsulfoniopropionate
DMSP
(CH3)3CCl
t-butyl chloride
(CH)3COH
t-butyl alcohol
(CH3)3COOC(CH3)3
di-t-butyl peroxide
DTBP
(CH3)3N
trimethylamine
CH4
methane
natural gas
CH4N2O2
hydroxycarbamide
CH5N3
Guanidine
CN−
cyanide ion
(CN)2
cyanogen
C(NH2)3NO3
guanidine nitrate
CNO−
cyanate ion
CO
carbon monoxide
COCl2
phosgene
CO2
carbon dioxide
CO3
carbon trioxide
123
133
CO32−
carbonate ion
CS2
carbon disulfide
C 2F 4
tetrafluoroethylene
C 2H 2
acetylene
C2H2O2
glyoxal
C2H3Cl
vinyl chloride
C2H3NO
glycolonitrile
C2H3O2−
acetate ion
C 2H 4
ethylene
C2H4Cl2
ethylene dichloride
C2H4N4
3-amino-1,2,4-triazole
C2H4O
ethylene oxide
C2H4O2
acetic acid
C2H5Br
bromoethane
C2H5NH2
ethylamine
C2H5NO2
glycine
Gly
C2H5O−
ethoxide ion
C2H5OH
ethanol
ethyl alcohol
(C2H5)2NH
diethylamine
C2H5OCs
caesium ethoxide
C2H5OK
potassium ethoxide
C2H5ONa
sodium ethoxide
C2H5ORb
rubidium ethoxide
C 2H 6
ethane
C2H6OS
dimethyl sulfoxide
DMSO
C2H7NO
ethanolamine
C2H7NO2
ammonium acetate
C2H7NO3S
taurine
C2O42−
oxalate ion
C3H3O4−
malonate ion
C3HN
cyanopolyyne
C3H3N
azete
C3H4N2
imidazole
C3H4N2S
aminothiazole
C3H4O3
pyruvic acid
C3H4O4
malonic acid
C3H5NO
acrylamide
C3H5N3
3-amino-1H-pyrazole
124
134
C3H5N3O9
nitroglycerine
C 3H 6
cyclopropane
propylene
C3H6O2
ethyl formate
C3H6O2S
2-Mercaptopropionic acid
C3H6O2S
3-Mercaptopropionic acid
C3H7N
azetidine
C3H7NO2
α-alanine
β-alanine
C3H7NO2S
cysteine
Cys
C3H7NO3
serine
Ser
C 3H 8
propane
C3H8NO5P
glyphosate
C3H8O
propanol
1-propanol
2-propanol
C3H8O2
propylene glycol
C3H8O2
1,3-propanediol
C3H8O3
glycerol
C3H9N3
1,3,5-triazinane
C3N3(OH)3
cyanuric acid
C3N12
cyanuric triazide
C4HCl2FN2
2,6-dichloro-5-fluoroacil
C 4H 2
diacetylene
C 4I 2
diiodobutadiyne
C4H2BrClN2
5-bromo-2-chloropyrimidine
C4H2Cl2N2
2,4-dichloropyrimidine
4,6-dichloropyrimidine
C4H3Cl2N3
2-amino-4,6-dichloropyrimidine
C4H3FN2O2
fluorouracil
C 4H 4
vinylacetylene
C4H4FN3O
flucytosine
C4H4N2O2
uracil
C4H4N4
diaminomaleonitrile
C4H4N4
3-aminopyrazole-4-carbonitrile
C4H4N4
1,3,5,7-tetrazocine
C4H4O
furan
C4H5N3O
cytosine
C4H6N2
fomepizole
125
135
C4H6N2
1-methylimidazole
C4H6N2
4-methylimidazole
C4H6N2S
methimazole
2-amino-4-methylthiazole
C4H6N4O
2,4-diamino-6-hydroxypyrimidine
C4H6O2
1,4-Butynediol
C4H6O2
gamma-Butyrolactone
C4H6O2
crotonic acid
C4H6O2
diacetyl
C4H6O2
diepoxybutane
C4H6O2
1,4-Dioxene
C4H6O2
isocrotonic acid
C4H6O2
methacrylic acid
C4H6O2
methyl acrylate
C4H6O2
succinaldehyde
C4H6O2
vinyl acetate
C4H6O4
succinic acid
C4H7BrO2
2-bromobutyric acid
4-bromobutyric acid
α-bromoisobutyric acid
ethyl bromoacetate
C4H7KO3
potassium oxybate
C4H7NaO3
sodium oxybate
C4H7NO2
1-Aminocyclopropanecarboxylic acid
C4H7NO3
aceturic acid
C4H7NO4
aspartic acid
Asp
C 4H 8
cyclobutane
C4H8N2O3
asparagine
Asn
C4H8O
tetrahydrofuran
THF
C4H8O2
ethyl acetate
C4H8O3
gamma-Hydroxybutyric acid
C4H9Li
n-butyllithium
C4H9NO2
γ-aminobutyric acid
C4H9NO3
threonine
Thr
C4H9OH
butyl alcohol
C4H10
butane
2-methylpropane
126
136
C4H10O
diethyl ether
C4H10O2
1,2-Butanediol
C4H10O2
1,3-Butanediol
C4H10O2
1,4-Butanediol
C4H10O2
2,3-Butanediol
C4H10O2
tert-Butyl hydroperoxide
C4H10O2
Dimethoxyethane
C4H10O2
2-Ethoxyethanol
C4H10O2
1-Methoxy-2-propanol
C4H10O3
diethylene glycol
C4H11NO2
diethanolamine
C5H3BrN2O2
2-bromo-5-nitropyridine
C5H3Br2N
3,5-dibromopyridine
C5H3ClN2O2
2-chloro-5-nitropyridine
C5H3ClN4
6-chloropurine
C5H4NCOOH
niacin
C5H4N2O2
pyrazinoic acid
C5H4N2O4
orotic acid
C5H4N4O
allopurinol
hypoxanthine
C5H4N4O2
xanthine
C5H4N4S
mercaptopurine
C5H4O
cyclopentadienone
C5H4O2
furfural
C5H4O2S
b-thiophenic acid
C5H5−
cyclopentadienyl anion
C5H5BrN2
2-amino-5-bromopyridine
C5H5ClN2
2-amino-4-chloropyridine
2-amino-5-chloropyridine
4-amino-2-chloropyridine
C5H5IN2
2-amino-5-iodopyridine
C5H5N
pyridine
C5H5NO
2-pyridone
3-pyridinol
C5H5N3O
pyrazinamide
C5H5N3O2
2-amino-nitropyridine
C5H5N5
adenine
C5H5N5O
guanine
C5H6BNO2
3-pyridinylboronic acid
C5H6N2
1,2-diazepine
127
137
1,3-diazepine
1,4-diazepine
1-vinylimidazole
2-aminopyridine
3-aminopyridine
4-aminopyridine
glutaronitrile
C5H6N2OS
methylthiouracil
C5H6N2O2
thymine
C5H6O
cyclopentenone
C5H6O5
α-Ketoglutaric acid
C5H7N3
3,4-diaminopyridine
C5H8O2
gamma-Valerolactone
C5H9NO2
allylglycine
C5H9NO2
proline
Pro
C5H9NO4
glutamic acid
Glu
C5H10
cyclopentane
C5H10N2O3
glutamine
Gln
C5H10O2
pivalic acid
C5H10O2
valeric acid
C5H10O2
3-Methylbutanoic acid
C5H10O4
deoxyribose
C5H11NO2
valine
Val
C5H11NO2S
methionine
Met
C5H12
pentane
C5H12O2
neopentyl glycol
C5H12O4
pentaerythritol
C5H12O5
xylitol
C6F5COOH
pentafluorobenzoic acid
C6H3Br3O
2,4,6-Tribromophenol
C6H3Cl3O
2,4,6-Trichlorophenol
C6H4BrNO2
5-bromonicotinic acid
C6H4ClNO2
2-chloronicotinic acid
C6H4ClN3
6-chloro-7-dezapurine
C6H4ClNO2
6-chloro-2-pyridinecarboxylic acid
6-chloronicotinic acid
128
138
C6H4N4
tricyanoaminopropene
C6H4O2
orthobenzoquinone
parabenzoquinone
quinone
C6H5Br
bromobenzene
C6H5CHO
benzaldehyde
C6H5CH2OH
benzyl alcohol
C6H5Cl
chlorobenzene
C6H5COCl
benzoyl chloride
C6H5COO−
benzoate ion
C6H5COOH
benzoic acid
C6H5F
fluorobenzene
C6H5I
iodobenzene
C6H5NO2
picolinic acid
C6H5NO3
4-nitrophenol
6-hydroxyniacin
C6H5OH
phenol
C6H5O73−
citrate ion
(C6H5)4Ge
tetraphenylgermane
(C6H5)2O
diphenyl ether
(C6H5)3N
triphenylamine
(C6H5)3P
triphenylphosphine
C 6H 6
benzene
C6H6BClO2
4-chlorophenylboronic acid
C6H6BFO2
4-fluorophenylboronic acid
C6H6IN
4-iodoaniline
C6H6N2O
nicotinamide
C6H6N2O2
6-aminonicotinic acid
C6H6O
phenol
C6H6O2
catechol
hydroquinone
resorcinol
C6H6O3
hydroxymethylfurfural
C6H7BO2
phenylboronic acid
C6H7CsO6
caesium ascorbate
C6H7KO6
potassium ascorbate
C6H7LiO6
lithium ascorbate
C6H7N3O
isoniazid
C6H7NaO6
sodium ascorbate
C6H7RbO6
rubidium ascorbate
C6H8N2
2-amino-3-methylpyridine
129
139
2-amino-4-methylpyridine
2-amino-5-methylpyridine
2-amino-6-methylpyridine
C6H8N2O2S
ethyl 2-aminothiazole-4-carboxylate
sulfanilamide
C6H8O7
citric acid
C6H9N3O2
histidine
His
ethyl 5-amino-1H-pyrazole-4-carboxylate
C6H9N3O3
metronidazole
C6H10O3
4-acetylbutyric acid
butyl glyoxylate
ethyl acetoacetate
2-hydroxypropyl acrylate
pantolactone
propyl pyruvate
C6H10O4
aceburic acid
C6H10O4
adipic acid
C6H10O4
conduritol
C6H10O4
dianhydrohexitol
C6H10O4
ethylidene diacetate
C6H10O4
glucal
C6H11NO2
cycloleucine
pipecolic acid
C6H12
cyclohexane
C6H12O3
4-Hydroxy-4-methylpentanoic acid
C6H12O6
fructose
glucose
C6H13NO
N-ethylmorpholine
C6H13NO2
aminocaproic acid
isoleucine
Ile
leucine
Leu
C6H14
hexane
C6H14N2O2
lysine
Lys
C6H14N4O2
arginine
Arg
C6H14O2
1,6-hexanediol
C6H14O3
dipropylene glycol
130
140
C6H14O3
trimethylolpropane
C6H14O4
triethylene glycol
C6H15NO3
triethanolamine
C 6N 4
tetracyanoethylene
C7H5Br3O
2,4,6-tribromoanisole
C7H5Cl3O
2,4,6-trichloroanisole
C7H5F3O
2,4,6-trifluoroanisole
C7H5FO2
2-fluorobenzoic acid
C7H5FO2
3-Fluorobenzoic acid
C7H5FO2
4-fluorobenzoic acid
C7H5NO4
quinolinic acid
dipicolinic acid
C7H5NS2
2-mercaptobenzothiazole
C7H5N3O2
7-nitroindazole
C7H6N2
7-azaindole
C7H6N2
Benzimidazole
C7H6O
tropone
C7H6O2
benzoic acid
4-hydroxybenzaldehyde
C7H6O3
salicylic acid
4-hydroxybenzoic acid
C7H6O4
protocatechuic acid
2,3-dihydroxybenzoic acid
C7H6O5
gallic acid
C7H7BO4
4-carboxyphenylboronic acid
C7H7NO2
4-aminobenzoic acid
C7H7NO3
mesalazine
C7H7N3
benomyl metabolite
C 7H 8
toluene
C7H8ClN3O4S2
hydrochlorothiazide
C7H8N4O2
theophylline
C7H8N4O2
theobromine
C7H9BO2
4-methylphenylboronic acid
C7H9BO3
4-boronoanisole
C7H10N2
4-dimethylaminopyridine
C7H11NO5
N-Acetylglutamic acid
C7H12O4
diethyl malonate
C7H12N2O4
aceglutamide
C7H14O6
bornesitol
C7H16
heptane
131
141
C8H5F3N2OS
riluzole
C8H5NO2
isatin
C8H6BrN
5-bromoindole
6-bromoindole
C8H6ClN
4-chloroindole
C8H6Cl2O3
2,4-dichlorophenoxyacetic acid
C8H6N2O
4-quinazolinol
C8H6N2O2
indazolium-3-carboxylate
C8H7N
indole
C8H7NO
indol-4-ol
oxindole
5-hydroxyindole
C 8H 8
cubane
C8H8N2OS
2-amino-6-methoxybenzothiazole
C8H8O3
4-hydroxyphenylacetic acid
isovanillin
C8H8O4
vanillic acid
C8H9NO2
acetaminophen
C8H9NO2
aminomethylbenzoic acid
C8H9NO2
hydroxydanaidal
C8H9NO2
methyl anthranilate
C8H10N4O2
caffeine
C8H11NO
tyramine
C8H11N5O3
aciclovir
C8H16O2
cyclohexanedimethanol
C8H16O6
pinpollitol
C8H16O6
viscumitol
C8H16O6
Eleutheroside C
ethyl galactoside
C8H18
octane
C9H6BrN
4-bromoisoquinoline
C9H6N2
5-cyanoindole
C9H6O3
umbelliferone
C9H6OS
thiochromone
C9H7NO
8-hydroxyquinoline
indole-3-carboxaldehyde
C9H7NO2
indole-2-carboxylic acid
indole-3-carboxylic acid
C9H8N2
5-aminoisoquinoline
5-aminoquinoline
6-aminoquinoline
132
142
8-aminoquinoline
C9H8O2
cinnamic acid
C9H8O3
o-coumaric acid
m-coumaric acid
p-coumaric acid
C9H8O4
aspirin
acetylsalicylic acid
caffeic acid
C9H9N
methylketol
skatole
C9H9NO
4-methoxyindole
5-methoxyindole
6-methoxyindole
indole-3-carbinol
C9H9NO3
hippuric acid
C9H10O
chavicol
C9H10O3
paeonol
C9H11NO2
phenylanine
LPA
phenylanine
DLPA
C9H10O
cinnamyl alcohol
C9H11NO3
tyrosine
Tyr
C9H11NO4
L-DOPA
C9H17NO2
gabapentin
C9H18N2O2
1-boc-piperazine
C9H20
nonane
C10H7NO2
quinaldic acid
C10H7N3S
tiabendazole
C10H8
azulene
C10H8
naphthalene
C10H8O3
hymecromone
C10H9NO2
indole-3-acetic acid
C10H9N5O
kinetin
C10H9NO2
5-methoxyindole-3-carboxaldehyde
C10H10N2O
edaravone
C10H10O2
safrole
C10H10O4
ferulic acid
C10H11N3O3S
sulfamethoxazole
C10H12N2
tryptamine
133
143
C10H12O
anethole
C10H12O
estragole
C10H12O2
hinokitiol
C10H12O2
eugenol
C10H12O2
isoeugenol
C10H12O2
pseudoisoeugenol
C10H12O3
coniferyl alcohol
C10H13N5O4
adenosine
C10H14O
mentha spicata herb oil
C10H15ON
ephedrine
C10H16
limonene
C10H16O
camphor
C10H17NO3
boc-4-piperidone
C10H19NO3
1-boc-4-piperidinol
C10H20N2O2
boc-4-aminopiperidine
C10H22
decane
C11H8O2
menadione
C11H11NO2
3-indolepropionic acid
C11H12N2O2
tryptophan
Trp
C11H12O3
myristicin
C11H14N2O
5-methoxytryptamine
C11H14O2
methyl eugenol
C11H14O2
methyl isoeugenol
C11H19NO4
boc-isonipecotic acid
C11H24
undecane
C12H4N4
tetracyanoquinodimethane
C12H8O4
methoxsalen
C12H10
biphenyl
C12H10ClN2O5S
furosemide
C12H11N5
6-benzylaminopurine
C12H11N7
triamterene
C12H13NO2
indole-3-butyric acid
(C12H14CaO12)n
calcium alginate
C12H14O4
apiole
C12H14O4
dillapiole
C12H15NO
1-benzyl-4-piperidone
C12H16N2
N,N-Dimethyltryptamine
C12H16O3
asarone
C12H16O3
elemicin
C12H16O3
isoelemicin
134
144
C12H16O3
oudenone
C12H16O4
2,4,5-Trimethoxypropiophenone
C12H16O7
arbutin
C12H18O
propofol
C12H22O11
maltose
sucrose
C12H26
dodecane
C13H10O
benzophenone
C13H12F2N6O
fluconazole
C13H12O
β-ionone
C13H12O2
monobenzone
C13H14N2O
harmaline
C13H16N2O2
melatonin
C13H18O2
ibuprofen
C13H28
tridecane
C14H10
anthracene
C14H10
phenanthrene
C14H10O14
benzoyl peroxide
C14H12O3
resveratrol
C14H14Cl2N2O
enilconazole
C14H18N2O5
aspartame
C14H18N4O3
trimethoprim
C14H30
tetradecane
C15H10O4
daidzein
C15H10O5
apigenin
emodin
genistein
C15H10O6
luteolin
C15H10O7
quercetin
C15H12N2O
carbamazepine
C15H12N2O2
phenytoin
C15H32
pentadecane
C16H14O3
ketoprofen
C16H28N2O6Zn
zinc acexamate
C16H34
hexadecane
C17H13ClN4
alprazolam
C17H14F3N3O2S
celecoxib
C17H18N2O6
nifedipine
C17H19N3O3S
omeprazole
C17H21NO4
cocaine
135
145
C17H22O2
cicutoxin
C17H22O2
oenanthotoxin
C17H24O
falcarinol
C17H24O9
Eleutheroside B
syringin
C17H36
heptadecane
C18H22O2
estrone
C18H24O2
estradiol
C18H24O3
estriol
C18H24O4
estetrol
C18H27NO3
capsaicin
C18H32O2
linoleic acid
C18H36O2
stearic acid
C18H38
octadecane
C19H16ClNO4
indometacin
C19H26O2
androstenedione
C19H28O2
dehydroepiandrosterone
C19H28O2
testosterone
C19H30O2
androstenediol
C19H30O2
dihydrotestosterone
C19H40
nonadecane
C20H24O2N2
quinine
C20H27NO11
amygdalin
C20H28O2
tretinoin
C20H32O5
prostacyclin
C20H32O5
prostaglandin E2
C20H34O5
dinoprost
C20H42
eicosane
C21H20O6
curcumin
C21H30O2
progesterone
C21H36N7O16P3S
Coenzyme A
C21H30O2
tetrahydrocannabinol
C22H23ClN2O2
loratadine
C23H19ClF3NO3
cyhalothrin
C30H19NO9
Dynemicin A
C34H46O18
Eleutheroside D
C35H60O6
Eleutheroside A
C40H56
lycopene
C44H69N15O9S
adrenorphin
C55H74IN3O21S4
calicheamicin
C59H80N4O22S4
esperamicin
136
146
C62H89CoN13O15P
hydroxocobalamin
C63H88CoN14O14P
Vitamin B12
C63H88CoN14O14P
cyanocobalamin
C63H91CoN13O14P
methylcobalamin
C72H100CoN18O17P
adenosylcobalamin
C77H120N18O26S
alpha-Endorphin
C83H131N19O27S
gamma-Endorphin
C131H200N30O43S2
amidorphin
C158H251N39O46S
beta-Endorphin
C161H236N42O48
leumorphin
C164H256Na2O68S2
maitotoxin
CaAl2O4
calcium aluminate
CaB6
calcium boride
CaBr2
calcium bromide
Ca(BrO)2
calcium hypobromite
Ca(BrO2)2
calcium bromite
Ca(BrO3)2
calcium bromate
Ca(BrO4)2
calcium perbromate
Ca(CN)2
calcium cyanide
CaCO3
calcium carbonate
spent lime
calcite
limestone
marble
CaC2
calcium carbide
Ca(CHO2)2
calcium formate
Ca(C2H3O2)2
calcium acetate
CaC2O4
calcium oxalate
CaCN2
calcium cyanamide
CaCl2
calcium chloride
Ca(ClO)2
calcium hypochlorite
Ca(ClO2)2
calcium chlorite
Ca(ClO3)2
calcium chlorate
Ca(ClO4)2
calcium perchlorate
CaF2
calcium fluoride
fluorite
CaH2
calcium hydride
CaHPO4
dicalcium phosphate
Ca(H2PO2)2
calcium hypophosphite
Ca(HS)2
calcium hydrosulfide
CaI2
calcium iodide
137
147
Ca(IO)2
calcium hypoiodite
Ca(IO2)2
calcium iodite
Ca(IO3)2
calcium iodate
Ca(IO4)2
calcium periodate
CaMoO4
calcium molybdate
Ca(NO2)2
calcium nitrite
Ca(NO3)2
calcium nitrate
Ca(NO3)2 · 4H2O
Calcium nitrate tetrahydrate
Ca(NbO3)2
calcium metaniobate
CaO
quicklime
calcium oxide
burnt lime
Ca(OH)2
calcium hydroxide
slaked lime
CaO2
calcium peroxide
CaP
calcium monophosphide
CaS
calcium sulfide
hepar calcies
sulfurated lime
oldhamite
CaSO3
calcium sulfite
CaSO4
calcium sulfate
CaSO4 · 0.5H2O
plaster of paris
calcium sulfate hemihydrate
CaSe
calcium selenide
CaSeO3
calcium selenite
CaSeO4
calcium selenate
CaSiO3
calcium metasilicate
wollastonite
CaTe
calcium telluride
CaTeO3
calcium tellurite
CaTeO4
calcium tellurate
CaTiO3
calcium titanate
Ca(VO3)2
calcium metavanadate
Ca(VO4)2
calcium orthovanadate
CaWO4
calcium tungstate
Ca3(AsO4)2
calcium arsenate
Ca3N2
calcium nitride
Ca3P2
calcium phosphide
Ca3(PO4)2
tricalcium phosphate
Ca4(PO4)2O
tetracalcium phosphate
138
148
Ca5(PO4)3F
calcium fluorophosphate
Ca5(PO4)3(OH)
hydroxyapatite
CdBr2
cadmium bromide
Cd(CN)2
cadmium cyanide
CdCO3
cadmium carbonate
Cd(C2H3O2)2
cadmium acetate
CdC2O4
cadmium oxalate
CdCl2
cadmium chloride
CdCrO4
cadmium chromate
CdF2
cadmium fluoride
CdI2
cadmium iodide
Cd(IO3)2
cadmium iodate
CdMoO4
cadmium molybdate
Cd(NO3)2
cadmium nitrate
Cd(N3)2
cadmium azide
CdO
cadmium oxide
Cd(OH)2
cadmium hydroxide
CdS
cadmium sulfide
greenockite
CdSO3
cadmium sulfite
CdSO4
cadmium sulfate
CdSb
cadmium antimonide
CdSe
cadmium selenide
cadmoselite
CdSeO3
cadmium selenite
CdSiO3
cadmium metasilicate
Cd(TaO3)2
cadmium metatantalate
CdTe
cadmium telluride
CdTeO4
cadmium tellurate
CdTiO3
cadmium titanate
CdWO4
cadmium tungstate
CdZrO3
cadmium metazirconate
Cd2Nb2O7
cadmium niobate
Cd3As2
cadmium arsenide
Cd3P2
cadmium phosphide
Cd3(PO4)2
cadmium phosphate
CeB6
cerium boride
CeBr3
cerium(III) bromide
CeC
cerium carbide
CeCl3
cerium(III) chloride
CeF3
cerium(III) fluoride
139
149
CeF4
cerium(IV) fluoride
CeI2
cerium(II) iodide
CeI3
cerium(III) iodide
CeN
cerium nitride
CeO2
cerium(IV) oxide
cerianite
CeS
cerium(II) sulfide
Ce(SO4)2
cerium(IV) sulfate
CeSi2
cerium silicide
Ce2C3
cerium(III) carbide
Ce2O3
cerium(III) oxide
Ce2S3
cerium(III) sulfide
CF3Cl
chlorotrifluoromethane
CF4
tetrafluoromethane
ClF
chlorine fluoride
ClF3
chlorine trifluoride
ClF5
chlorine pentafluoride
ClOClO3
chlorine perchlorate
ClO2
chlorine dioxide
ClO3F
chlorine trioxide fluoride
Cl2
chlorine
Cl2O3
chlorine trioxide
Cl2O6
chlorine hexoxide
Cl2O7
chlorine heptoxide
Cl2O8
Chlorine octaoxide
CoAl2O4
cobalt(II) aluminate
CoAs
cobalt arsenide
CoAs2
cobalt(II) arsenide
CoB
cobalt(II) boride
CoBr2
cobalt(II) bromide
Co(CN)2
cobalt(II) cyanide
Co(C2H3O2)2
cobalt(II) acetate
Co(C2H3O2)3
cobalt(III) acetate
CoC2O4
cobalt(II) oxalate
Co(ClO4)2
cobalt(II) perchlorate
CoCl2
cobalt(II) chloride
CoCrO4
cobalt(II) chromate
CoCr2O4
cobalt(II) chromite
CoF2
cobalt(II) fluoride
CoF3
cobalt(III) fluoride
Co(IO3)2
cobalt(II) iodate
140
150
CoI2
cobalt(II) iodide
CoMoO4
cobalt(II) molybdate
Co(NO3)2
cobalt(II) nitrate
Co(NO3)3
cobalt(III) nitrate
CoO
cobalt(II) oxide
Co(OH)2
cobalt(II) hydroxide
Co(OH)3
cobalt(III) hydroxide
CoS
cobalt(II) sulfide
CoS2
cobalt disulfide
CoSb
cobalt antimonide
CoSe
cobalt(II) selenide
CoSeO3
cobalt(II) selenite
CoTe
cobalt(II) telluride
CoTiO3
cobalt(II) titanate
CoWO4
cobalt(II) tungstate
Co2B
cobalt boride
Co2SO4
cobalt(II) sulfate
Co2S3
cobalt(III) sulfide
Co2SiO4
cobalt(II) orthosilicate
Co2SnO4
cobalt(II) stannate
Co2TiO4
cobalt(II) titanite
Co3(AsO4)2
cobalt arsenate
Co3(Fe(CN)6)2
cobalt(II) ferricyanide
CrBr2
chromium(II) bromide
CrBr3
chromium(III) bromide
CrCl2
chromium(II) chloride
CrCl3
chromium(III) chloride
CrCl4
chromium(IV) chloride
CrF2
chromium(II) fluoride
CrF3
chromium(III) fluoride
CrF4
chromium(IV) fluoride
CrF5
chromium(V) fluoride
CrF6
chromium(VI) fluoride
CrI2
chromium(II) iodide
CrI3
chromium(III) iodide
Cr(NO3)3
chromium(III) nitrate
Cr(NO2)3
chromium(III) nitrite
Cr(OH)3
chromium(III) hydroxide
CrO2
chromium(IV) oxide
CrO3
chromium(VI) oxide
141
151
CrO42−
chromate ion
CrO2Cl2
chromium(VI) oxychloride
CrPO4
chromium(III) phosphate
CrSb
chromium antimonide
CrSe
chromium(II) selenide
CrSi2
chromium(II) silicide
CrVO4
chromium(III) orthovanadate
Cr2O3
chromium(III) oxide
eskolaite
Cr2(SO4)3
chromium(III) sulfate
Cr2S3
chromium(III) sulfide
Cr2Se3
chromium(III) selenide
Cr2(TeO4)3
chromium(III) tellurate
Cr2Te3
chromium(III) telluride
Cr3As2
chromium(II) arsenide
Cr3C2
chromium(II) carbide
Cr3Sb2
chromium(II) antimonide
CsBO2
caesium borate
CsBr
caesium bromide
CsBrO
caesium hypobromite
CsBrO2
caesium bromite
CsBrO3
caesium bromate
CsBrO4
caesium perbromate
CsBr3
caesium tribromide
CsCN
caesium cyanide
CsCNO
caesium cyanate
CsCNO
caesium fulminate
CsC2H3O2
caesium acetate
CsCl
caesium chloride
CsClO
caesium hypochlorite
CsClO2
caesium chlorite
CsClO3
caesium chlorate
CsClO4
caesium perchlorate
CsF
caesium fluoride
CsH
caesium hydride
CsHS
caesium hydrosulfide
CsI
caesium iodide
CsIO
caesium hypoiodite
CsIO2
caesium iodite
CsIO3
caesium iodate
CsIO4
caesium periodate
142
152
CsI3
caesium triiodide
CsNH2
caesium amide
CsNO2
caesium nitrite
CsNO3
caesium nitrate
CsN3
caesium azide
CsNbO3
caesium niobate
Cs2NbO3
caesium metaniobate
CsOH
caesium hydroxide
CsO2
caesium superoxide
Cs2O2
caesium peroxide
Cs2S
caesium sulfide
CsSCN
caesium thiocyanate
CsSeO4
caesium selenate
CsTaO3
caesium metatantalate
Cs2CO3
caesium carbonate
CsHCO3
caesium bicarbonate
CsH2PO3
monocaesium phosphite
CsH2PO4
monocaesium phosphate
CsHSO3
caesium bisulfite
CsHSO4
caesium hydrogen sulfate
Cs2C2O4
caesium oxalate
Cs2CrO4
caesium chromate
Cs2Cr2O7
caesium dichromate
Cs2HPO4
caesium hydrogen orthophosphate
Cs2MoO4
caesium molybdate
Cs2O
caesium oxide
Cs2SO3
caesium sulfite
Cs2SO4
caesium sulfate
Cs2SiO3
caesium metasilicate
Cs2TeO4
caesium tellurate
Cs2TiO3
caesium titanate
caesium metatitanate
Cs2WO4
caesium orthotungstate
Cs2HPO3
dicaesium phosphite
Cs2HPO4
dicaesium phosphate
Cs3PO3
tricaesium phosphite
Cs3PO4
caesium orthophosphate
Cs3VO4
caesium orthovanadate
CuBr
copper(I) bromide
Cu(BrO3)2 · 6H2O
copper(II) bromate hexahydrate
CuBr2
copper(II) bromide
143
153
CuC2O4
copper oxalate
Cu(CH3COO)
copper(I) acetate
Cu(CH3COO)2
copper(II) acetate
CuCl
copper(I) chloride
Cu(ClO3)2 · 6H2O
copper(II) chlorate hexahydrate
CuCl2
copper(II) chloride
CuF
copper(I) fluoride
CuF2
copper(II) fluoride
CuFeS2
copper iron sulfide
chalcopyrite
CuFe2O4
copper(II) iron(II) oxide
CuFe2S3
copper iron sulfide
cubanite
[Cu(H2O)4]SO4 · H2O
blue vitriol
CuI
copper(I) iodide
CuIO3
copper(I) iodate
Cu(IO3)2
copper(II) iodate
CuMoO4
copper(II) orthomolybdate
Cu(NO3)2
copper(II) nitrate
Cu(NO3)2 · 3H2O
copper(II) nitrate trihydrate
Cu(NO3)2 · 6H2O
copper(II) nitrate hexahydrate
Cu(NbO3)2
copper(II) orthoniobate
CuO
copper(II) oxide
Cu2O
copper(I) oxide
Cu(OH)2
copper(II) hydroxide
Cu2(OH)2CO3
basic copper carbonate
CuS
copper(II) sulfide
covellite
CuSCN
copper(I) thiocyanate
CuSO4
copper(II) sulfate
CuSO4 · 5H2O
copper(II) sulfate pentahydrate
CuSe
copper(II) selenide
CuSeO3 · 2H2O
copper(II) selenite dihydrate
CuSeO4 · 5H2O
copper(II) selenate pentahydrate
CuSiO3
copper(II) metasilicate
CuTe
copper(II) telluride
CuTeO3
copper(II) tellurite
CuTiO3
copper(II) metatitanate
Cu(VO3)2
copper(II) metavanadate
CuWO4
copper(II) orthotungstate
Cu2CO3(OH)2
malachite
144
154
Cu2S
copper(I) sulfide
chalcocite
Cu2Se
copper(I) selenide
Cu2Te
copper(I) telluride
Cu3As
copper(I) arsenide
Cu3P
copper(I) phosphide
Cu3(PO4)2
copper(II) phosphate
Cu3Sb
copper(III) antimonide
Cu9S5
copper sulfide
digenite
DBr
deuterium bromide
DI
deuterium iodide
DLi
lithium deuteride
DNa
sodium deuteride
D 2O
deuterium oxide
heavy water
D 3O +
trideuterium oxide cation
DyBr3
dysprosium(III) bromide
DyCl2
dysprosium(II) chloride
DyCl3
dysprosium(III) chloride
DySi2
dysprosium(II) silicide
Dy2O3
dysprosium(III) oxide
Dy2S3
dysprosium(III) sulfide
ErCl3
erbium(III) chloride
ErF
erbium monofluoride
ErF2
erbium difluoride
ErF3
erbium trifluoride
ErI3
erbium triiodide
ErI4Na
erbium sodium tetraiodide
ErO
erbium monoxide
EuCl2
europium(II) chloride
EuCl3
europium(III) chloride
EuF
europium monofluoride
EuF3
europium trifluoride
EuI2
europium diiodide
EuNbO2
europium niobium dioxide
EuNb2O6
europium diniobium hexaoxide
EuO
europium monoxide
EuO2V
monoeuropium monovandium dioxide
EuO3Ti
europium titanium trioxide
EuO3V
europium metavanadate
145
155
EuO4W
europium tungsten tetraoxide
EuS
europium monosulfide
EuSO4
europium(II) sulfate
EuS2
europium disulfide
Eu2O
dieuropium monoxide
Eu2O2
dieuropium dioxide
Eu2O3
europium(III) oxide
Eu2S
dieuropium monosulfide
Eu2S2
dieuropium disulfide
Eu2(SO4)3
europium(III) sulfate
FGa
gallium monofluoride
FGaO
gallium monofluoride monoxide
FGd
gadolinium monofluoride
FGe
germanium monofluoride
FHo
holmium monofluoride
FI
iodine monofluoride
FI2
monofluorodiiodine
FIn
indium monofluoride
FLa
lanthanum monofluoride
FLi
lithium fluoride
FLiO
lithium hypofluorite
FLi2
dilithium monofluoride
FMg
magnesium monofluoride
FMn
monomanganese monofluoride
FMnO3
manganese fluoride trioxide
FMo
molybdenum monofluoride
FN
fluoroimidogen
FNO
nitrosyl fluoride
FNO2
nitryl fluoride
FNO3
fluorine nitrate
FNS
thiazyl fluoride
FNa
sodium fluoride
FNa2
disodium monofluoride
FNd
neodymium monofluoride
FO
oxygen monofluoride
FOTh
thorium monofluoride monoxide
FOTi
titanium fluoride oxide
FO2
dioxygen monofluoride
FO3S
fluorosulfate radical
FP
phosphorus monofluoride
146
156
FPS
phosphenothious fluoride
FPS2
phosphenodithioic fluoride
FPb
lead monofluoride
FPu
plutonium monofluoride
FRb
rubidium fluoride
FS
monosulfur monofluoride
FSc
scandium monofluoride
FSm
samarium monofluoride
FSn
tin monofluoride
FSr
strontium monofluoride
FTh
thorium monofluoride
FTi
titanium fluoride
FTl
thallium monofluoride
FW
tungsten monofluoride
FXe
xenon monofluoride
FY
yttrium monofluoride
FZr
zirconium fluoride
F2
fluorine
F2Fe
ferrous fluoride
F2Ga
gallium difluoride
F2Gd
gadolinium difluoride
F2Ge
germanium difluoride
F2GeO
difluorogermanone
F2Hg
mercury fluoride
F2Hg2
mercury fluoride
F2Ho
holmium difluoride
F2IP
difluoroiodophosphine
F 2K 2
dipotassium difluoride
F2Kr
krypton difluoride
F2La
lanthanum difluoride
F2Li2
lithium fluoride
F2Mg
magnesium fluoride
F2Mn
manganese difluoride
F2Mo
molybdenum difluoride
F2MoO2
molybdenum difluoride dioxide
F 2N
difluoroamino radical
F2N2O
nitrosodifluoroamine
F2Na2
disodium difluoride
F2Nd
neodymium difluoride
F2Ni
nickel difluoride
147
157
F 2O
oxygen difluoride
F2OS
thionyl fluoride
F2OSi
difluorooxosilane
F2OTi
titanium fluoride oxide
F 2O 2
perfluoroperoxide
F2O2S
sulfuryl fluoride
F2O2W
tungsten difluoride dioxide
F2O5S3
peroxydisulfuryl difluoride
F 2P
phosphorus difluoride
F2Pb
lead difluoride
F2Pt
platinum difluoride
F2Pu
plutonium difluoride
F 2S
sulfur difluoride
F2SW
tungsten difluoride monosulfide
F 2S 2
difluorodisulfane
F 2S 2
thiothionyl fluoride
F 2S 2
thiothionyl fluoride
F2S2W
tungsten difluoride disulfide
F2Sc
scandium difluoride
F2Se
selenium difluoride
F2Si
difluorosilylene
F2Sn
tin difluoride
F2Sr
strontium fluoride
F2Th
thorium difluoride
F2Ti
titanium difluoride
F2Tl2
dithallium difluoride
F 2W
tungsten difluoride
F2Xe
xenon difluoride
F 2Y
yttrium difluoride
F2Zn
zinc difluoride
F2Zr
zirconium fluoride
F3Fe
iron trifluoride
F3Ga
gallium trifluoride
F3Gd
gadolinium trifluoride
F3Ho
holmium trifluoride
F3La
lanthanum trifluoride
F3Li3
trilithium trifluoride
F3Lu
lutetium trifluoride
F3Mn
manganese trifluoride
F3Mo
molybdenum trifluoride
148
158
F3MoO
molybdenum trifluoride oxide
F3MoS
molybdenum trifluoride sulfide
F 3N
nitrogen trifluoride
F3NO
nitrogen trifluoride oxide
F3NO2S
difluoroaminosulfonyl fluoride
F3NO3S
difluoraminooxysulfonyl fluoride
F3NS
thiazyl trifluoride
F3NaSn
sodium trifluorostannate
F3Nd
neodymium trifluoride
F3OP
phosphoryl fluoride
F3OTa
tantalum monoxide trifluoride
F3OV
vanadium trifluoride oxide
F 3P
phosphorus trifluoride
F3PS
thiophosphoryl fluoride
F3Pr
praseodymium trifluoride
F3Pu
plutonium trifluoride
F3Rh
rhodium fluoride
F 3S
sulfur trifluoride
F3SW
tungsten trifluoride monosulfide
F3Sb
antimony trifluoride
F3Sc
scandium fluoride
F3Si
trifluorosilyl radical
F3Sm
samarium trifluoride
F3Tb
terbium trifluoride
F3Th
thorium trifluoride
F3Ti
titanium trifluoride
F3Tl
thallium trifluoride
F3Tm
thulium trifluoride
F 3W
tungsten trifluoride
F 3Y
yttrium trifluoride
F3Yb
ytterbium trifluoride
F3Zr
zirconium trifluoride
F4Ge
germanium tetrafluoride
F4Ge2
digermanium tetrafluoride
F4Hf
hafnium fluoride
F4Mg2
dimagnesium tetrafluoride
F4Mg2
magnesium fluoride
F4Mo
molybdenum tetrafluoride
F4MoO
molybdenum tetrafluoride oxide
F4MoS
molybdenum tetrafluoride monosulfide
149
159
F 4N 2
tetrafluorohydrazine
F4Na2Sn
disodium tetrafluorostannate
F4OOs
osmium oxide tetrafluoride
F4OP2
diphosphorus tetrafluoride oxide
F4ORe
rhenium tetrafluoride oxide
F4OS
sulfur tetrafluoride oxide
F4OW
tungsten tetrafluoride oxide
F4OXe
xenon tetrafluoride oxide
F 4P 2
diphosphorus tetrafluoride
F4Pb
lead tetrafluoride
F4Pt
platinum tetrafluoride
F4Pu
plutonium tetrafluoride
F 4S
sulfur tetrafluoride
F4SW
tungsten tetrafluoride monosulfide
F4Se
selenium tetrafluoride
F4Si
silicon tetrafluoride
F4Sn2
ditin tetrafluoride
F4Ti
titanium fluoride
F 4U
uranium tetrafluoride
F 4W
tungsten tetrafluoride
F4Xe
xenon tetrafluoride
F4Zr
zirconium tetrafluoride
F 5I
iodine pentafluoride
F5Mo
molybdenum pentafluoride
F5ORe
rhenium monoxide pentafluoride
F 5P
phosphorus pentafluoride
F5Pu
plutonium pentafluoride
F 5S
disulfur decafluoride
F5Sb
antimony pentafluoride
F5Ta
tantalum pentafluoride
F 5U
uranium pentafluoride
F 5W
tungsten pentafluoride
F6Fe2
diiron hexafluoride
F6La2
lanthanum trifluoride dimer
F6Mo
molybdenum hexafluoride
F6NP3
nitridotriphosphorous hexafluoride
F6Os
osmium hexafluoride
F6Pu
plutonium hexafluoride
F6Re
rhenium hexafluoride
F 6S
sulfur hexafluoride
150
160
F6Se
selenium hexafluoride
F6Si2
hexafluorodisilane
F6Sn3
tritin hexafluoride
F6Te
tellurium hexafluoride
F 6U
uranium hexafluoride
F 6W
tungsten hexafluoride
F6Xe
xenon hexafluoride
F 7I
iodine fluoride
F7NS
pentafluorosulfanyldifluoroamine
F7Re
rhenium heptafluoride
F8Si3
octafluorotrisilane
F10Mo2
molybdenum fluoride
F10S2
sulfur fluoride
F15Mo3
molybdenum fluoride
FeAsS
iron arsenic sulfide
arsenopyrite
FeBr2
iron(II) bromide
FeBr3
iron(III) bromide
FeBr3 · 6H2O
iron(III) bromide hexahydrate
FeCO3
siderite
FeC2O4
iron oxalate
FeC5O5
iron pentacarbonyl
pentacarbonyl iron
FeC10H10
ferrocene
FeCl2
iron(II) chloride
FeCl3
iron(III) chloride
FeCr2O4
chromite (ore)
FeF2
iron fluoride
FeF2 · 4H2O
iron(II) fluoride tetrahydrate
FeI
iron monoiodide
FeI2
iron diiodide
iron(II) iodide
FeI2 · 4H2O
iron(II) iodide tetrahydrate
FeI3
iron(III) iodide
FeMoO4
iron(II) orthomolybdate
FeO
iron monoxide
iron(II) oxide
wüstite
FeO2
iron dioxide
FeO2H
goethite
FeO2H · nH2O
limonite
151
161
Fe(OH)2
iron(II) hydroxide
Fe(OH)3
iron(III) hydroxide
Fe(SCN)3
iron(III) Thiocyanate
FeO4S
ferrous sulfate
FeO4Se
iron(II) selenate
ferrous selenate
FeO8H4P2
iron(II) dihydrogen phosphate
FeP
iron(III) phosphide
FePO4
iron(III) phosphate
FeS
iron sulfide
iron(II) sulfide
FeS2
pyrite
fool's gold
iron(IV) sulfide
marcasite
FeSe
iron(II) selenide
FeTe
iron(II) telluride
FeTiO3
iron(II) metatitanate
ilmenite
FeVO4
iron(III) orthovanadate
FeWO4
iron(II) orthotungstate
FeZrO3
iron(II) metazirconate
Fe2I2
diiron diiodide
Fe2I4
diiron tetraiodide
Fe2O3
iron oxide
iron(III) oxide
hematite
Fe2O3
venetian red
Fe2O12S3
ferric sulfate
iron(III) sulfate
Fe2O12W3
iron(III) orthotungstate
Fe2P
diiron phosphide
Fe2SiO4
fayalite
Fe3H2Na2O45Si
chrysotile
white asbestos
Fe3O4
iron(II,III) oxide
magnetite
triiron(II, III) tetraoxide
Fe3P
iron(tri) phosphide
Fe4(P2O7)3
iron(III) pyrophosphate
Fe7Si8O24H2
amosite
152
162
brown asbestos
grunerite
GaAs
gallium(III) arsenide
GaAsO4
gallium(III) orthoarsenate
GaBr3
gallium(III) bromide
Ga(C2H3O2)3
gallium(III) acetate
GaCl2
gallium(II) chloride
GaCl3</
gallium trichloride
Ga(ClO4)3
gallium(III) perchlorate
GaI2
gallium(II) iodide
GaI3
gallium(III) iodide
GaN
gallium(III) nitride
Ga(OH)3
gallium(III) hydroxide
GaPO4
gallium(III) orthophosphate
GaSb
gallium(III) antimonide
GaTe
gallium(II) telluride
Ga2O3
gallium(III) oxide
Ga2(SO4)3·18H2O
gallium(III) sulfate octadecahydrate
Ga2S3
gallium(III) sulfide
Ga2Te3
gallium(III) telluride
GeBr4
germanium(IV) bromide
GeH3COOH
2-germaacetic acid
GeI2
germanium(II) iodide
GeI4
germanium(IV) iodide
GeO
germanium(II) oxide
HArF
argon fluorohydride
HAt
hydrogen astatide
HBr
hydrogen bromide
hydrobromic acid
HBrO
hypobromous acid
HBrO2
bromous acid
HBrO3
bromic acid
HBrO4
perbromic acid
HCCH
acetylene
ethyne
HCN
hydrocyanic acid
hydrogen cyanide
HCNO
fulminic acid
HCONH2
formamide
methanamide
HCOO−
formate ion
153
163
HCOOH
formic acid
methanoic acid
HCOONH4
ammonium formate
HCO3−
hydrogen carbonate ion
HC3H5O3
lactic acid
HC5H5N+
pyridinium ion
HC6H7O6
ascorbic acid
HC9H7O4
acetylsalicylic acid
HC12H17ON4SCl2
thiamine hydrochloride
vitamin B1 hydrochloride
HCl
hydrochloric acid
hydrogen chloride
HClO
hypochlorous acid
HClO2
chlorous acid
HClO3
chloric acid
HClO4
perchloric acid
HDO
semiheavy water
water-d1
HF
hydrofluoric acid
HI
hydroiodic acid
HIO
hypoiodous acid
HIO2
iodous acid
HIO3
iodic acid
HIO4
periodic acid
HNCO
isocyanic acid
HNO
nitroxyl
HNO2
nitrous acid
HNO3
nitric acid
hydrogen nitrate
HN3
hydrazoic acid
HOBr
hypobromous acid
HOCl
hypochlorous acid
HOF
hypofluorous acid
HOOCCOOH
oxalic acid
HPO42−
hydrogen phosphate ion
HSO3−
hydrogen sulfite ion
HSO4−
hydrogen sulfate
HTO
partially tritiated water
water-t
H2
hydrogen
H2C(CH)CN
acrylonitrile
154
164
H2CO
formaldehyde
H2CO3
carbonic acid
H2CSO
sulfine
H2C2O4
oxalic acid
H2C4H4O6
tartaric acid
H2C8H4O4
phthalic acid
H2Ph
H2CrO4
chromic acid
H2NCH2COOH
glycine
H2N2O2
hyponitrous acid
H2NNH2
hydrazine
H 2O
water
H 2O 2
hydrogen peroxide
H2PO4−
dihydrogen phosphate ion
H 2S
hydrogen sulfide
hydrosulfuric acid
H2SO3
sulfurous acid
H2SO4
sulfuric acid
hydrogen sulfate
H2S2O2
thiosulfurous acid
H2S2O3
thiosulfuric acid
H2S2O4
dithionous acid
H2S2O5
disulfurous acid
H2S2O6
dithionic acid
H2S2O7
disulfuric acid
H2S2O8
peroxydisulfuric acid
H2SeO3
selenous acid
H2SeO4
selenic acid
H2SiO3
silicic acid
H2TeO3
tellurous acid
H2TiO3
titanic acid
H3AsO4
arsenic acid
H3CCH2CH3
propane
H3N+CH2COO−
zwitterion
H 3O +
hydronium ion
H3PO2
hypophosphorous acid
H3PO3
phosphorous acid
H3PO4
phosphoric acid
H4XeO6
perxenic acid
H6TeO6
telluric acid
HfBr4
hafnium(IV) bromide
155
165
HfF4
hafnium(IV) fluoride
HfOCl2 · 8H2O
hafnium(IV) oxychloride octahydrate
HfOH(C2H3O2)3
hafnium(IV) acetate, basic
Hf(SO4)2
hafnium(IV) sulfate
Hg(BrO3)2 · 2H2O
mercury(II) bromate dihydrate
Hg2Br2
mercury(I) bromide
HgBr2
mercury(II) bromide
Hg(C2H3O2)2
mercury(II) acetate
Hg(C7H5O2)2 · H2O
mercury(II) benzoate monohydrate
HgClO4 · 4H2O
mercury(I) perchlorate tetrahydrate
Hg(ClO4)2 · 3H2O
mercury(II) perchlorate trihydrate
HgCl2
mercury(II) chloride
Hg(IO3)2
mercury(II) iodate
HgI2
mercury(II) iodide
Hg(NO3)2 · H2O
mercury(II) nitrate monohydrate
Hg(CNO)2
mercury(II) fulminate
HgO
mercury(II) oxide
Hg(OH)2
mercury(II) hydroxide
HgS
mercury(II) sulfide
cinnabar
Hg(SCN)2
mercury(II) thiocyanate
HgSe
mercury(II) selenide
HgSeO3
mercury(II) selenite
HgTe
mercury(II) telluride
HgTeO3
mercury(II) tellurite
HgWO4
mercury(II) tungstate
Hg2Br2
mercury(I) bromide
Hg2Cl2
mercury(I) chloride
Hg2I2
mercury(I) iodide
Hg3(AsO4)2
mercury(II) orthoarsenate
Hg3(PO4)2
mercury(II) phosphate
IBr
iodine(I) bromide
IBr3
iodine(III) bromide
ICl
Iodine monochloride
ICl3
iodine(III) chloride
IO3−
iodate ion
I2
iodine
I 2O 5
iodine pentoxide
I 3−
triiodide ion
InAs
indium(III) arsenide
InBr
indium(I) bromide
156
166
InBrI2
indium(III) bromodiiodide
InBr2I
indium(III) dibromoiodide
InBr3
indium(III) bromide
InCl
indium(I) chloride
InCl2
indium(II) chloride
InCl3
indium(III) chloride
InCl3·4H2O
indium(III) chloride tetrahydrate
InI
indium(I) iodide
In(IO3)3
indium(III) iodate
InI2
indium(II) iodide
InI3
indium(III) iodide
In(NO3)3·4.5H2O
indium(III) nitrate tetrahemihydrate
In(OH)3
indium(III) hydroxide
InP
indium(III) phosphide
InPO4
indium(III) orthophosphate
InS
indium(II) sulfide
InSb
indium(III) antimonide
InTe
indium(II) telluride
In2O3
indium(III) oxide
In2(SO4)3·H2O
indium(III) sulfate monohydrate
In2S3
indium(III) sulfide
In2Se3
indium(III) selenide
In2Te3
indium(III) telluride
IrBr3
iridium(III) bromide
KAl(SO4)2
potassium alum
KAsO2
potassium arsenite
KH2AsO4
potassium dihydrogen arsenate
KBr
potassium bromide
KBrO
potassium hypobromite
KBrO2
potassium bromite
KBrO3
potassium bromate
KBrO4
potassium perbromate
KCN
potassium cyanide
KCNO
potassium cyanate
KCNO
potassium fulminate
KCNS
potassium thiocyanate
KCl
potassium chloride
KClO
potassium hypochlorite
KClO2
potassium chlorite
KClO3
potassium chlorate
157
167
KClO4
potassium perchlorate
K2CrO4
potassium chromate
K2Cr2O7
potassium dichromate
K2HAsO4
dipotassium hydrogen arsenate
K2HPO3
dipotassium phosphite
K2HPO4
dipotassium phosphate
K3AsO4
potassium arsenate
K3C6H5O7
potassium citrate
K3PO3
tripotassium phosphite
K3PO4
tripotassium phosphate
KF
potassium fluoride
KOF
potassium hypofluorite
KH
potassium hydride
KHCO3
potassium bicarbonate
KHS
potassium hydrosulfide
KHSO3
potassium bisulfite
KHSO4
potassium bisulfate
KH2PO3
monopotassium phosphite
KH2PO4
monopotassium phosphate
KI
potassium iodide
KIO
potassium hypoiodite
KIO2
potassium iodite
KIO3
potassium iodate
KIO4
potassium periodate
KMnO4
potassium permanganate
KNO3
potassium nitrate
KNO2
potassium nitrite
K2CO3
potassium carbonate
K2MnO4
potassium manganate
K2N2O2
potassium hyponitrite
KNbO3
potassium niobate
K 2O
potassium oxide
K 2O 2
potassium peroxide
K 2S
potassium sulfide
K2S2O3
potassium thiosulfate
K2S2O5
potassium metabisulfite
K2S2O8
potassium persulfate
K2SO3
potassium sulfite
K2SO4
potassium sulfate
KOH
potassium hydroxide/custic potash
158
168
LaBr3
lanthanum(III) bromide
LaCl3
lanthanum(III) chloride
LaI3
lanthanum(III) iodide
La2O3
lanthanum(III) oxide
La(OH)3
lanthanum hydroxide
LaPO4
lanthanum(III) phosphate
LaPO4·0.5H2O
lanthanum(III) phosphate crystal
hemihydrate
LiAlH4
lithium aluminium hydride
Li(AlSi2O6)
keatite
LiBH4
lithium borohydride
LiBr
lithium bromide
LiBr·2H2O
lithium bromide dihydrate
LiBrO
lithium hypobromite
LiBrO2
lithium bromite
LiBrO3
lithium bromate
LiBrO4
lithium perbromate
LiCl
lithium chloride
LiClO
lithium hypochlorite
LiClO2
lithium chlorite
LiClO3
lithium chlorate
LiClO4
lithium perchlorate
LiCN
lithium cyanide
LiCNO
lithium cyanate
LiC2H5O
lithium ethoxide
LiF
lithium fluoride
LiH
lithium hydride
LiHCO3
lithium bicarbonate
LiHS
lithium hydrosulfide
LiHSO3
lithium bisulfite
LiHSO4
lithium hydrogen sulfate
LiH2AsO4
lithium dihydrogen arsenate
LiH2PO3
monolithium phosphite
LiH2PO4
monolithium phosphate
LiI
lithium iodide
LiIO
lithium hypoiodite
LiIO2
lithium iodite
LiIO3
lithium iodate
LiIO4
lithium periodate
LiNa
sodium lithium
LiNbO3
lithium niobate
159
169
LiNO2
lithium nitrite
LiNO3
lithium nitrate
LiNO3·H2O
lithium nitrate monohydrate
LiOH
lithium hydroxide
LiTaO3
lithium tantalate
lithium metatantalate
LiVO3·2H2O
lithium metavanadate dihydrate
Li2HAsO4
dilithium hydrogen arsenate
Li2B4O7·5H2O
lithium tetraborate pentahydrate
Li2CO3
lithium carbonate
Li2CrO4
lithium chromate
Li2CrO4·2H2O
lithium chromate dihydrate
Li2Cr2O7
lithium dichromate
Li2HPO3
dilithium phosphite
Li2HPO4
dilithium phosphate
Li2MoO4
lithium orthomolybdate
Li2NbO3
lithium metaniobate
Li2N2O2
lithium hyponitrite
Li2O
lithium oxide
Li2O2
lithium peroxide
Li2S
lithium sulfide
Li2SO3
lithium sulfite
Li2SO4
lithium sulfate
Li2SeO3
lithium selenite
Li2SeO4
lithium selenate
Li2SiO3
lithium metasilicate
lithium orthosilicate
Li2TeO3
lithium tellurite
Li2TeO4
lithium tellurate
Li2TiO3
lithium metatitanate
Li2WO4
lithium orthotungstate
Li2ZrO3
lithium metazirconate
Li3AsO4
trilithium arsenate
Li3PO3
trilithium phosphite
Li3PO4
trilithium phosphate
MgBr2
magnesium bromide
Mg(BrO)2
magnesium hypobromite
Mg(BrO2)2
magnesium bromite
Mg(BrO3)2
magnesium bromate
Mg(BrO4)2
magnesium perbromate
Mg(AlO2)2
magnesium aluminate
160
170
As2Mg3
magnesium arsenide
MgCO3
magnesium carbonate
magnesite
MgC2O4
magnesium oxalate
Mg(ClO)2
magnesium hypochlorite
Mg(ClO2)2
magnesium chlorite
Mg(ClO3)2
magnesium chlorate
Mg(ClO3)2·xH2O
magnesium chlorate hydrate
Mg(ClO4)2
magnesium perchlorate
MgCl2
magnesium chloride
MgCrO4
magnesium chromate
MgCrO4·5H2O
magnesium chromate pentahydrate
MgF2
magnesium fluoride
MgHPO4
dimagnesium phosphate
MgI2
magnesium iodide
Mg(IO)2
magnesium hypoiodite
Mg(IO2)2
magnesium iodite
Mg(IO3)2
magnesium iodate
Mg(IO4)2
magnesium periodate
MgMoO4
magnesium molybdate
MgNH4PO4·6H2O
magnesium ammonium phosphate
hexahydrate
Mg(NO2)2
magnesium nitrite
Mg(NO3)2
magnesium nitrate
Mg(NO3)2·6H2O
magnesium nitrate hexahydrate
MgNaAl5(Si4O10)3(OH)6
montmorillonite (clay)
MgO
magnesium oxide
magnesia
periclase
Mg(OH)2
magnesium hydroxide
milk of magnesia
MgPo
magnesium polonide
MgS
magnesium sulfide
MgSO3
magnesium sulfite
MgSO4
magnesium sulfate
MgSe
magnesium selenide
MgSeO3
magnesium selenite
MgSeO4
magnesium selenate
MgSiO3
magnesium metasilicate
enstatite
MgTiO3
magnesium metatitanate
161
171
Mg(VO3)2
magnesium metavanadate
MgWO4
magnesium tungstate
Mg2Al(AlSiO5)(OH)4
amesite
Mg2P2O7
magnesium pyrophosphate
Mg2SiO4
forsterite
Mg3As2
magnesium arsenide
Mg3Bi2
magnesium bismuthide
Mg3P2
magnesium phosphide
Mg3(Si2O5)(OH)4
chrysotile
Mg3(Si4O10)(OH)2
talc
Mg3(VO4)2
magnesium orthovanadate
MnAs
manganese(III) arsenide
MnBi
manganese(III) bismuthide
MnBr2
manganese(II) bromide
MnBr2·4H2O
manganese(II) bromide tetrahydrate
Mn(CHO2)2
manganese(II) formate
Mn(CHO2)2·2H2O
manganese(II) formate dihydrate
MnCO3
manganese(II) carbonate
MnCl2
manganese(II) chloride
MnF2
manganese(II) fluoride
MnI2
manganese(II) iodide
MnMoO4
manganese(II) orthomolybdate
Mn(NO3)2
manganese(II) nitrate
Mn(NO3)2·4H2O
manganese(II) nitrate tetrahydrate
MnO
manganese(II) oxide
Mn(OH)2
manganese hydroxide
MnOOH
manganite
MnO2
manganese dioxide
pyrolusite
MnO4−
permanganate ion
MnPb8(Si2O7)3
barysilate
MnS
manganese sulfide
MnTe
manganese(II) telluride
MnZrO3
manganese(II) metazirconate
Mn2O3
manganese(III) oxide
Mn3As2
manganese(II) arsenide
Mn3O4
manganese(II,III) oxide
trimanganese tetroxide
hausmannite
Mn3P2
manganese(II) phosphide
Mn3Sb2
manganese(II) antimonide
162
172
MoBr2
molybdenum(II) bromide
MoBr3
molybdenum(III) bromide
MoCl2
molybdenum(II) chloride
MoCl3
molybdenum(III) chloride
MoCl5
molybdenum(V) chloride
MoO2
molybdenum(IV) oxide
MoO3
Molybdenum trioxide
MoO42−
molybdate ion
MoSe2
molybdenum(IV) selenide
MoS2
molybdenum sulfide
molybdenum disulfide
molybdenite
NCl3
nitrogen trichloride
NHCl2
dichloramine
NH2Cl
monochloramine
NH2−
amide ion
NH2CH2CH2NH2
ethylenediamine
NH2CH2CN
aminoacetonitrile
NH2COOH
carbamic acid
NH2CONH2
urea
NH2C6H4SO3H
sulfanilic Acid
NH2OH
hydroxylamine
(NH2)2CO
urea
NH3
ammonia
NH4+
ammonium ion
(NH4)3N
ammonium nitride
NH4Br
ammonium bromide
NH4CO2NH2
ammonium carbamate
(NH4)2CO3
ammonium carbonate
NH4Cl
ammonium chloride
NH4ClO4
Ammonium perchlorate
NH4HS
ammonium hydrosulfide
(NH4)H2AsO4
ammonium dihydrogen arsenate
NH4NO3
ammonium nitrate
NH4OCONH2
ammonium carbamate
NH4OH
ammonium hydroxide
(NH4)2Ce(NO3)6
ammonium cerium(IV) nitrate
ceric ammonium nitrate
CAN
(NH4)3PO4
ammonium phosphate
(NH4)2CrO4
ammonium chromate
163
173
(NH4)2Hg(SCN)4
mercury(II) ammonium thiocyanate
(NH4)2[PtCl6]
ammonium hexachloroplatinate(IV)
(NH4)2[Pt(SCN)6]
ammonium hexathiocyanoplatinate(IV)
(NH4)2SO4
ammonium sulfate
NI3
nitrogen triiodide
NO
nitric oxide
nitrogen oxide
nitrogen(II) oxide
NOCl
nitrosyl chloride
NOBr
nitrosyl bromide
NOI
nitrosyl iodide
NO2
nitrogen dioxide
nitrogen(IV) oxide
NO2−
nitrite ion
NO2Cl
nitryl chloride
NO3−
nitrate ion
N2
nitrogen
N 2H 2
diazene
N 2H 4
hydrazine
N 2O
nitrous oxide
dinitrogen oxide
nitrogen(I) oxide
N 2O 3
dinitrogen trioxide
nitrogen(III) oxide
N 2O 4
dinitrogen tetroxide
nitrogen(IV) oxide
N 2O 5
dinitrogen pentaoxide
nitrogen(V) oxide
N 4H 4
trans-tetrazene
NaAlSi3O3
albite
NaAsO2
sodium metaarsenite
NaH2AsO4
sodium dihydrogen arsenate
NaAu(CN)2
sodium dicyanoaurate(I)
Na2Cr2O7 · 2H2O
Sodium dichromate dihydrate
Na[B(NO3)4]
sodium tetranitratoborate(III)
NaBr
sodium bromide
NaBrO
sodium hypobromite
NaBrO2
sodium bromite
NaBrO3
sodium bromate
NaBrO4
sodium perbromate
NaCN
sodium cyanide
164
174
NaCNO
sodium cyanate
NaCNO
sodium fulminate
NaC6F5COO
pentafluorobenzoate
NaC6H5COO
sodium benzoate
NaC6H7O7
monosodium citrate
NaCa2(Al5Si5O20) · 6H2O
thomsonite
NaCl
sodium chloride
rock-salt
halite
NaClO2
sodium chlorite
NaClO3
sodium chlorate
NaClO4
sodium perchlorate
NaF
sodium fluoride
NaOF
sodium hypofluorite
NaH
sodium hydride
NaHCOO
sodium formate
NaHCO3
sodium bicarbonate
baking soda
NaHS
sodium hydrosulfide
NaHSO3
sodium bisulfite
NaHSO4
sodium bisulfate
NaH2PO3
monosodium phosphite
NaH2PO4
monosodium phosphate
NaI
sodium iodide
NaIO
sodium hypoiodite
NaIO2
sodium iodite
NaIO3
sodium iodate
NaIO4
sodium periodate
NaNH2C6H4SO3
sodium sulfanilate
NaNO2
sodium nitrite
NaNO3
sodium nitrate
NaNbO3
sodium metaniobate
NaNbO3 · 7H2O
sodium metaniobate heptahydrate
NaOCl
sodium hypochlorite
NaOH
sodium hydroxide
NaO2As(CH3)2 · 3H2O
sodium salt of cacodylic acid
NaSeO3
sodium selenite
NaTaO3
sodium metatantalate
NaVO3
sodium metavanadate
Na2CO3
sodium carbonate
soda ash
165
175
Na2C2O4
sodium oxalate
Na2C6H6O7
disodium citrate
Na2HAsO4
disodium hydrogen arsenate
Na2HPO3
disodium phosphite
Na2HPO4
disodium phosphate
Na2MoS4
sodium thiomolybdate
Na2N2O2
sodium hyponitrite
Na2O2
sodium peroxide
Na2O
sodium oxide
Na2S
sodium monosulfide
Na2SO3
sodium sulfite
Na2SO4
sodium sulfate
salt cake
Na2S2O3
sodium thiosulfate
Na2S2O5
sodium disulfite
Na2S2O8
sodium persulfate
Na2S4
sodium tetrasulfide
Na2SeO3
sodium selenite
Na2SeO4
sodium selenate
Na2TeO3
sodium tellurite
Na2TeO4
sodium tellurate
Na2TiO3
sodium metatitanate
Na2Zn(OH)4
sodium zincate
Na2ZnO2
sodium zincate
Na2ZrO3
sodium metazirconate
Na3AlF6
cryolite
Na3AsO4
sodium arsenate
Na3[Co(CO3)3]
sodium tricarbonatocobaltate(III)
Na3VO4
sodium orthovanadate
Na3C6H5O7
trisodium citrate
Na3PO3
trisodium phosphite
Na3PO4
trisodium phosphate
Na4V2O7
sodium pyrovanadate
NbBr5
niobium(V) bromide
NbCl3
niobium(III) chloride
NbCl5
niobium(V) chloride
NbI5
niobium(V) iodide
Nb2O3
niobium(III) oxide
NdCl2
neodymium(II) chloride
neodymium dichloride
NdI2
neodymium(III) iodide
166
176
neodymium diiodide
Nd(OH)3
neodymium hydroxide
Nd2O3
neodymium(III) oxide
dineodymium trioxide
NiAs
nickel(III) arsenide
NiAsS
nickel arsenic sulfide
gersdorffite
NiBr2
nickel(II) bromide
NiBr2 · 3H2O
nickel(II) bromide trihydrate
NiBr2 · 6H2O
nickel(II) bromide hexahydrate
Ni(CO)3
nickel(II) carbonate
Ni(CO)4
nickel tetracarbonyl
NiC2O4 · 2H2O
nickel(II) oxalate dihydrate
NiCl2
nickel(II) chloride
NiFe2O4
nickel(II) iron(III) oxide
NiI2
nickel(II) iodide
Ni(H2PO)2 · 6H2O
nickel(II) hypophosphite hexahydrate
NiMoO4
nickel(II) orthomolybdate
Ni(NO3)2 · 6H2O
nickel(II) nitrate hexahydrate
NiOOH
nickel oxo-hydroxide
NiO
nickel(II) oxide
Ni(OH)2
nickel(II) hydroxide
NiS
nickel(II) sulfide
millerite
NiSO4
nickel sulfate
NiS2
nickel sulfide
NiSb
nickel antimonide
NiSe
nickel(II) selenide
NiTiO3
nickel(II) metatitanate
Ni(VO3)2
nickel(II) metavanadate
NiWO4
nickel(II) orthotungstate
Ni2SiO4
nickel(II) orthosilicate
Ni3(PO4)2
nickel(II) orthophosphate
Ni3Sb2
nickel(II) antimonide
O
oxygen
O2
dioxygen
O 2−
superoxide ion
O22−
peroxide ion
OF2
oxygen difluoride
O 2F 2
dioxygen difluoride
OH−
hydroxide ion
167
177
O3
ozone
O 3−
ozonide ion
PCl3
phosphorus trichloride
PCl5
phosphorus pentachloride
POCl3
phosphoryl chloride
P 2I 4
diphosphorus tetraiodide
P 2O 5
phosphorus pentoxide
P 2S 3
diphosphorus trisulfide
P2Se3
diphosphorus triselenide
P 3N 5
triphosphorus pentanitride
PH3
phosphine
POCl3
phosphoryl chloride
PbCl2
lead(II) chloride
PbCl4
lead(IV) chloride
PbHAsO4
lead hydrogen arsenate
PbI2
lead(II) iodide
Pb(IO3)2
lead(II) iodate
Pb(N3)2
lead(II) nitride
Pb(NO3)2
lead(II) nitrate
Pb(OH)2
lead(II) hydroxide
Pb(OH)4
lead(IV) hydroxide
PbC2O4
lead oxalate
PbCO3
lead carbonate
PbCrO4
lead chromate
PbF2
lead(II) fluoride
PbO
lead(II) oxide
PbO2
lead dioxide
PbS
lead(II) sulfide
PbSO4
lead(II) sulfate
PoBr2
polonium dibromide
PoCl2
polonium dichloride
PoCl4
polonium tetrachloride
PoF6
polonium hexafluoride
PoH2
polonium hydride
PoO
polonium monoxide
PoO2
polonium dioxide
PoO3
polonium trioxide
RaCl2
radium chloride
RbBr
rubidium bromide
RbBrO
rubidium hypobromite
168
178
RbBrO2
rubidium bromite
RbBrO3
rubidium bromate
RbBrO4
rubidium perbromate
RbCl
rubidium chloride
RbClO
rubidium hypochlorite
RbClO2
rubidium chlorite
RbClO3
rubidium chlorate
RbClO4
rubidium perchlorate
RbCN
rubidium cyanide
RbCNO
rubidium cyanate
RbCNO
rubidium fulminate
RbF
rubidium fluoride
RbH
rubidium hydride
RbH2PO3
monorubidium phosphite
RbH2PO4
monorubidium phosphate
RbHS
rubidium hydrosulfide
RbI
rubidium iodide
RbIO
rubidium hypoiodite
RbIO2
rubidium iodite
RbIO3
rubidium iodate
RbIO4
rubidium periodate
RbOH
rubidium hydroxide
Rb2O
rubidium oxide
Rb2O2
rubidium peroxide
Rb2CO3
rubidium carbonate
Rb2S
rubidium sulfide
Rb2SO3
rubidium sulfite
Rb2SO4
rubidium sulfate
Rb2HPO3
dirubidium phosphite
Rb2HPO4
dirubidium phosphate
Rb3PO3
trirubidium phosphite
Rb3PO4
trirubidium phosphate
RbHCO3
rubidium bicarbonate
RbHSO3
rubidium bisulfite
RbHSO4
rubidium bisulfate
RbNbO3
rubidium niobate
RbNO2
rubidium nitrite
RbNO3
rubidium nitrate
RnF2
radon difluoride
RuCl3
ruthenium(III) chloride
169
179
RuF6
ruthenium hexafluoride
RuO4
ruthenium tetroxide
SCN−
thiocyanate
SF4
sulfur tetrafluoride
SF6
sulfur hexafluoride
SOF2
thionyl difluoride
SO2
sulfur dioxide
SO2Cl2
sulfuryl chloride
SO2F2
sulfuryl difluoride
SO2OOH−
peroxymonosulfurous acid (aqueous)
SO3
sulfur trioxide
SO32−
sulfite ion
SO42−
sulfate ion
S2Br2
sulfur(II) bromide
S2O32−
thiosulfate ion
S2O72−
disulfate ion
SbBr3
antimony(III) bromide
SbCl3
antimony(III) chloride
SbCl5
antimony(V) chloride
SbI3
antimony(III) iodide
SbPO4
antimony(III) phosphate
Sb2OS2
antimony oxysulfide
kermesite
Sb2O3
antimony(III) oxide
Sb2O5
antimony(V) oxide
Sb2S3
antimony(III) sulfide
Sb2Se3
antimony(III) selenide
Sb2Se5
antimony(V) selenide
Sb2Te3
antimony(III) telluride
Sc2O3
scandium oxide
scandia
SeBr4
selenium(IV) bromide
SeCl
selenium(I) chloride
SeCl4
selenium(IV) chloride
SeOCl2
selenium(IV) oxychloride
SeOF2
selenyl difluoride
SeO2
selenium(IV) oxide
SeO42−
selenate ion
SeTe
selenium(IV) telluride
SiBr4
silicon(IV) bromide
SiC
silicon carbide
170
180
SiCl4
silicon(IV) chloride
SiH4
silane
SiI4
silicon(IV) iodide
SiO2
silicon(IV) dioxide
silica
quartz
SiO44−
silicate ion
Si2O76−
disilicate ion
Si3N4
silicon nitride
Si6O1812−
cyclosilicate ion
SnBrCl3
tin(IV) bromotrichloride
SnBr2
tin(II) bromide
SnBr2Cl2
tin(IV) dibromodichloride
SnBr3Cl
tin(IV) tribromochloride
SnBr4
tin(IV) bromide
Sn(CH3COO)2
tin(II) acetate
Sn(CH3COO)4
tin(IV) acetate
SnCl2
tin(II) chloride
SnCl2I2
tin(IV) dichlorodiiodide
SnCl4
tin(IV) chloride
Sn(CrO4)2
tin(IV) chromate
SnI4
tin(IV) iodide
Sn(OH)2
tin(II) hydroxide
Sn(OH)4
tin(IV) hydroxide
SnO
tin(II) oxide
SnO2
tin(IV) oxide
SnO32−
stannate ion
SnS
tin(II) sulfide
SnS2
tin(IV) sulfide
Sn(SO4)2·2H2O
tin(IV) sulfate dihydrate
SnSe
tin(II) selenide
SnSe2
tin(IV) selenide
SnTe
tin(II) telluride
SnTe4
tin(IV) telluride
Sn(VO3)2
tin(II) metavanadate
Sn3Sb4
tin(IV) antimonide
SrBr2
strontium bromide
SrBr2·6H2O
strontium bromide hexahydrate
SrCO3
strontium carbonate
SrCl2
strontium chloride
Sr(ClO)2
strontium hypochlorite
171
181
Sr(ClO2)2
strontium chlorite
Sr(ClO3)2
strontium chlorate
Sr(ClO4)2
strontium perchlorate
SrC2O4
strontium oxalate
SrF2
strontium fluoride
SrHfO3
strontium hafnate
Sr(HS)2
strontium hydrosulfide
SrI2
strontium iodide
SrI2·6H2O
strontium iodide hexahydrate
Sr(IO)2
strontium hypoiodite
Sr(IO2)2
strontium iodite
Sr(IO3)2
strontium iodate
Sr(IO4)2
strontium periodate
Sr(MnO4)2
strontium permanganate
SrMoO4
strontium orthomolybdate
Sr(NbO3)2
strontium metaniobate
SrO
strontium oxide
Sr(OH)2
strontium hydroxide
Sr2RuO4
strontium ruthenate
SrS
strontium sulfide
SrSeO3
strontium selenite
SrSeO4
strontium selenate
SrTeO3
strontium tellurite
SrTeO4
strontium tellurate
SrTiO3
strontium metatitanate
T 2O
tritium oxide
tritiated water
TaBr3
tantalum(III) bromide
TaBr5
tantalum(V) bromide
TaCl5
tantalum(V) chloride
TaI5
tantalum(V) iodide
TaO3−
tantalate ion
TcO4−
pertechnetate ion
TeBr2
tellurium(II) bromide
TeBr4
tellurium(IV) bromide
TeCl2
tellurium(II) chloride
TeCl4
tellurium(IV) chloride
TeI2
tellurium(II) iodide
TeI4
tellurium(IV) iodide
TeO2
tellurium(IV) oxide
TeO4−
tellurate ion
172
182
TeY
yttrium telluride
Th(CO3)2
thorium carbonate
Th(NO3)4
thorium nitrate
ThO2
thorium(IV) oxide
Th(SO4)2
thorium(IV) sulfate
TiBr4
titanium(IV) bromide
TiCl2I2
titanium(IV) dichlorodiiodide
TiCl3I
titanium(IV) trichloroiodide
TiCl4
titanium tetrachloride
TiH2
titanium hydride
TiO2
titanium dioxide
rutile
TiO32−
titanate ion
TlBr
thallium(I) bromide
TlBr3
thallium(III) bromide
Tl(CHO2)
thallium(I) formate
TlC2H3O2
thallium(I) acetate
Tl(C3H3O4)
thalliium(I) malonate
TlCl
thallium(I) chloride
TlCl3
thallium(III) chloride
TlF
thallium(I) fluoride
TlI
thallium(I) iodide
TlIO3
thallium(I) iodate
TlI3
thallium(III) iodide
TiI4
titanium(IV) iodide
TiO(NO3)2 · xH2O
titanium(IV) oxynitrate hydrate
TlNO3
thallium(I) nitrate
TlOH
thallium(I) hydroxide
TlPF6
thallium(I) hexafluorophosphate
TlSCN
thallium thiocyanate
Tl2MoO4
thallium(I) orthomolybdate
Tl2SeO3
thallium(I) selenite
Tl2TeO3
thallium(I) tellurite
Tl2WO4
thallium(I) orthotungstate
Tl3As
thallium(I) arsenide
TmCl3
thulium(III) chloride
Tm(NO3)3
thulium(III) nitrate
Tm2(SO4)3
thullium(III) sulfate
UBr2
uranium dibromide
UBr3
uranium tribromide
UBr5
uranium pentabromide
173
183
UC2
uranium carbide
UCl3
uranium trichloride
UCl4
uranium tetrachloride
UF4
uranium(IV) fluoride
UF6
uranium(VI) fluoride
UI3
uranium(III) iodide
UN
uranium nitride
UO2
uranium dioxide
UO2(CH3COO)2
uranyl acetate
UO2Cl2
uranyl chloride
UO2(HCOO)2
uranyl formate
UO2(NO3)2
uranyl nitrate
UO2SO4
uranyl sulfate
UO3
uranium trioxide
U 3O 8
triuranium octoxide
USe2
uranium diselenide
US2
uranium sulfide
UTe2
uranium ditelluride
VBr2
vanadium(II) bromide
VBr3
vanadium(III) bromide
VCl2
vanadium(II) chloride
VCl3
vanadium(III) chloride
VI3
vanadium(III) iodide
VN
vanadium nitride
VOC2O4
vanadyl oxalate
VOSO4
vanadium oxysulfate
V 2O 3
vanadium(III) oxide
V 2O 5
vanadium pentoxide
V2O74−
divanadate ion
pyrovanadate ion
WBr2
tungsten(II) bromide
WBr3
tungsten(III) bromide
WBr4
tungsten(IV) bromide
WBr5
tungsten(V) bromide
WBr6
tungsten(VI) bromide
W(CO)6
tungsten(VI) carbonyl
WCl2
tungsten(II) chloride
WCl3
tungsten(III) chloride
WCl4
tungsten(IV) chloride
WCl5
tungsten(V) chloride
WCl6
tungsten(VI) chloride
174
184
WF4
tungsten(IV) fluoride
WF5
tungsten(V) fluoride
WF6
tungsten(VI) fluoride
WI2
tungsten(II) iodide
WI4
tungsten(IV) iodide
WOBr3
tungsten(V) oxytribromide
WOBr4
tungsten(VI) oxytetrabromide
WOCl3
tungsten(V) oxytrichloride
WOCl4
tungsten(VI) oxytetrachloride
WOF4
tungsten(VI) oxytetrafluoride
WO2
tungsten(IV) oxide
WO2Br2
tungsten(VI) dioxydibromide
WO2Cl2
tungsten(VI) dioxydichloride
WO2I2
tungsten(VI) dioxydiiodide
WO3
tungsten(VI) oxide
WO42−
tungstate ion
WS2
tungsten(IV) sulfide
WS3
tungsten(VI) sulfide
WSe2
tungsten(IV) selenide
WTe2
tungsten(IV) telluride
WC
tungsten carbide
YAs
yttrium arsenide
YB6
yttrium boride
YBr3
yttrium bromide
YC2
yttrium carbide
YCl3
yttrium chloride
YF3
yttrium fluoride
YP
yttrium phosphide
YSb
yttrium antimonide
YVO4
yttrium vanadate
Y 2O 3
yttria
yttrium oxide
Y 2S 3
yttrium sulfide
YbBr2
ytterbium(II) bromide
YbBr3
ytterbium(III) bromide
YbCl2
ytterbium(II)chloride
YbCl3
ytterbium(III) chloride
YbCl3·6H2O
ytterbium(III) chloride hexahydrate
Yb(ClO4)3
ytterbium(III) perchlorate
YbF2
ytterbium(II) fluoride
YbF3
ytterbium(III) fluoride
175
185
YbI2
ytterbium(II) iodide
YbI3
ytterbium(III) iodide
YbPO4
ytterbium(III) phosphate
YbSe
ytterbium(II) selenide
YbSi2
ytterbium(II) silicide
Yb2O3
ytterbium(III) oxide
Yb2S3
ytterbium(III) sulfide
Yb2Se3
ytterbium(III) selenide
YbTe
ytterbium(II) telluride
Zn(AlO2)2
zinc aluminate
Zn(AsO2)2
zinc arsenite
ZnBr2
zinc bromide
Zn(CN)2
zinc cyanide
ZnCO3
zinc carbonate
Zn(C8H15O2)2
zinc caprylate
Zn(ClO3)2
zinc chlorate
ZnCl2
zinc chloride
ZnCr2O4
zinc chromite
ZnF2
zinc fluoride
Zn(IO3)2
zinc iodate
ZnI2
zinc iodide
ZnMoO4
zinc orthomolybdate
Zn(NO2)2
zinc nitrite
Zn(NO3)2
zinc nitrate
Zn(NbO3)2
zinc metaniobate
ZnO
zinc(II) oxide
zinc oxide
ZnO2
zinc peroxide
Zn(OH)2
zinc hydroxide
Zn(OH)42−
zincate ion
ZnS
zinc sulfide
sphalerite
Zn(SCN)2
zinc thiocyanate
Zn(SeCN)2
zinc selenocyanate
ZnSO3
zinc sulfite
ZnS2O3
zinc thiosulfate
ZnSO4
zinc sulfate
ZnSb
zinc antimonide
ZnSe
zinc selenide
ZnSeO3
zinc selenite
ZnSeO4
zinc selenate
176
186
ZnSnO3
zinc stannate
Zn(TaO3)2
zinc metatantalate
ZnTe
zinc telluride
ZnTeO3
zinc tellurite
ZnTeO4
zinc tellurate
ZnTiO3
zinc metatitanate
Zn(VO3)2
zinc metavanadate
ZnWO4
zinc orthotungstate
ZnZrO3
zinc metazirconate
Zn2P2O7
zinc pyrophosphate
Zn2SiO4
zinc orthosilicate
Zn3(AsO4)2
zinc arsenate
Zn3As2
zinc arsenide
Zn3N2
zinc nitride
Zn3P2
zinc phosphide
Zn3(PO4)2
zinc phosphate
Zn3Sb2
zinc antimonide
ZrB2
zirconium boride
ZrBr4
zirconium bromide
ZrC
zirconium carbide
ZrCl4
zirconium tetrachloride
ZrF4
zirconium fluoride
ZrI4
zirconium iodide
ZrN
zirconium nitride
Zr(NO3)4
zirconium(IV) nitrate
Zr(OH)4
zirconium hydroxide
ZrO2
zirconium dioxide
baddeleyite
ZrO32−
zirconate ion
ZrP2
zirconium phosphide
ZrS2
zirconium sulfide
ZrSi2
zirconium silicide
ZrSiO4
zirconium(IV) silicate
Zr(SO4)2
zirconium(IV) sulfate
Zr3(PO4)4
zirconium phosphate
Ten most common elements in the Milky Way Galaxy estimated spectroscopically
177
187
Atomic no
Element
Mass fraction (ppm)
1
Hydrogen
739,000
2
Helium
240,000
8
Oxygen
10,400
6
Carbon
4,600
10
Neon
1,340
26
Iron
1,090
7
Nitrogen
960
14
Silicon
650
12
Magnesium
580
16
Sulfur
440
Total
999,500
Most abundant nuclides in the Solar System
Nuclide
Atomic mass
Mass fraction in parts
Atom fraction in parts
per million
per million
178
188
Sulfur-32
32
396
16
Sodium-23
23
33
2
Silicon-30
30
23
1
Silicon-29
29
34
2
Silicon-28
28
653
30
Oxygen-16
16
9,592
477
Nitrogen-14
14
1,105
102
Nickel-58
58
49
1
Neon-22
22
208
12
Neon-20
20
1,548
100
Magnesium-26
26
79
4
Magnesium-25
25
69
4
Magnesium-24
24
513
28
Iron-57
57
28
1
Iron-56
56
1,169
27
Iron-54
54
72
2
179
189
Hydrogen-2
2
23
15
Hydrogen-1
1
705,700
909,964
Helium-4
4
275,200
88,714
Helium-3
3
35
15
Carbon-13
13
37
4
Carbon-12
12
3,032
326
Calcium-40
40
60
2
Argon-36
36
77
3
Aluminium-27
27
58
3
Electron configurations of the elements
1 H hydrogen: 1s1
2 He helium: 1s2
3 Li lithium: [He] 2s1
4 Be beryllium: [He] 2s2
5 B boron: [He] 2s2 2p1
180
190
6 C carbon: [He] 2s2 2p2
7 N nitrogen: [He] 2s2 2p3
8 O oxygen: [He] 2s2 2p4
9 F fluorine: [He] 2s2 2p5
10 Ne neon: [He] 2s2 2p6
11 Na sodium: [Ne] 3s1
12 Mg magnesium: [Ne] 3s2
13 Al aluminium: [Ne] 3s2 3p1
14 Si silicon: [Ne] 3s2 3p2
15 P phosphorus: [Ne] 3s2 3p3
16 S sulfur: [Ne] 3s2 3p4
17 Cl chlorine: [Ne] 3s2 3p5
18 Ar argon: [Ne] 3s2 3p6
19 K potassium: [Ar] 4s1
20 Ca calcium: [Ar] 4s2
181
191
21 Sc scandium: [Ar] 3d1 4s2
22 Ti titanium: [Ar] 3d2 4s2
23 V vanadium: [Ar] 3d3 4s2
24 Cr chromium: [Ar] 3d5 4s1
25 Mn manganese: [Ar] 3d5 4s2
26 Fe iron: [Ar] 3d6 4s2
27 Co cobalt: [Ar] 3d7 4s2
28 Ni nickel: [Ar] 3d8 4s2 or [Ar] 3d9 4s1
29 Cu copper: [Ar] 3d10 4s1
30 Zn zinc: [Ar] 3d10 4s2
31 Ga gallium: [Ar] 3d10 4s2 4p1
32 Ge germanium: [Ar] 3d10 4s2 4p2
33 As arsenic: [Ar] 3d10 4s2 4p3
34 Se selenium: [Ar] 3d10 4s2 4p4
35 Br bromine: [Ar] 3d10 4s2 4p5
182
192
36 Kr krypton: [Ar] 3d10 4s2 4p6
37 Rb rubidium: [Kr] 5s1
38 Sr strontium: [Kr] 5s2
39 Y yttrium: [Kr] 4d1 5s2
40 Zr zirconium: [Kr] 4d2 5s2
41 Nb niobium: [Kr] 4d4 5s1
42 Mo molybdenum: [Kr] 4d5 5s1
43 Tc technetium: [Kr] 4d5 5s2
44 Ru ruthenium: [Kr] 4d7 5s1
45 Rh rhodium: [Kr] 4d8 5s1
46 Pd palladium: [Kr] 4d10
47 Ag silver: [Kr] 4d10 5s1
48 Cd cadmium: [Kr] 4d10 5s2
49 In indium: [Kr] 4d10 5s2 5p1
50 Sn tin: [Kr] 4d10 5s2 5p2
183
193
51 Sb antimony: [Kr] 4d10 5s2 5p3
52 Te tellurium: [Kr] 4d10 5s2 5p4
53 I iodine: [Kr] 4d10 5s2 5p5
54 Xe xenon: [Kr] 4d10 5s2 5p6
55 Cs caesium: [Xe] 6s1
56 Ba barium: [Xe] 6s2
57 La lanthanum: [Xe] 5d1 6s2
58 Ce cerium: [Xe] 4f1 5d1 6s2
59 Pr praseodymium: [Xe] 4f3 6s2
60 Nd neodymium: [Xe] 4f4 6s2
61 Pm promethium: [Xe] 4f5 6s2
62 Sm samarium: [Xe] 4f6 6s2
63 Eu europium: [Xe] 4f7 6s2
64 Gd gadolinium: [Xe] 4f7 5d1 6s2
65 Tb terbium: [Xe] 4f9 6s2
184
194
66 Dy dysprosium: [Xe] 4f10 6s2
67 Ho holmium: [Xe] 4f11 6s2
68 Er erbium: [Xe] 4f12 6s2
69 Tm thulium: [Xe] 4f13 6s2
70 Yb ytterbium: [Xe] 4f14 6s2
71 Lu lutetium: [Xe] 4f14 5d1 6s2
72 Hf hafnium: [Xe] 4f14 5d2 6s2
73 Ta tantalum: [Xe] 4f14 5d3 6s2
74 W tungsten: [Xe] 4f14 5d4 6s2
75 Re rhenium: [Xe] 4f14 5d5 6s2
76 Os osmium: [Xe] 4f14 5d6 6s2
77 Ir iridium: [Xe] 4f14 5d7 6s2
78 Pt platinum: [Xe] 4f14 5d9 6s1
79 Au gold: [Xe] 4f14 5d10 6s1
80 Hg mercury: [Xe] 4f14 5d10 6s2
185
195
81 Tl thallium: [Xe] 4f14 5d10 6s2 6p1
82 Pb lead: [Xe] 4f14 5d10 6s2 6p2
83 Bi bismuth: [Xe] 4f14 5d10 6s2 6p3
84 Po polonium: [Xe] 4f14 5d10 6s2 6p4
85 At astatine: [Xe] 4f14 5d10 6s2 6p5
86 Rn radon: [Xe] 4f14 5d10 6s2 6p6
87 Fr francium: [Rn] 7s1
88 Ra radium: [Rn] 7s2
89 Ac actinium: [Rn] 6d1 7s2
90 Th thorium: [Rn] 6d2 7s2
91 Pa protactinium: [Rn] 5f2 6d1 7s2
92 U uranium: [Rn] 5f3 6d1 7s2
93 Np neptunium: [Rn] 5f4 6d1 7s2
94 Pu plutonium: [Rn] 5f6 7s2
95 Am americium: [Rn] 5f7 7s2
186
196
96 Cm curium: [Rn] 5f7 6d1 7s2
97 Bk berkelium: [Rn] 5f9 7s2
98 Cf californium: [Rn] 5f10 7s2
99 Es einsteinium: [Rn] 5f11 7s2
100 Fm fermium: [Rn] 5f12 7s2
101 Md mendelevium: [Rn] 5f13 7s2
102 No nobelium: [Rn] 5f14 7s2
103 Lr lawrencium: [Rn] 5f14 7s2 7p1
104 Rf rutherfordium: [Rn] 5f14 6d2 7s2
105 Db dubnium: [Rn] 5f14 6d3 7s2
106 Sg seaborgium: [Rn] 5f14 6d4 7s2
107 Bh bohrium: [Rn] 5f14 6d5 7s2
108 Hs hassium: [Rn] 5f14 6d6 7s2
109 Mt meitnerium: [Rn] 5f14 6d7 7s2
110 Ds darmstadtium: [Rn] 5f14 6d8 7s2
187
197
111 Rg roentgenium: [Rn] 5f14 6d9 7s2
112 Cn copernicium: [Rn] 5f14 6d10 7s2
113 Nh nihonium: [Rn] 5f14 6d10 7s2 7p1
114 Fl flerovium: [Rn] 5f14 6d10 7s2 7p2
115 Mc moscovium: [Rn] 5f14 6d10 7s2 7p3
116 Lv livermorium: [Rn] 5f14 6d10 7s2 7p4
117 Ts tennessine: [Rn] 5f14 6d10 7s2 7p5
118 Og oganesson: [Rn] 5f14 6d10 7s2 7p6
119 Uue ununennium: [Og] 8s1
120 Ubn unbinilium: [Og] 8s2
121 Ubu unbiunium: [Og] 8s2 8p1
122 Ubb unbibium: [Og] 7d1 8s2 8p1
123 Ubt unbitrium: [Og] 6f1 7d1 8s2 8p1
124 Ubq unbiquadium: [Og] 6f3 8s2 8p1
125 Ubp unbipentium: [Og] 5g1 6f3 8s2 8p1
188
198
126 Ubh unbihexium: [Og] 5g2 6f2 7d1 8s2 8p1
127 Ubs unbiseptium: [Og] 5g3 6f2 8s2 8p2
128 Ubo unbioctium: [Og] 5g4 6f2 8s2 8p2
129 Ube unbiennium: [Og] 5g5 6f2 8s2 8p2
130 Utn untrinilium: [Og] 5g6 6f2 8s2 8p2
131 Utu untriunium: [Og] 5g7 6f2 8s2 8p2
132 Utb untribium: [Og] 5g8 6f2 8s2 8p2
133 Utt untritrium: [Og] 5g8 6f3 8s2 8p2
134 Utq untriquadium: [Og] 5g8 6f4 8s2 8p2
135 Utp untripentium: [Og] 5g9 6f4 8s2 8p2
136 Uth untrihexium: [Og] 5g10 6f4 8s2 8p2
137 Uts untriseptium: [Og] 5g11 6f3 7d1 8s2 8p2
138 Uto untrioctium: [Og] 5g12 6f3 7d1 8s2 8p2
139 Ute untriennium: [Og] 5g13 6f2 7d2 8s2 8p2
140 Uqn unquadnilium: [Og] 5g14 6f3 7d1 8s2 8p2
189
199
141 Uqu unquadunium: [Og] 5g15 6f2 7d2 8s2 8p2
142 Uqb unquadbium: [Og] 5g16 6f2 7d2 8s2 8p2
143 Uqt unquadtrium: [Og] 5g17 6f2 7d2 8s2 8p2
144 Uqq unquadquadium: [Og] 5g18 6f1 7d3 8s2 8p2
145 Uqp unquadpentium: [Og] 5g18 6f3 7d2 8s2 8p2
146 Uqh unquadhexium: [Og] 5g18 6f4 7d2 8s2 8p2
147 Uqs unquadseptium: [Og] 5g18 6f5 7d2 8s2 8p2
148 Uqo unquadoctium: [Og] 5g18 6f6 7d2 8s2 8p2
149 Uqe unquadennium: [Og] 5g18 6f6 7d3 8s2 8p2
150 Upn unpentnilium: [Og] 5g18 6f6 7d4 8s2 8p2
151 Upu unpentunium: [Og] 5g18 6f8 7d3 8s2 8p2
152 Upb unpentbium: [Og] 5g18 6f9 7d3 8s2 8p2
153 Upt unpenttrium: [Og] 5g18 6f11 7d2 8s2 8p2
154 Upq unpentquadium: [Og] 5g18 6f12 7d2 8s2 8p2
155 Upp unpentpentium: [Og] 5g18 6f13 7d2 8s2 8p2
190
200
156 Uph unpenthexium: [Og] 5g18 6f14 7d2 8s2 8p2
157 Ups unpentseptium: [Og] 5g18 6f14 7d3 8s2 8p2
158 Upo unpentoctium: [Og] 5g18 6f14 7d4 8s2 8p2
159 Upe unpentennium: [Og] 5g18 6f14 7d4 8s2 8p2 9s1
160 Uhn unhexnilium: [Og] 5g18 6f14 7d5 8s2 8p2 9s1
161 Uhu unhexunium: [Og] 5g18 6f14 7d6 8s2 8p2 9s1
162 Uhb unhexbium: [Og] 5g18 6f14 7d8 8s2 8p2
163 Uht unhextrium: [Og] 5g18 6f14 7d9 8s2 8p2
164 Uhq unhexquadium: [Og] 5g18 6f14 7d10 8s2 8p2
165 Uhp unhexpentium: [Og] 5g18 6f14 7d10 8s2 8p2 9s1
166 Uhh unhexhexium: [Og] 5g18 6f14 7d10 8s2 8p2 9s2
167 Uhs unhexseptium: [Og] 5g18 6f14 7d10 8s2 8p2 9s2 9p1
168 Uho unhexoctium: [Og] 5g18 6f14 7d10 8s2 8p2 9s2 9p2
169 Uhe unhexennium: [Og] 5g18 6f14 7d10 8s2 8p3 9s2 9p2
170 Usn unseptnilium: [Og] 5g18 6f14 7d10 8s2 8p4 9s2 9p2
191
201
171 Usu unseptunium: [Og] 5g18 6f14 7d10 8s2 8p5 9s2 9p2
172 Usb unseptbium: [Og] 5g18 6f14 7d10 8s2 8p6 9s2 9p2
173 Ust unsepttrium: [Usb] 6g1
Reactivity series
Metal
Ion
Caesium Cs
Cs+
Francium Fr
Fr+
Rubidium Rb
Rb+
Potassium K
K+
Sodium Na
Na+
Lithium Li
Li+
Barium Ba
Ba2+
Radium Ra
Ra2+
Strontium Sr
Sr2+
Calcium Ca
Ca2+
Magnesium Mg
Mg2+
Reactivity
Extraction
reacts with cold
water
electrolysis
reacts very slowly
with cold water, but
rapidly
192
202
in boiling water, and
very vigorously
with acids
Beryllium Be
Be2+
reacts with acids and
steam
Aluminium Al
Al3+
Titanium Ti
Ti4+
reacts with
concentrated mineral
acids
pyrometallurgical extraction
using magnesium,
or less commonly other alkali
metals, hydrogen or calcium in
the Kroll process
Manganese Mn
Mn2+
reacts with acids;
very poor reaction
with steam
smelting with coke
Zinc Zn
Zn2+
Chromium Cr
Cr3+
aluminothermic reaction
Iron Fe
Fe2+
smelting with coke
Cadmium Cd
Cd2+
Cobalt Co
Co2+
Nickel Ni
Ni2+
Tin Sn
Sn2+
Lead Pb
Pb2+
Antimony Sb
Sb3+
Bismuth Bi
Bi3+
Copper Cu
Cu2+
may react with some
strong oxidizing
acids
reacts slowly with
air
193
203
heat or physical extraction
Tungsten W
W3+
may react with some
strong oxidizing
acids
Mercury Hg
Hg2+
Silver Ag
Ag+
Gold Au
Au3+[5][6]
Platinum Pt
Pt4+
The four fundamental interactions of nature
Property/ Interaction
Mediating particles
Gravitation
Electroweak
Strong
Weak
Electromagnetic
Fundamental
Residual
Not yet observed
W+, W− and
γ (photon)
Gluons
π, ρ and ω
(Graviton
Z0
mesons
hypothesized)
Affected particles
All particles
Left- handed
Electrically charged
Quarks, gluons
Hadrons
fermions
Acts on
Mass, energy
Flavor
Electric charge
Color charge
Bound states formed
Planets, stars,
n/a
Atoms, molecules
Hadrons
Atomic
nuclei
galaxies, galaxy
groups
Strength at the scale
10−41
10−4
1
194
204
60
Not
of quarks
(predicted)
applicable
(relative to
to quarks
electromagnetism)
Strength at the scale
10−36 (predicted)
10−7
1
of
Not applicable
to hadrons
protons/neutrons
(relative to
electromagnetism)
Formulas in Chemistry
Ideal Gas Law
The ideal gas law is given by:
PV = nRT
where:
P: the absolute pressure of the gas
V: volume of the gas
n: number of moles, which is the ratio of mass and molar mass
R: universal gas constant, which is R = 8.3145 J mol−1 K−1
T: the absolute temperature
Henry's Law
Henry's law is given by:
p=K· x
where:
p: partial pressure of the solute
K: Henry's constant
Raoult's Law
195
205
20
Raoult's law is given by:
pi = xi ∙ pi*
where:
pi : pressure of component i
xi : mole fraction in the solution
pi *: vapor pressure of the pure substance i
In a solution with two liquids A and B, if no gas are present, the total vapor pressure is given by:
Ptot = PA + PB
where:
PA: vapor pressure of liquid A
PB: vapor pressure of liquid B
For an ideal solution of liquids A and B, which obeys Raoult's law over the full range of composition. The total
pressure is given by:
ptot = xA pA* + xB pB*
which is equal to:
ptot = (1− xB) pA* + xB pB*
or
ptot = pA* + xB (pB*− pA*)
Hess' Law
Hess' Law can be expressed in 3 ways and they are:
For enthalpy we have:
∆H = ∑ ∆Hproducts − ∑ ∆Hreactants
For entropy we have:
∆S = ∑ ∆Sproducts − ∑ ∆Sreactants
196
206
For Gibbs' free energy we have:
∆G = ∑ ∆GOproducts − ∑ ∆GOreactants
Acid and Base
For a chemical reaction:
A + H2O ↔ H3O+ + B
where:
A: acid
B: base
To determine the strength of the acid, we use the acid dissociation constant, which is given by:
KA =
For a chemical reaction:
[H3 O+ ][B]
[A]
B + H2O ↔ A + HO−
where:
A: acid
B: base
To determine the strength of the base, we use the base dissociation constant, which is given by:
KB =
[OH− ][A]
[B]
pH
pH = −log10[H+]
H2O ↔ H+ + OH−
197
207
The dissociation constant:
K=
[H+ ][OH− ]
Here [H2O] is constant, So, K [H2O] = [H+] [OH−] = Kw
[H2 O]
Kw is an ionic product of water and its value is 1×10−14 at 25°C.
[H+] [OH−] = 1×10−14
Pure water dissociates completely and has equal concentration. Thus [H+] = [OH−]
[H+] [H+] = 1×10−14
[H+] = 10−7
pH = 7
Thus, pure water is a neutral solution having pH equal to 7.0.
Acidic soution pH < 7
Basic solution pH > 7
Types of Chemical Reaction
Synthesis
In a synthesis reaction, two or more simple substances combine to form a more complex substance.
A+B → AB
"Two or more reactants giving one product" is another way to identify a synthesis reaction. One example of a
synthesis reaction is the combination of iron and sulfur to form iron (II) sulfide:
8Fe + S8→ 8FeS
198
208
Another example is simple hydrogen gas combined with simple oxygen gas to produce a more complex substance,
such as water.
Decomposition
A decomposition reaction is when a more complex substance breaks down into its more simple parts. It is thus the
opposite of a synthesis reaction, and can be written as:
AB → A+B
One example of a decomposition reaction is the electrolysis of water to make oxygen and hydrogen gas:
2H2O → 2H2 +O2
Single replacement
In a single replacement reaction, a single uncombined element replaces another in a compound; in other words, one
element trades places with another element in a compound. These reactions come in the general form of:
A+BC → AC+B
One example of a single displacement reaction is when magnesium replaces hydrogen in water to make magnesium
hydroxide and hydrogen gas:
Mg+2H2O →Mg (OH) 2 +H2
Double replacement
In a double replacement reaction, the anions and cations of two compounds switch places and form two entirely
different compounds. These reactions are in the general form:
AB + CD → AD + CB
For example, when barium chloride (BaCl2) and magnesium sulfate (MgSO4) react, the SO4 2− anion switches places
with the 2Cl− anion, giving the compounds BaSO4 and MgCl2. Another example of a double displacement reaction
is the reaction of lead(II) nitrate with potassium iodide to form lead(II) iodide and potassium nitrate:
Pb (NO3) 2 + 2KI → PbI2 +2KNO3
199
209
experimental value – theoretical value
Percent difference from theoretical value =
magnification = power of ocular lens × power of objective lens
molar concentration =
number of moles =
percent by volume concentration =
parts per million =
theoretical value
× 100%
number of moles (mol)
volume (L)
mass (g)
molar mass (
𝑚𝑠𝑜𝑙𝑢𝑡𝑒
𝑚𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛
g
)
mol
𝑉𝑠𝑜𝑙𝑢𝑡𝑒
× 100%
𝑉𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛
× 106 ppm
1 amu = 1.66054 × 10−27 kg = 931.494 MeV/c2
1 MeV = 1.60 × 10−13 J
Particle
Electric
Atomic
Charge (C)
Charge
Protons
+1.6022 × 10-19
+1
1.6726 × 10-24
1.0073
1/2
Neutrons
0
0
1.6740 × 10-24
1.0078
1/2
Electrons
-1.6022 × 10-19
-1
9.1094 × 10-28
0.00054858
1/2
200
210
Mass (g)
Atomic Mass
Spin
(Au)
Enthalpy Formula
Enthalpy is a thermodynamic function that is equal to the total internal energy of the system plus the product of
pressure and volume. The equation is as follows:
H = E + PV
where H is the enthalpy, E is the energy and PV is the pressure multiplied by the volume.
Molality Formula
Molality (m) =
Molar Mass Formula
moles of solute
kilograms of solvent
Molar mass =
mass (grams)
Molarity Formula
Molarity (M) =
moles
moles of solute
Liters of solution
Structural Formula
Substance
Chemical Formula
Structural Formula
Methane
CH4
H
|
H−C–H
|
H
Carbon Dioxide
CO2
O=C=O
Chemical Equilibrium Formula
Equilibrium Constant (K):
K=
rate constant of forward reaction
rate constant of backward reaction
201
211
=
𝑘1
𝑘2
Equilibrium constant in terms of concentration (KC) is given by
KC =
𝑘1
𝑘2
=
[𝐶]𝑐 [𝐷]𝑑
[𝐴]𝑎 [𝐵]𝑏
Equilibrium constant in the terms of partial pressure (KP) is given by
KP =
𝑘1
𝑘2
=
[𝑃𝐶 ]𝑐 [𝑃𝐷 ]𝑑
[𝑃𝐴 ]𝑎 [𝑃𝐵 ]𝑏
The equilibrium constant is in terms of mole fraction (Kx) is given by
Kx =
𝑘1
𝑘2
=
[𝑥𝐶 ]𝑐 [𝑥𝐷 ]𝑑
[𝑥𝐴 ]𝑎 [𝑥𝐵 ]𝑏
The Relation between KP and KC is given by
KP = KC (RT) ∆n
where: Δn = (c + d) − (a + b)
Relation between equilibrium constant and standard free energy change
ΔG° = −2.303 RT log K
where:
ΔG° = standard free energy change
202
212
T = Absolute temperature
R = universal gas constant.
Normality Formula
Normality (N) =
gram equivalent weight
liter of solution
Normality (N) = Molarity (M) × number of equivalents
Photosynthesis Formula
6CO2 + 6H2O + light → C6H12O6 + 6O2
Boyle's Law Formula
P1V1 = P2V2
where:
P1 = Initial Pressure (atm or mmHg)
V1 = Initial Volume (L or mL)
P2 = Final Pressure (atm or mmHg)
V2 = Final Volume (L or mL)
Titration Formula
Macid × Vacid = Mbase × Vbase
where:
Macid = Molarity of the acid
Vacid = Volume of the acid
Mbase = Molarity of the base
Vbase = Volume of the base
Charles' Law Formula
203
213
𝑉1
𝑉2
=
𝑇1
𝑇2
where:
T1 = Initial Temperature (Kelvin - K)
V1 = Initial Volume (L or mL)
T2 = Final Temperature (Kelvin - K)
V2 = Final Volume (L or mL)
Gay-Lussac's Law Formula
𝑃2
𝑃1
=
𝑇2
𝑇1
where:
T1 = Initial Temperature (Kelvin - K)
P1 = Initial Pressure (atm or mmHg)
T2 = Final Temperature (Kelvin - K)
P2 = Final Pressure (atm or mmHg)
Dilution Formula
M1 × V1 = M2 × V2
where:
M1 = the molarity of the original solution
V1 = the volume of the original solution
M2 = the molarity of the diluted solution
V2 = the volume of the diluted solution
Heat of Fusion Formula
Hf =
𝑞
𝑚
where:
204
214
Hf = heat of fusion
q = heat
m = mass
Heat of Vaporization Formula
𝑞
Hv =
𝑚
where:
Hv = heat of vaporization
q = heat
m = mass
Lattice Energy Formula
LE =
𝑘𝑄1 𝑄2
𝑟
LE = lattice energy
k = 2.31 × 10−19 J ∙ nm
Q1 and Q2 = numerical ion charges
r = the distance between the ion centers
Mass Percent Formula
Mass percent =
𝑔𝑟𝑎𝑚𝑠 𝑜𝑓 𝑠𝑜𝑙𝑢𝑡𝑒
𝑔𝑟𝑎𝑚𝑠 𝑜𝑓 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛
× 100
Mole Fraction Formula
Mole fraction (xa) =
205
215
moles of a
total moles
a = the component that is being identified for mole fraction
Osmotic Pressure Formula
Osmotic pressure (π) = MRT
M = the molar concentration of the solution
R = the gas laws constant (0.0821
T = the Kelvin temperature
L∙atm
)
K∙mol
Electric Potential Energy Formula
Eel =
𝑘𝑄1 𝑄2
𝑑
Eel = electrostatic potential energy
k = 8.99 × 109
J−m
C2
Q1 and Q2 = electrical charges on the two particles
d = the distance between the charges
Percent Composition Formula
% composition =
𝑔𝑟𝑎𝑚𝑠 𝑜𝑓 𝑒𝑙𝑒𝑚𝑒𝑛𝑡
𝑔𝑟𝑎𝑚𝑠 𝑜𝑓 𝑐𝑜𝑚𝑝𝑢𝑛𝑑
Rate of Decay Formula
Nt = N0 e−λt
206
216
× 100
Nt = the amount of radioactive particles at time (t)
N0 = the amount of radioactive particles at time = 0
λ = rate of decay constant
t = time
Specific Heat Capacity Formula
s=
s = specific heat capacity
𝑞
𝑚 × ∆𝑇
q = heat
m = mass
Δ T = change in temperature
Vapor Pressure Formula
Psolution = xsolvent × Posolvent
Psolution = the vapor pressure of the solution
xsolvent = the mole fraction of the solvent in the solution
Posolvent = the vapor pressure of the pure solvent at standard conditions
Degree of unsaturation Formula
Degrees of unsaturation =
(2 × #𝐶) + 2 + #𝑁 −#𝐻 −#𝑋
2
where #C, #N, #H, #X mean the number of carbon, nitrogen, hydrogen and halogen atoms present in the molecular
formula.
Arrhenius equation
207
217
−𝐸𝑎
k = A 𝑒 𝑅𝑇
where:
A is the pre-exponential factor for the reaction (that is nearly a constant that depends on the temperature), Ea is the
activation energy, R is the gas constant, T is the temperature and k is the reaction rate constant.
Boiling point Formula
ΔHvap = Hvapor − Hliquid
where:
ΔHvap is the change of enthalpy of vaporization, H vapor is the enthalpy or heat of the gas state of a compound and
Hliquid is the enthalpy of the liquid state of a compound.
Avogadro's law Formula
V=k×n
where:
V is the gas volume, n is the number of moles of gas and k is a constant, which is defined as
𝑅𝑇
𝑃
, where R is a
constant called the constant of the gases (8.314 JK−1 mol−1), T is the temperature in Kelvin and P is the pressure.
Dalton's law Formula
For a mixture of n gases, the total pressure is:
Ptotal =P1 + P2 + P3 + ... + Pn
where P1, P2, P3 ... Pn represent the partial pressure of each gas in the mixture.
Ionic strength formula
208
218
Ionic strength (I) =
where:
1
2
∑𝑛1 𝐶𝑖 𝑧𝑖2
Ci – ionic concentration
Zi – ion charges
Calculate the ionic strength of KCl if its concentration is 2 M.
Ions
Z
C
Z2
K+
1
2
1
Cl–
1
2
1
The ionic strength is given by
I=
1
2
[(2 × 1) + (2 × 1)] = 2
Percent by volume Formula
% volume =
𝑣𝑜𝑙𝑢𝑚𝑒𝑠𝑜𝑙𝑢𝑡𝑒
𝑣𝑜𝑙𝑢𝑚𝑒𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛
× 100%
pOH
pOH = − log [OH−]
For any aqueous solution at 25oC:
pH + pOH = 14
Complete List of Inorganic Acids
Acid Name
Formula
Acetic Acid
CH3COOH
209
219
Antimonic Acid
HSbO3
Antimonous Acid
H3SbO3
Arsenic Acid
H3AsO4
Boric Acid
H3BO3
Bromic Acid
HBrO3
Bromous Acid
HBrO2
Carbonic Acid
H2CO3
Carbonous Acid
H2CO2
Chloric Acid
HClO3
Chlorous Acid
HClO2
Chromic Acid
H2CrO4
Chromous Acid
H2CrO3
Citric Acid
C6H8O7
Cyanic Acid
HCNO
Dichromic Acid
H2Cr2O7
Disulfurous Acid
H2S2O5
Dithionous Acid
H2S2O4
Diuranic Acid
H2U2O7
Ferricyanic Acid
H3[F3(CN)6]
Fluoric Acid
HFO3
Fluorous Acid
HFO2
Formic Acid
HCOOH
Hydroarsenic Acid
H3As
Hydrobromic Acid
HBr
Hydrochloric Acid
HCl
Hydrocyanic Acid
HCN
Hydrofluoric Acid
HF
Hydroiodic Acid
HI
Hydronitric Acid
HN3
Hydrophosphoric Acid
H3P
Hydroselenic Acid
H2Se
Hydrosulfuric Acid
H2S
Hypobromous Acid
HBrO
Hypocarbonous Acid
H2CO
Hypochlorous Acid
HClO
Hypochromous Acid
H2CrO2
Hypofluorous Acid
HFO
210
220
Hypoiodous Acid
HIO
Hyponitrous Acid
HNO
Hypooxalous Acid
H2C2O2
Hypophosphoric Acid
H4P2O6
Hypophosphous Acid
H3PO2
Hyposulfurous Acid
H2SO2
Iodic Acid
HIO3
Iodous Acid
HIO2
Manganic Acid
H2MnO4
Metastannic Acid
H2SnO3
Molybdic Acid
H2MoO4
Nitric Acid
HNO3
Nitrous Acid
HNO2
Oxalic Acid
H2C2O4
Percarbonic Acid
H2CO4
Perchloric Acid
HClO4
Perchromic Acid
H2CrO5
Perfluoric Acid
HFO4
Periodic Acid
HIO4
Permanganic Acid
HMnO4
Pernitric Acid
HNO4
Peroxydisulfuric Acid
H2S2O8
Perphosphoric Acid
H3PO5
Persulfuric Acid
H2SO5
Pertechnetic Acid
HTcO4
Perxenic Acid
H4XeO6
Phosphoric Acid
H3PO4
Phosphorous Acid
H3PO3
Pyroantimonic Acid
H4Sb2O7
Pyrophosphoric Acid
H4P2O7
Pyrosulfuric Acid
H2S2O7
Selenic Acid
H2SeO4
Selenous Acid
H2SeO3
Silicic Acid
H2SiO3
Silicofluoric Acid
H2SiF6
Silicous Acid
H2SiO2
Sulfuric Acid
H2SO4
211
221
Sulfurous Acid
H2SO3
Telluric Acid
H6TeO6
Tellurous Acid
H2TeO3
Tetraboric Acid
H2B4O7
Tetrathionic Acid
H2S4O6
Thiocyanic Acid
HSCN
Thiosulfurous Acid
H2S2O2
Titanic Acid
H2TiO3
Tungstic Acid
H2WO4
Uranic Acid
H2UO4
Xenic Acid
H2XeO4
Complete List of Organic Acids
Acid Name
Formula
Acetylsalicylic Acid
HC9H7O4
Ascorbic Acid
HC6H7O6
Azelaic Acid
H2C9H14O4
Barbituric Acid
HC4H3N2O3
Benzilic Acid
HC14H11O3
Cinnamic Acid
C9H8O2
Citric Acid
H2C6H6O7
Folic Acid
C19H19N7O6
Fumaric Acid
C4H4O4
Gallic Acid
HC7H5O5
Gluconic Acid
C6H12O7
Glutamic Acid
HC5H8NO4
Glutaric Acid
C5H8O4
Hexanoic Acid
C5H11COOH
Lactic Acid
HC3H5O3
Malic Acid
H2C4H4O5
Malonic Acid
CH2(COOH)2
Oleic Acid
HC18H33O2
Phthalic Acid
H2C8H4O4
Propiolic Acid
HC2COOH
212
222
Propionic Acid
CH3CH2COOH
Rosolic Acid
C19H14O3
Stearic Acid
C17H35COOH
Tannic Acid
C76H52O46
Tartartic Acid
H2C4H4O6
Trifluoroacetic Acid
C2HF3O2
Uric Acid
H2C5H2N4O3
Physics Formulas
Acceleration Formula
a=
𝑣𝑓 − 𝑣𝑖
𝑡
a = acceleration (m/s2)
=
∆𝑣
𝑡
vf = the final velocity (m/s)
vi = the initial velocity (m/s)
t = the time in which the change occurs (s)
Δv = short form for "the change in" velocity (m/s)
Force Formula
Force = mass × acceleration
F=m×a
Frequency Formula
Frequency, the cycles in a unit of time =
Frequency =
𝟏
period, the time required for one cycle
number of cycles
𝑡𝑖𝑚𝑒
Velocity Formula
Velocity =
𝑓𝑖𝑛𝑎𝑙 𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛−𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛
𝑡𝑖𝑚𝑒
213
223
=
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑡ℎ𝑒 𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛
𝑡𝑖𝑚𝑒
Wavelength Formula
Wavelength =
frequency
Angular Velocity Formula
Angular velocity =
wave velocity
𝑓𝑖𝑛𝑎𝑙 𝑎𝑛𝑔𝑙𝑒 − 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑎𝑛𝑔𝑙𝑒
𝑡𝑖𝑚𝑒
=
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛
𝑡𝑖𝑚𝑒
Displacement Formula
Displacement = (final position) − (initial position) = change in position
Density Formula
Density =
mass
volume
Kinematic Equations Formula
1
D = vi t + at2
2
vf 2 = vi 2 + 2aD
vf = vi + at
D = displacement
a = acceleration
t = time
vf = final velocity
vi = initial velocity
214
224
The heaviest element is a hard, brittle, bluish-white transition metal
in the platinum group (osmium)
Approximately 20% of our body is carbon.
Lightning can reach temperature greater than
30,000 degrees Celsius.
The hardest substance in the human body is enamel (made mostly of an
extremely hard mineral called calcium phosphate)
Rotten eggs float in water
Glass is an amorphous solid that lacks an ordered internal structure
Water is blue because it absorbs colors in the red part of the light
spectrum
Dry ice is the solid form of carbon dioxide (CO2)
If we were to urinate in space, it would vaporize and turn into a gas immediately
215
Tangential Velocity Formula
Vt = ω r
Vt = tangential velocity
ω = angular velocity
r = radius of wheel
Kinetic Energy Formula
1
Ek = mv2
2
Ek = Kinetic energy
m = mass
v = velocity
Buoyancy Formula
Fb = ρgV = ρghA
Fb = buoyant force of a liquid acting on an object (N)
ρ = density of the liquid (kg/m3)
g = gravitational acceleration (9.8 m/s2)
V = volume of liquid displaced (m3 or liters, where 1 m3 = 1000 L)
h = height of water displaced by a floating object (m)
A = surface area of a floating object (m2)
Efficiency Formula
Efficiency =
Static Friction Formula
𝑒𝑛𝑒𝑟𝑔𝑦 𝑜𝑢𝑡𝑝𝑢𝑡
𝑒𝑛𝑒𝑟𝑔𝑦 𝑖𝑛𝑝𝑢𝑡
Fs ≤ μs η
Fsmax = μs η
216
225
× 100%
Fs = force of static friction
μs = coefficient of static friction
η = normal force
Fsmax = maximum force of static friction
Potential Energy: Elastic Formula
1
U = kx2
2
U = potential energy of a spring at a certain position
k = the spring constant, specific to the spring, with units N/m.
x = distance the spring is stretched or compressed away from equilibrium
Tangential Acceleration Formula
Tangential acceleration = radius of the rotation × angular acceleration
Potential Energy: Earth's Gravity Formula
Potential energy = mass of the object × acceleration due to gravity × height
Potential Energy: Electric Potential Formula
Potential energy = charge of particle × electric potential
Potential Energy: Two-Body Gravitation Formula
U=−
𝐺𝑚1 𝑚2
217
226
𝑟
U = potential energy of gravity between two objects
G = the universal gravitational constant, G = 6.673 × 10−11 (Nm2) / kg2
m1 = mass of one of the objects
m2 = mass of the second object
r = the distance between the centers of mass of the two objects
Potential Energy: Electrostatic Point Particles Formula
U=−k
𝑞1 𝑞2
𝑟
U = potential energy of electrostatic point particles
k = the Coulomb constant, k = 8.99 × 109 Nm2/C2 =
1
4𝜋𝜀0
ϵ0 = the permittivity of free space, ϵ0 = 8.854 x 10−12 C2/ (Nm2)
q1 = charge of one of the point particles
q2 = charge of the other point particle
r = distance between the two point charges
Doppler Shift Formula
f=
f = frequency heard by listener
𝑓𝑠 (𝑣+ 𝑣𝐿 )
(𝑣 − 𝑣𝐿 )
for sound
fs = frequency of the source
v = velocity of sound
vs = velocity of the source (positive if moving towards listener, negative if moving away from listener)
vL = velocity of listener (positive if moving toward the source, negative if moving away from the source)
Current Density Formula
J=
I
A
218
227
J = current density in amperes/m2
I = current through a conductor (in amperes)
A = cross-sectional area of the conductor (m2)
Heat Transfer Formula
Heat transfer = mass × specific heat × temperature change
Centripetal Force Formula
Fc =
𝑚𝑣 2
𝑟
Fc = centripetal force
m = mass
v = velocity
r = radius of circular path
Kelvin to Celsius Formula
K = °C + 273.15
K = temperature, Kelvin
°C = temperature, degrees Celsius (Centigrade)
Acceleration Due to Gravity Formula
g=
𝐺𝑚
𝑟2
g = acceleration due to gravity (units m/s2)
G = the universal gravitational constant, G = 6.673 ×10−11 (Nm2) / kg2
219
228
m = mass of a large body (for example, Earth)
r = the distance from the center of mass of the large body
Momentum Formula
Momentum = mass × velocity
Power Formula
Power =
𝑡𝑖𝑚𝑒 𝑖𝑛𝑡𝑒𝑟𝑣𝑎𝑙
Specific Gravity Formula
Specific gravity =
𝑤𝑜𝑟𝑘 𝑑𝑜𝑛𝑒
density of the substance
density of water at 4.0°C
Torque Formula (Moment of Inertia and Angular Acceleration)
Torque = moment of inertia × angular acceleration
Spring Constant Formula
F = −kx
F = restoring force of the spring (directed toward equilibrium)
k = spring constant (units N/m)
x = displacement of the spring from its equilibrium position
Amplitude Formula
x = A sin (ωt + ϕ)
220
229
x = displacement (m)
A = amplitude (m)
ω = angular frequency (radians/s)
t = time (s)
ϕ = phase shift (radians)
Torque Formula (Force at a Distance)
Torque = (distance between a center of rotation and a force) × force
Tension Formula
T = mg + ma
T = tension, N, kg-m/s2
m = mass, kg
g = gravitational force, 9.8 m/s2
a = acceleration, m/s2
Centripetal Acceleration Formula
ac =
𝑣2
𝑟
ac = centripetal acceleration
v = velocity
r = radius of circular path
Impulse Formula
Impulse = Force × time
Capacitance Formula
221
230
C=
Q
V
C = capacitance (Farads, F)
Q = the charge built up on the capacitor (Coulombs, C)
V = voltage difference between two sides of a capacitor (Volts, V)
Distance Speed Time Formula
Distance = speed × time
Orbital Velocity Formula
vorbit = √
GM
R
G = gravitational constant,
M = mass of the body at centre,
R = radius of the orbit.
Resistance Formula
R=
V
I
R = resistance (Ohms, Ω)
V = voltage difference between the two ends of a resistor (Volts, V)
I = the current flowing through a resistor (Amperes, A)
222
231
Reynold's Number Formula
Reynold's Number =
Reynold's Number =
inertial force
viscous force
density × velocity ×diameter
viscosity
Angular Momentum Formula
Angular momentum = (distance from the center of rotation) × linear momentum
Unit Vector Formula
Unit vector =
vector
magnitude of the vector
Work Formula
W = Fd cosθ
W = work (units J)
F = force (units N)
d = distance (m)
θ = the angle between the force direction and movement direction
Air Resistance Formula
F = kv2 =
𝜌 𝐶𝐷 𝐴
223
232
2
v2
F = force due to air resistance, or drag (N)
k = a constant that collects the effects of density, drag, and area (kg/m)
v = the velocity of the moving object (m/s)
ρ = the density of the air the object moves through (kg/m3)
CD = the drag coefficient, includes hard-to-measure effects (unitless)
A = the area of the object the air presses on (m2)
Angular Momentum Formula (Moment of Inertia and Angular Velocity)
Angular Momentum = moment of inertia × angular velocity
Center of Mass Formula
Center of Mass =
sum of all (position × mass)
sum of all masses
Flow Rate Formula
Q = Av
Q = liquid flow rate (m3/s or L/s)
A = area of the pipe or channel (m2)
v = velocity of the liquid (m/s)
Stopping Distance Formula
d=
𝑣2
2𝜇𝑔
d = stopping distance (m)
v = velocity of the car (m/s)
μ = coefficient of friction (unitless)
g = acceleration due to gravity (9.8 m/s2)
224
233
Escape Velocity Formula
G = universal gravitational constant
escape velocity = √
2𝐺𝑀
𝑅
M = mass of the planet (kg)
R = radius of the planet (m)
Inelastic Collision Formula
(mass of object 1) (initial velocity 1) + (mass of object 2) (initial velocity 2) = (mass of object 1 + mass of
object 2) (final velocity of combined objects)
Newton's Law of Cooling Formula
T(t) = Ts + (T0 - Ts) e−kt
T(t) = temperature of an object at a certain time (Kelvin, K)
t = time (s)
Ts = temperature of the surroundings (Kelvin, K)
T0 = starting temperature of the object (Kelvin, K)
k = a cooling constant, specific to the object (1/s)
Pressure Formula
𝐹
Pressure = , where F is a force, and A is the area it acts on.
𝐴
P = ρgh
P = pressure (Pa)
ρ = density of a gas or fluid (kg/m3)
g = acceleration due to gravity (9.8 m/s2)
h = the height of a column of gas or fluid (m)
225
234
De Broglie Wavelength Formula
de Broglie wavelength =
The Planck constant
momentum
=
The Planck constant
mass × velocity
Horizontal Range Formula
R=
v20 sin2θ
g
R = horizontal range (m)
v0 = initial velocity (m/s)
g = acceleration due to gravity (9.8 m/s2)
θ = angle of the initial velocity from the horizontal plane (radians or degrees)
Maximum Height Formula
H=
v20 sin2 θ
2g
H = maximum height (m)
v0 = initial velocity (m/s)
g = acceleration due to gravity (9.8 m/s2)
θ = angle of the initial velocity from the horizontal plane (radians or degrees)
Rotational Kinetic Energy Formula
rotational kinetic energy =
1
2
(moment of inertia) × (angular velocity) 2
Strain Formula (general form)
226
235
strain =
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛
𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛
Time of Flight Formula
t=
2v0 sinθ
g
t = time of flight (s)
v0 = initial velocity (m/s)
g = acceleration due to gravity (9.8 m/s2)
θ = angle of the initial velocity from the horizontal plane (radians or degrees)
Trajectory Formula
y = x tanθ −
g𝑥 2
2v20 cos2 θ
y = vertical position (m)
x = horizontal position (m)
v0 = initial velocity (combined components, m/s)
g = acceleration due to gravity (9.8 m/s2)
θ = angle of the initial velocity from the horizontal plane (radians or degrees)
Capacitors in Parallel Formula
Ceq = C1 + C2 + C3 + …
Ceq = equivalent capacitance (F)
C1 = capacitance of first capacitor (F)
C2 = capacitance of second capacitor (F)
C3 = capacitance of third capacitor (F)
227
236
Capacitors in Series Formula
1
=
Ceq
1
C1
+
1
C2
+
1
C3
+ ….
Ceq = equivalent capacitance (F)
C1 = capacitance of first capacitor (F)
C2 = capacitance of second capacitor (F)
C3 = capacitance of third capacitor (F)
Electric Power Formula
electric power = voltage difference × current
Resistors in Parallel Formula
1
Req
=
1
R1
+
1
R2
+
1
R3
+ ….
Req = equivalent resistance (Ω)
R1 = resistance of first resistor (Ω)
R2 = resistance of second resistor (Ω)
R3 = resistance of third resistor (Ω)
Resistors in Series Formula
Req = R1 + R2 + R3 + …
Req = equivalent resistance (Ω)
R1 = resistance of first resistor (Ω)
228
237
R2 = resistance of second resistor (Ω)
R3 = resistance of third resistor (Ω)
Length Contraction Formula
observed length = proper length √1 −
velocity 2
speed of light 2
Snell's Law Formula
sin i
sin r
where:
= constant = n
i is the angle of incidence and r is the angle of refraction. This constant value is called the refractive index of the
second medium with respect to the first.
n1 sinθ1 = n2 sinθ2
n1 and n2 are the two different mediums that will impact the refraction.θ1 is the angle of incidence; θ2 is the angle of
refraction.
Time Dilation Formula
observer time =
proper time
√1−
velocity 2
speed of light 2
Kirchhoff's Junction Rule Formula
sum of the currents in and out of a circuit junction = 0
∑I=0
I = current, (Amperes, A)
Kirchhoff's Loop Rule Formula
229
238
sum of voltage differences around a circuit loop = 0
∑V=0
V = voltage difference, (Volts, V)
Decibel Formula
β = 10 decibels × log
I
I0
β = sound intensity, in decibels (dB)
I = sound intensity (W/m2)
I0 = reference sound intensity (10 −12 W/m2)
Einstein's Mass-Energy Equivalence Formula
Energy = mass × (speed of light) 2
Kinetic Energy of Gas Formula
3
<KE> = kBT
2
<KE> = average kinetic energy per molecule of gas (J)
kB = Boltzmann's constant (1.38 × 10−23 J/K)
T = temperature (K)
Impulse-Momentum Theorem Formula
Impulse = final momentum − initial momentum
230
239
Magnetic Field Formula
B=
B = magnetic field magnitude (Tesla, T)
μ0 I
2πr
μ0 = permeability of free space (4π × 10−7 Tm/A)
I = magnitude of the electric current (Amperes, A)
r = distance (m)
Parallel Axis Theorem Formula
IP = Icm + Md2
IP = moment of inertia for rotation around a parallel axis (kg∙m2)
Icm = moment of inertia for rotation around an axis through the center of mass (kg∙m2)
M = total mass of the object (kg)
d = distance between the two rotation axes (m)
Bernoulli's Equation Formula
1
P + ρ v2 + ρ g h = constant
2
P is the pressure exerted by the fluid
v is the velocity of the fluid
ρ is the density of the fluid
h is the height of the container
g is the acceleration due to gravity
Drag Formula
1
FD = ρ v2 CD A
2
FD: Drag force
231
240
ρ: fluid density
v: Relative velocity between the fluid and the object
CD: Drag coefficient
A: Transversal area or cross sectional area
Dynamic Viscosity Formula
Dynamic viscosity =
Shear rate
Kinematic Viscosity Formula
Kinematic viscosity =
Shearing stress
Dynamic viscosity
Fluid mass density
Mass Flow Rate Formula
m=ρvA
ρ: Density of the fluid
v: Velocity of the fluid
A: Area of the cross section
Volume Flow Rate Formula
Volume Flow Rate =
variation of volume
variation of time
Pressure in a Fluid Formula
P=ρgh
232
241
ρ: Density of the fluid
g: Acceleration of gravity
h: Depth of the fluid
Bulk modulus Formula
Bulk modulus =
change in volume / original volume
Froude number Formula
Froude number =
change in pressure
Velocity of the fluid
√gravitational acceleration × depth of flow
Latent Heat Formula
Q=mL
Q: Latent heat
m: Mass of the body
L: Specific latent heat coefficient of the material
Liquid Expansion Formula
ΔL= L α ΔT
ΔL: Expansion of the liquid
L: Length of the liquid before the change of temperature
ΔT: Change of the temperature
α: Coefficient of expansion of the liquid
Shear modulus Formula
233
242
Shear modulus =
shear stress
Entropy Formula
strain
S= kB ln Ω
S: Entropy
kB: Boltzmann constant. (1.38 ×10 −23 J/ K)
Ω: number of microstates.
Surface tension Formula
γ=
γ: Surface tension
F
d
F: Force applied on the liquid
d: length along which the force acts
Heat Flow Rate Formula
Heat flow = −
heat transfer coefficient × area of the emitting body × variation of the temperature
length of the material
Maxwell-Boltzmann Distribution Formula
f=
1
exp(−𝐸 /𝑘𝐵 𝑇)
f: Energy distribution
E: energy of the system
kB: Boltzmann constant
T: Absolute Temperature in Kelvin.
234
243
Molecular Speed Formula
v=√
3RT
m
v: molecular speed
R: Ideal gas constant
T: Absolute Temperature in Kelvin.
m: molar mass
Stephan-Boltzmann Law Formula
P = є σ T4 A
P: total power radiated
σ: The Stefan-Boltzmann Constant
T: absolute temperature in Kelvin
є: Emissivity of the material.
A: Area of the emitting body
Thermodynamic Work Formula
Thermodynamic work = number of moles × ideal gas constant × change of temperature
Wien Displacement Law Formula
λmax=
λmax: The peak of the wavelength
b
T
b: Wien's displacement constant (2.9 × 10−3 m K)
T: Absolute Temperature in Kelvin
Capacitor potential energy Formula
235
244
U=
1
2
C V2
C: Capacitance
V: Voltage
U: Energy stored in the capacitor
Period of a Pendulum Formula
T = 2π √
L
g
where L represents the length of the pendulum and g is the value of the acceleration of gravity.
Work done by gravity Formula
W=m×g×h
W = work done by gravity
m = mass
g = gravitational acceleration
h = height
Weight Formula
Weight = mass × gravitational acceleration
Inductance Formula
L=
ΦN
I
236
245
L = Inductance
Φ = Magnetic flux
N = Number of coil turns
I = current intensity
Resonant Frequency Formula
fr =
1
2𝜋√LC
fr: resonant frequency
L: Inductance.
C: capacitance.
Intensity Formula
I=
P
S
I = Intensity
P = power
S = surface perpendicular to the direction of propagation
Voltage divider Formula
Vout =
𝑍𝑖
𝑛
∑𝑖=1 𝑍𝑖
Vin
Vout = output voltage.
Zi = generic impedance.
∑𝑛𝑖=1 𝑍𝑖 = the sum from the first to the nth impedance of the circuit.
Vin = input voltage.
237
246
Transformer Formula
Vp × Ip = Vs × Is
Vp
Vs
=
np
ns
Vp = input voltage on the primary coil.
Vs = input voltage on the secondary coil.
Ip = input current on the primary coil.
Is = input current on the secondary coil.
np = number of turns of wire on the primary coil.
ns = number of turns of wire on the secondary coil.
Speed of sound Formula
γP
v=√
v = speed of sound.
ρ
γ = the coefficient of adiabatic expansion.
P = the pressure of the gas.
ρ = the density of the medium.
Sound intensity Formula
sound intensity =
acoustic power
normal area to the direction of propagation
Friction loss Formula
Q 2
L
FL = C × [
] ×
100
100
238
247
FL = friction loss.
C = friction loss coefficient.
Q = flow rate.
L = hose length.
Archimedes Principle Formula
push = density of fluid × gravitational acceleration × volume of object
Uncertainty Principle Formula
Δx Δp ≤≥
ℏ
ΔE Δt ≤≥
ℏ
2
2
ℏ: reduced Planck's constant
Δx: Position uncertainty
Δp: Momentum uncertainty
ΔE: Energy uncertainty
Δt: Time uncertainty
Rydberg Formula
1
λ
=R[
1
𝑛12
R: Rydberg's constant (R=1.097 × 107 m−1)
λ: Wavelength of the emitted photon
n1 and n2 are integers and n2 is always greater than n1
248
239
−
1
𝑛22
]
Half-Life Formula
ln(2)
t1/2 =
λ
λ: disintegration constant of the system
t1/2: Half life time
Relativistic Momentum Formula
Relativistic momentum =
velocity 2
speed of light 2
rest mass
√1−
velocity 2
speed of light 2
Relativistic Energy Formula
Relativistic energy =
√1−
Relativistic Mass Formula
Relativistic mass =
rest mass × velocity
rest mass × speed of light squared
√1−
velocity 2
speed of light 2
Relativistic Doppler Effect Formula
𝑣
1+ 𝑐
frequency observed = frequency emitted × √
𝑣
1− 𝑐
c: speed of light
v: velocity of the observer respect to the source
240
249
Relative Velocity Formula
vAB = vA – vB
vAB: relative velocity of the body A respect body B
vA: velocity of the body A
vB: velocity of the body B
Photon Energy Formula
E=
hc
λ
E: photon's energy
h: Plank's constant
λ: photon's wavelength
c: speed of light
Photoelectric Effect Formula
photon energy = work function + electron kinetic energy
Energy momentum Formula
E = √p 2 c 2 + (m0 c 2 )2
E: Energy
p: momentum
c: speed of light
m0: rest mass
Ampere's Law Formula
∫B∙dl = μ0I
241
250
B: magnetic field
dl: infinitesimal segment of the integration path
μ0: vacuum permeability
I: enclosed electric current by the path
Motional Electromotive Force Formula
EMF = v × B × L
EMF: Electromotive force
v: Velocity of the charge
B: Magnetic field
L: Length of the wire where the charge is moving
Magnetic Flux Formula
Magnetic flux = Magnetic field × Area × (angle between the planar area and the magnetic flux)
Induced Electromotive Force Formula
EMF = −
ΔΦ
EMF: Electromotive force
ΔΦ: Change of the magnetic flux
Δt: change in time
Gauss's Law
Φ=
Q
ε0
242
251
Δt
Φ: Electric flux
Q: Enclosed charge by the surface
ϵ0: absolute permittivity
Electric Flux Formula
Φ = E A cosθ
Φ: Electric Flux
A: Area
E: Electric field
θ: angle between a perpendicular vector to the area and the electric field
Spherical mirror Formula
1
object distance
+
image distance
Focal length ≈
1
1
focal length
curvature radius
2
Resistivity-Conductivity Formula
Resistivity =
=
1
conductivity
Image size Formula
image height
object height
243
252
=−
image distance
object distance
Electric resistance Formula
R=ρ
L
A
R: Electric Resistance
ρ: Resistivity
L: Length of the material
A: cross sectional area of the material
Moment of Inertia Formula (common shapes)
Object Type
Formula
Thin rod, axis through the center
I=
1
12
ML2
1
Thin rod, axis through one end
I = ML2
3
Rectangular plate, axis through center
I=
1
12
M (a2 + b2)
1
Rectangular plate, axis along edge
I = Ma2
3
Hollow cylinder, with a wall thickness
1
I = M (R12 + R22)
2
1
Solid cylinder
I = MR2
2
244
253
Thin-walled hollow cylinder
I = MR2
Solid sphere
2
I = MR2
5
2
Thin-walled hollow sphere
I = MR2
3
I = moment of inertia (kg∙m2)
M = total mass of the rotating object (kg)
L = the total length of the rod (m)
a = the length of two sides of the plate (m)
b = the length of the other two sides of the plate (m)
R1 = the inner radius of the cylinder (m)
R2 = the outer radius of the cylinder (m)
R = the radius of the cylinder or sphere (m)
Rotational Kinematics Formula
ω = ω0 + αt
1
θ = θ0 + ω0t + 2 αt2
ω2 = ω02 + 2α (θ − θ0)
1
θ − θ0 = 2 (ω0 + ω)t
θ0 is initial angle
θ is final angle
t is the time interval
ω0 is initial angular velocity
ω is final angular velocity
α is angular acceleration
245
254
Electric Field
E=
𝐹
𝑞
E = Electric field (N/C)
F = Force (N)
q = charge (C)
Kepler's Third Law
𝐺𝑀
𝑟3
=
2
4𝜋 2
𝑇
r = radius of motion (m)
T = period of motion (s)
G = universal gravitation constant (6.673 × 10-11 Nm2 kg−2)
M = M1+M2 = total mass of system (kg)
Magnetic force on a current-carrying wire of length L in a magnetic field
F=B×I×L
F = force (N)
B= Magnetic Field (T)
I = current (A)
L = length (m)
Force per unit length
246
255
II
F
k 1 2
d
l
F = force (N)
l = length (m) per unit
I1, I2 = two currents
d = separation of the two currents (m)
k = magnetic constant (2 × 10−7 NC−1m−1)
Torque on a coil immersed in a magnetic field
= n× B× I× A× cosθ
= torque (Nm)
n = number of turns of coil
B = magnetic field (T)
I = current (A)
A = area of coil immersed in magnetic field (m2)
cosθ = angle between the coil and the magnetic field
Magnetic force on a charge in a magnetic field
F = q × v × B × sinθ
F = force (N)
q = charge (C)
v = velocity (m/s)
B = magnetic field (T)
sinθ = angle between the velocity and the magnetic field
247
256
Acoustic Impedance
Z=ρ×v
Z = Acoustic impedance
ρ = acoustic density
v = speed of sound in medium
Astronomical Distance
M m 5 log(
d
)
10
M = absolute magnitude
m = relative magnitude
d = distance in parsecs
Amplifier Gain
Amplifier Gain =
Vout
Vin
Vout = output voltage (V)
Vin = input voltage (V)
Amplifier Gain =
output voltage
positive input voltage − negative input voltage
248
257
Water expands as it freezes due to the hydrogen bonding in the water.
The taste cells in our taste buds live for only about two weeks.
There are 10 times more bacterial cells in our
body than human cells.
The human brain (made up of more than 100 billion nerves
that communicate in trillions of connections) uses just as
much power as a 10-watt light bulb.
An adult is made up of 7 octillion atoms.
We spend about five years of our lives eating.
Adult humans spend about 33% of their lives asleep. A python spends
about 75% of their life, and a dog spends about 44%.
We will eat approximately 35 tons of food in our lifetime.
Emetophobia → The fear of vomiting
Bromidrophobia → The fear of body odors
On average, a person will blink approximately about 12,000 times a day.
249
Percentage uncertainty (%) =
absolute uncertainty
measurement
×100
Heating processes
Latent heat of fusion for water
Lf = 3.34 × 105 J kg −1
Latent heat of vaporization for water
LV = 2.26 × 106 J kg −1
ci = 2.05 × 103 J kg −1 K −1
Specific heat capacity of ice
Specific heat capacity of steam
cs = 2.00 × 103 J kg −1 K −1
Specific heat capacity of water
cw = 4.18 × 103 J kg −1 K −1
Electrical circuits
Charge on an electron
𝑒 = −1.60 × 10−19 C
Waves
Speed of sound in air at 25 °C
ws = 346 m s−1
List of Phytochemicals
Phytochemicals
Carotenoids
(beta‐carotene, lycopene,
lutein, zeaxanthin)
Plant Source
Uses
Red, orange and green fruits and
May inhibit cancer cell
vegetables including broccoli,
growth, work as
carrots, cooked tomatoes, leafy
antioxidants and improve
greens, sweet potatoes, winter
immune response
squash, apricots, cantaloupe,
oranges and watermelon.
Flavonoids
(anthocyanins, quercetin)
Apples, citrus fruits, onions, soybeans
May inhibit inflammation
and soy products (tofu, soy milk,
and tumor growth; may
edamame, etc.), coffee and tea
aid immunity and boost
production of detoxifying
250
258
enzymes in the body
Indoles and Glucosinolates
(sulforaphane)
Cruciferous vegetables (broccoli,
May induce detoxification of
cabbage, collard greens, kale,
carcinogens, limit
cauliflower and Brussels sprouts)
production of
cancer‐related hormones,
block carcinogens and
prevent tumor growth
Inositol
(phytic acid)
Bran from corn, oats, rice rye and
May retard cell growth and
wheat, nuts, soybeans and soy
work as antioxidant
products (tofu, soy milk, edamame,
etc.)
Isoflavones
Soybeans and soy products (tofu,
May inhibit tumor growth,
soy milk, edamame, etc.)
limit production of
(daidzein, genistein)
cancer‐related hormones and
generally work as
antioxidant
Isothiocyanates
Cruciferous vegetables (broccoli,
May induce detoxification of
cabbage, collard greens, kale,
carcinogens, block tumor
cauliflower and Brussels sprouts)
growth and work as
antioxidants
Polyphenols
(ellagic acid, resveratrol)
Green tea, grapes, wine, berries,
May prevent cancer
citrus fruits, apples, whole grains
formation, prevent
and peanuts
inflammation and
work as antioxidants
Terpenes
Cherries, citrus fruit peel, rosemary
May protect cells from
becoming cancerous, slow
(perillyl alcohol, limonene,
cancer cell growth,
carnosol)
strengthen immune
function, limit production
of cancer‐related
hormones, fight viruses,
work as antioxidant
251
259
Refractive index =
real depth
apparent depth
Conics
Ellipse
𝑥2
Standard
form
𝑎2
+
Asymptotes
𝑦2
𝑏2
Parabola
𝑥2
y2 = 4ax
=1
Hyperbola
𝑎2
none
−
𝑥
none
𝑎
𝑦2
𝑏2
𝑦
|𝑎ℎ+𝑏𝑘+𝑐|
The acute angle between lines with gradients m1 and m2 is tan−1 |
The resolved part of a in the direction of b is
The point dividing AB in the ratio λ : μ is
1 atm =1.01×105 Nm−2 =101kPa = 760mmHg
1 radian (rad) =
1 parsec (pc) = 3.26 light year
If y = a ± b then Δy = Δa + Δb
If y =
ab
c
then
180o
π
∆𝑦
𝑦
=
∆𝑎
𝑎
+
∆𝑏
𝑏
+
∆𝑐
𝑐
252
260
λ+ μ
x = 0, y = 0
=±𝑏
The perpendicular distance from (h, k) to ax + by + c = 0 is
μa+λb
xy = c2
=1
𝑎 ∙𝑏
|𝑏|
Rectangular
hyperbola
√𝑎2 +𝑏2
𝑚1 −𝑚2
1+ 𝑚1 𝑚2
|
Star Colors and Corresponding Approximate Temperatures
Star Color
Approximate Temperature
Example
Blue
25,000 K
Spica
White
10,000 K
Vega
Yellow
6000 K
Sun
Orange
4000 K
Aldebaran
Red
3000 K
Betelgeuse
total scattered power
Albedo =
dose equivalent = absorbed dose × quality factor
For small angle θ, measured in radians:
total incident power
sinθ ≈ θ
cosθ ≈ 1 –
tanθ ≈ θ
θ2
2
Constructive interference:
path difference = nλ
Destructive interference:
1
T = 2π √
𝑚
path difference = ( n + 2 ) λ
𝑘
T is the time period of motion
k is the spring constant
m is the mass attached to the spring
253
261
Nitrogen Base
Classification
Abbreviation
Adenine
Purine
A
Guanine
Purine
G
Pyrimidine
C
Cytosine
Thymine
Uracil
Pyrimidine
Pyrimidine
Abbreviations for Some Hormones
Hormone
Abbreviation
Adrenocorticotropic hormone
ACTH
Antidiuretic hormone
ADH
Follicle-stimulating hormone
FSH
Gonadotropin-releasing hormone
GnRH
Human chorionic gonadotropin
hCG
Human growth hormone
hGH
Luteinizing hormone
LH
Parathyroid hormone
PTH
Prolactin
PRL
Thyroid-stimulating hormone
TSH
254
262
T
U
Statistical Analysis
𝑥̅ =
1
𝑛
∑𝑛𝑖=1 𝑥𝑖
s=√
∑(𝑥𝑖 − 𝑥̅ 2 )
𝑛−1
Standard Error of the Mean = SE =
Chi-Square = χ = ∑
2
s
√n
(𝑜−𝑒)2
𝑒
𝑥̅ = sample mean
n = sample size
s = sample standard deviation
o = observed results
e = expected results
Σ = sum of all
Hardy-Weinberg Equations
p2 + 2pq + q2 = 1
p + q= l
p = frequency of allele 1 in a population
q = frequency of allele 2 in a population
255
263
Water Potential = pressure potential + solute potential
The Solute Potential of a Solution = − i CRT
i = ionization constant (1.0 for sucrose because sucrose does not ionize in water)
C = molar concentration
R = pressure constant (R = 0.0831 liter bars / mole K)
T = temperature in Kelvin (oC + 273)
Simpson's Diversity Index
Diversity Index = I – ∑
(
total number of organisms of a particular species
total number of organisms of all species
Rate and Growth
Rate
Rate =
dY
dt
Population Growth
dN
dt
=B–D
Exponential Growth
256
264
)2
dN
dt
= rmax N
Logistic Growth
dN
dt
= rmax N (
K−N
)
N
dY = amount of change
dt = change in time
B =birthrate
D = death rate
N = population size
K = carrying capacity
r max = maximum per capita growth rate of population
Shares and Dividends
Money invested = number of shares × market value of one share.
Annual income = number of shares × rate of dividend × face value of one share
Rate of return =
Number of shares purchased (or held) =
annual income
investment
× 100 %
=
investment
market value of one share
annual income
income on one share
257
265
Investment = No. of shares × Market value per share
Sales Proceeds = No. of shares × selling price of each share (Market Value of
each share)
Matrices
Size of Matrix = No. of rows × No. of columns.
Identity matrix = [
Null matrix = [
0
0
1
0
0
]
0
0
]
1
Matrix A m × n can only be multiplied with matrix B p × q if n = p and the resultant
matrix will have m rows and q columns i.e. R m × q
Matrix multiplication is not commutative. (i.e. AB ≠ BA)
Matrix multiplication is associative.
A (BC) = (AB) C
A × I = I × A = A where I is a unit matrix of suitable order.
A (B + C) = AB + AC (distributive property)
If AB = AC then B ≠ C, A may or may not be zero.
Height of water risen =
Time taken to fill a tank =
Volume of Big Sphere = No. of lead shots × Volume of each lead shot
Volume of solid immersed
Area of base of container
Volume of tank
Volume of water given by pipe /sec
258
266
Volume = Area of cross section × length (height)
1m3 = 1000 ltrs = 106 cm3
Probability of certain event = 1
Probability of an impossible event = 0
All possible outcomes added = 1
Sample space denotes all possible outcomes.
Complementary event
P (A) + P (A) = 1
P (A) = 1 – P (A)
BODMAS Rule: This Rule depicts the correct sequence in which the operations are to be
executed, so as to find out the value of a given expression.
B – Bracket
O – Of
D – Division
M – Multiplications
A – Addition
S – Subtractions
Time taken to cross a stationary Engine =
Time taken to Cross a signal Post =
(Length of the train + Length of engine)
Length of the train
Speed of the Train
259
267
Speed of the train
Acute angle = 0° – 90°
Right Angle = 90°
Obtuse angle = 90° – 180°
Straight Angle = 180°
Reflex Angle = 180° – 360°
Complete angle = 360°
Complementary Angle = sum of two angles = 90°
Supplementary angle = sum of two angles = 180°
Right Angle Triangle: One angle 90°
Obtuse Angle Triangle: One angle more than 90°
Acute Angle Triangle: All angles less than 90°
When AC2 < AB2 + BC2 (Acute angle triangle)
When AC2 > AB2 + BC2 (Obtuse angle triangle)
When AC2 = AB2 + BC2 (Right angle triangle)
A median divides triangle into 2 equal parts:
1
2 × ( median ) 2 + 2 × ( the third side ) 2 = Sum of the square of other sides
2
Each diagonal of a parallelogram divides it into triangles of the same area.
The diagonals of a rectangle are equal and bisect each other.
The diagonals of a square are equal and bisect each other at right angles.
The diagonals of a rhombus are unequal and bisect each other at right angles.
Class Width =
The diagonals of a parallelogram bisect each other.
highest value − lowest value
number classes
260
268
upper limit + lower limit
Class Midpoint =
Midrange =
Range = Highest value − Lowest value
Sample variance = (Sample standard deviation) 2
Coefficient of Determination =
2
highest value + lowest value
2
explained variation
total variation
List of mathematically significant natural numbers
1, the multiplicative identity. Also the only natural number (not including 0) that
isn't prime or composite.
2, the base of the binary number system, used in almost all modern computers and
information systems.
3, 22-1, the first Mersenne prime. It is the first odd prime, and it is also the 2
bit integer maximum value.
4, the first composite number
6, the first of the series of perfect numbers, whose proper factors sum to the
number itself.
9, the first odd number that is composite
11, the fifth prime and first palindromic multi-digit number in base 10.
12, the first sublime number.
17, the sum of the first 4 prime numbers, and the only prime which is the sum of 4
consecutive primes.
24, all Dirichlet characters mod n are real if and only if n is a divisor of 24.
25, the first centered square number besides 1 that is also a square number
27, the cube of 3, the value of 3 ↑↑ 2, where ↑ is Knuth's up-arrow notation.
261
269
28, the second perfect number.
30, the smallest sphenic number.
32, the smallest nontrivial fifth power.
36, the smallest number which is perfect power but not prime power.
72, the smallest Achilles number.
255, 28 − 1, the smallest perfect totient number that is neither a power of three
nor thrice a prime; it is also the largest number that can be represented using
an 8-bit unsigned integer
341, the smallest base 2 Fermat pseudoprime.
496, the third perfect number.
1729, the Hardy–Ramanujan number, also known as the second taxicab number; that is,
the smallest positive integer that can be written as the sum of two positive cubes
in two different ways.
8128, the fourth perfect number.
142857, the smallest base 10 cyclic number.
9814072356, the largest perfect power that contains no repeated digits in base ten.
List of integers notable in computing
8, the number of bits in a byte
256, The number of possible combinations within 8 bits, or a byte.
1024, the number of bytes in a kibibyte. It's also the number of bits in a kibibit.
65535, 216 − 1, the maximum value of a 16-bit unsigned integer.
65536, 216, the number of possible 16-bit combinations.
65537, 216 + 1, the most popular RSA public key prime exponent in most SSL/TLS
certificates on the Web/Internet.
16777216, 224, or 166; the hexadecimal "million" (0x1000000), and the total number
of possible color combinations in 24/32-bit True Color computer graphics.
262
270
2147483647, 231 − 1, the maximum value of a 32-bit signed integer using two's
complement representation.
9223372036854775807, 263 − 1, the maximum value of a 64-bit signed
integer using two's complement representation.
Properties of Water
Heat energy gained during melting . . . . . . . . . . 334 J/g
Heat energy released during freezing . . . . . . . . 334 J/g
Heat energy gained during vaporization . . . . . 2260 J/g
Heat energy released during condensation . . . 2260 J/g
Density at 3.98°C . . . . . . . . . . . . . . . . . . . . . . . . 1.0 g/mL
Eccentricity =
Gradient =
distance between foci
length of major axis
change in field value
distance
Average Chemical Composition of Earth's Crust, Hydrosphere, and Troposphere
CRUST
ELEMENT
Percent by mass
Oxygen (O)
Silicon (Si)
Aluminum (Al)
Iron (Fe)
Calcium (Ca)
Sodium (Na)
Magnesium (Mg)
Potassium (K)
Nitrogen (N)
Hydrogen (H)
Other
46.10
28.20
8.23
5.63
4.15
2.36
2.33
2.09
HYDROSPHERE
Percent by volume
94.04
0.88
0.48
0.49
1.18
1.11
0.33
1.42
Percent by volume
33.0
TROPOSPHERE
Percent by volume
21.0
78.0
0.91
66.0
1.0
0.07
263
271
1.0
Angle
0°
30°
45°
60°
90°
sinθ
0
1
2
1
√3
2
1
√3
Undefined
cosθ
tanθ
cotθ
secθ
cosecθ
1
0
√3
2
Undefined
√3
√2
1
√2
1
1
1
√3
1
2
√2
2
√2
√3
Undefined
1
2
Mo = l + (
𝑓1 −𝑓0
2𝑓1 − 𝑓0 −𝑓2
0
2
Undefined
2
1
√3
)h
where:
l = lower limit of the modal class,
h = size of the class interval (assuming all class sizes to be equal),
f1 = frequency of the modal class,
f0 = frequency of the class preceding the modal class,
f2 = frequency of the class succeeding in the modal class
264
272
1
√3
Mode is obtained using the modal class:
0
Approximate coefficients of friction
Material
Against
Material
Static Friction
Dry
contact
Lubricated
contact
0.61
Kinetic Friction
Dry
contact
0.47
Aluminium
Steel
Aluminum
Aluminum
Gold
Gold
Platinum
Platinum
1.2
0.25
3.0
Silver
Silver
1.4
0.55
1.5
Alumina ceramic
Silicon Nitride
ceramic
BAM (Ceramic alloy
AlMgB14)
Titanium
boride (TiB2)
0.04–0.05
0.02
Brass
Steel
0.35-0.51
0.19
Cast iron
Copper
1.05
0.29
Cast iron
Zinc
0.85
0.21
Concrete
Rubber
Concrete
Wood
0.62
Copper
Glass
0.68
Copper
Steel
0.53
1.05-1.35
Lubricated
contact
0.3
1.4-1.5
2.5
0.004
(wet)
1.0
265
273
0.30 (wet)
0.44
0.6-0.85
0.36
0.45-0.75
(wet)
0.9-1.0
Glass
Glass
Human synovial fluid
Cartilage
Ice
Ice
Polyethene
Steel
PTFE (Teflon)
0.4
0.01
0.003
0.02-0.09
0.2
0.2
PTFE (Teflon)
0.04
0.04
0.04
Steel
Ice
0.03
Steel
PTFE (Teflon)
0.04-0.2
0.04
0.04
Steel
Steel
0.74-0.80
0.16
Wood
Metal
0.2–0.6
0.2 (wet)
Wood
Wood
0.25–0.5
0.2 (wet)
0.42-0.62
The Resistor Colour Code Table
Colour
Digit
Multiplier
Black
0
1
Brown
1
10
± 1%
Red
2
100
± 2%
Orange
3
1,000
266
274
Tolerance
Yellow
4
10,000
Green
5
100,000
± 0.5%
Blue
6
1,000,000
± 0.25%
Violet
7
10,000,000
± 0.1%
Grey
8
White
9
± 0.05%
Gold
0.1
± 5%
Silver
0.01
± 10%
None
± 20%
Resistivities at 20°C
Element
Resistivity at 20 °C (Ω m)
Aluminum
2.82 × 10-8
Carbon (Graphite)
3.5 × 10-5
Constantan
4.9 × 10-7
Copper
1.7 × 10-8
Germanium
4.6 × 10-1
Glass
1010 to 1014
267
275
Gold
2.44 × 10-8
Iron
1.0 × 10-7
Lead
2.2 × 10-7
Manganin
4.82 × 10-7
Mercury
9.8 × 10-7
Platinum
1.1 × 10-7
Quartz (fused)
7.5 × 1017
Silicon
6.40 × 102
Silver
1.59 × 10-8
Tungsten
5.6 × 10-8
Properties of Minerals
Property
Description
Example of Mineral
Fluorescence
Mineral glows under ultraviolet light
Fluorite
Magnetism
Mineral is attracted to a magnet
Magnetite
Radioactivity
Mineral gives off radiation that can be measured with Geiger counter
Uraninite
Reactivity
Bubbles form when mineral is exposed to a weak acid
Calcite
Smell
Some minerals have a distinctive smell
Sulfur (smells like rotten eggs)
Taste
Some minerals taste salty
Halite
268
276
Etymology of period names
Period
Started
Siderian
c.2500 Ma
Greek sideros
iron
the banded iron formations
Rhyacian
c.2300 Ma
Gk. rhyax
lava flow
much lava flowed
Orosirian
c.2050 Ma
Gk. oroseira
mountain
much orogeny in this period's
range
latter half
steady
continents became
Statherian
c.1800 Ma
Root word
Gk. statheros
Meaning
Reason for name
stable cratons
Calymmian
c.1600 Ma
Gk. calymma
cover
platform covers developed or
expanded
Ectasian
c.1400 Ma
Gk. ectasis
stretch
platform covers expanded
Stenian
c.1200 Ma
Gk. stenos
narrow
much orogeny, which survives
as narrow metamorphic belts
Tonian
c.1000 Ma
Gk. tonos
stretch
The continental crust
stretched as Rodinia broke up
Cryogenian
Ediacaran
c.720 Ma
c.635 Ma
Gk. cryogenicos
Ediacara Hills
cold-
In this period all the Earth
making
froze over
stony
place in Australia where
ground
the Ediacaran biota fossils
were found
Cambrian
c.541 Ma
Latin Cambria
Wales
269
277
the place in Great
Britain where Cambrian rocks
are best exposed
Ordovician
c.485.4
Celtic Ordovices
Tribe in north Wales, where
the rocks were first
Ma
identified
Silurian
c.443.8
Ctc. Silures
Tribe in south Wales, where
the rocks were first
Ma
identified
Devonian
c.419.2
Devon
County in England in which
rocks from this period were
Ma
first identified
Carboniferous
c.358.9
Lt. carbo
coal
Ma
Permian
c.298.9
Global coal beds were laid in
this period
Perm Krai
Region in Russia where rocks
from this period were first
Ma
identified
Triassic
c.251.902
Lt. trias
triad
Ma
Jurassic
c.201.3
In Germany this period forms
three distinct layers
Jura Mountains
Mountain range in the Alps in
which rocks from this period
Ma
were first identified
Cretaceous
c.145 Ma
Lt. creta
chalk
More chalk formed in this
period than any other
Paleogene
c.66 Ma
Gk. palaiogenos
"ancient
born"
270
278
Neogene
c.23.03
Gk. neogenos
"new born"
Lt. quaternarius
"fourth"
Ma
Quaternary
c.2.58 Ma
This was initially deemed the
"fourth" period after the
now-obsolete "primary",
"secondary" and "tertiary"
periods.
Abbreviations yr and ya
Non-SI
Short for...
abbreviation
SI-
Comments and examples
prefixed
equivalent
Thousand years
Ma
Million years
Ga
Billion years (thousand
kyr
kilo years
ka
myr
million years
Myr
Mega years
byr
billion years
million years)
kya
kilo years ago
ka ago
Appearance of Homo
sapiens, circa 200 kya
Out-of-Africa migration, circa 60
kya
mya
million years ago
Mya
Mega years ago
Ma ago
271
279
Last Glacial Maximum, circa 20 kya
Neolithic Revolution, circa 10 kya
Pliocene, 5.3 to 2.6 mya
o
The last geomagnetic
reversal was 0.78 mya
o
The (Eemian Stage) Ice
Age started 0.13 mya
bya
billion years ago
Gya
giga years ago
Ga ago
The Holocene started 0.01 mya
oldest Eukaryotes, 2 bya
formation of the Earth, 4.5 bya
Big Bang, 13.8 bya
Ionization Energies (1st, 2nd, 3rd and 4th) of Gaseous Atoms (kJ/mol)
Atomic number
First
Second
Third
Fourth
1
H
1,312
2
He
2,372
5,251
3
Li
520.3
7,298
11,815
4
Be
899.5
1,757
14,849
21,007
5
B
800.7
2,427
3,660
25,026
6
C
1,086
2,353
4,621
6,223
7
N
1,402
2,856
7,475
9,445
8
O
1,314
3,388
5,301
7,469
9
F
1,681
3,374
6,051
8,408
10
Ne
2,081
3,952
6,122
9,370
11
Na
495.9
4,563
6,913
9,544
12
Mg
737.8
1,451
7,733
10,541
13
Al
577.6
1,817
2,745
11,578
14
Si
786.5
1,577
3,232
4,356
15
P
1,012
1,903
2,912
4,957
16
S
999.6
2,251
3,361
4,564
17
Cl
1,251
2,297
3,822
5,158
18
Ar
1,521
2,666
3,931
5,771
19
K
418.9
3,051
4,412
5,877
20
Ca
589.8
1,145
4,912
6,474
272
280
21
Sc
631
1,235
2,389
7,089
22
Ti
658
1,310
2,653
4,175
23
V
650
1,414
2,828
4,507
24
Cr
652.9
1,592
2,987
4,740
25
Mn
717.4
1,509
3,249
4,940
26
Fe
759.4
1,561
2,958
5,290
27
Co
758
1,646
3,232
4,950
28
Ni
736.7
1,753
3,394
5,300
29
Cu
745.5
1,958
3,554
5,330
30
Zn
906.4
1,733
3,833
5,730
31
Ga
578.8
1,979
2,963
6,200
32
Ge
762.2
1,537
3,302
4,411
33
As
947
1,798
2,736
4,837
34
Se
941
2,045
2,974
4,144
35
Br
1,140
2,100
3,500
4,560
36
Kr
1,351
2,368
3,565
5,070
37
Rb
403
2,632
3,900
5,080
38
Sr
549.5
1,064
4,210
5,500
39
Y
616
1,181
1,980
5,960
40
Zr
660
1,267
2,218
3,313
41
Nb
664
1,382
2,416
3,700
42
Mo
685
1,558
2,621
4,480
43
Tc
702
1,472
2,850
44
Ru
711
1,617
2,747
45
Rh
720
1,745
2,997
46
Pd
805
1,875
3,177
47
Ag
731
2,074
3,361
48
Cd
867.7
1,631
3,616
49
In
558.3
1,821
2,705
5,200
50
Sn
708.6
1,412
2,943
3,930
51
Sb
833.8
1,595
2,440
4,260
52
Te
869.3
1,790
2,698
3,610
53
I
1,008
1,846
3,200
54
Xe
1,170
2,047
3,100
55
Cs
375.7
2,420
56
Ba
502.9
965.3
57
La
538.1
1,067
273
281
1,850
4,820
58
Ce
527.4
1,047
1,949
3,547
59
Pr
523.2
1,018
2,086
3,761
60
Nd
529.6
1,035
2,130
3,899
61
Pm
535.9
1,052
2,150
3,970
62
Sm
543.3
1,068
2,260
3,990
63
Eu
546.7
1,085
2,405
4,110
64
Gd
592.6
1,167
1,991
4,250
65
Tb
564.7
1,112
2,114
3,839
66
Dy
571.9
1,126
2,200
4,001
67
Ho
580.7
1,139
2,204
4,100
68
Er
588.7
1,151
2,194
4,115
69
Tm
596.7
1,163
2,544
4,119
70
Yb
603.4
1,176
2,415
4,220
71
Lu
523.6
1,340
2,022
4,360
72
Hf
680
1,440
2,250
3,215
73
Ta
761
74
W
770
75
Re
760
76
Os
840
77
Ir
880
78
Pt
870
1,791
79
Au
890.1
1,980
80
Hg
1,007
1,810
3,300
81
Tl
589.4
1,971
2,878
82
Pb
715.6
1,450
3,082
4,083
83
Bi
703.3
1,610
2,466
4,370
84
Po
812
85
At
890
86
Rn
1,037
87
Fr
384
88
Ra
509.4
89
Ac
499
90
Th
587
91
Pa
568
92
U
584
93
Np
597
94
Pu
585
971.9
274
282
95
Am
578
96
Cm
581
97
Bk
601
98
Cf
608
99
Es
619
100
Fm
627
101
Md
635
102
No
642
Ionic radii
Ionic Radius
Name
Symbol
Atomic number
0.012 Å
1.2 pm
Hydrogen
H
1
0.13 Å
13 pm
Nitrogen
N
7
0.23 Å
23 pm
Boron
B
5
0.35 Å
35 pm
Beryllium
Be
4
0.38 Å
38 pm
Phosphorus
P
15
0.4 Å
40 pm
Silicon
Si
14
0.46 Å
46 pm
Manganese
Mn
25
0.5 Å
50 pm
Selenium
Se
34
0.52 Å
52 pm
Uranium
U
92
0.52 Å
52 pm
Chromium
Cr
24
0.53 Å
53 pm
Germanium
Ge
32
0.535 Å
53.5 pm
Aluminum
Al
13
0.56 Å
56 pm
Rhenium
Re
75
0.56 Å
56 pm
Technetium
Tc
43
0.58 Å
58 pm
Arsenic
As
33
0.59 Å
59 pm
Vanadium
V
23
0.605 Å
60.5 pm
Titanium
Ti
22
0.62 Å
62 pm
Tungsten
W
74
0.62 Å
62 pm
Gallium
Ga
31
0.625 Å
62.5 pm
Platinum
Pt
78
0.625 Å
62.5 pm
Iridium
Ir
77
0.63 Å
73 pm
Osmium
Os
76
0.64 Å
64 pm
Tantalum
Ta
73
275
283
0.645 Å
64.5 pm
Iron
Fe
26
0.65 Å
65 pm
Molybdenum
Mo
42
0.68 Å
68 pm
Rhodium
Rh
45
0.68 Å
68 pm
Ruthenium
Ru
44
0.69 Å
69 pm
Nickel
Ni
28
0.69 Å
69 pm
Niobium
Nb
41
0.69 Å
69 pm
Tin
Sn
50
0.71 Å
71 pm
Hafnium
Hf
72
0.72 Å
72 pm
Zirconium
Zr
40
0.72 Å
72 pm
Magnesium
Mg
12
0.73 Å
73 pm
Copper
Cu
29
0.74 Å
74 pm
Zinc
Zn
30
0.745 Å
74.5 pm
Cobalt
Co
27
0.745 Å
74.5 pm
Scandium
Sc
21
0.75 Å
75 pm
Neptunium
Np
93
0.76 Å
76 pm
Lithium
Li
3
0.76 Å
76 pm
Antimony
Sb
51
0.78 Å
78 pm
Protactinium
Pa
91
0.8 Å
80 pm
Indium
In
49
0.848 Å
84.8 pm
Lutetium
Lu
71
0.85 Å
85 pm
Gold
Au
79
0.858 Å
85.8 pm
Ytterbium
Yb
70
0.86 Å
86 pm
Palladium
Pd
46
0.869 Å
86.9 pm
Thulium
Tm
69
0.881 Å
88.1 pm
Erbium
Er
68
0.887 Å
88.7 pm
Plutonium
Pu
94
0.9 Å
90 pm
Yttrium
Y
39
0.901 Å
90.1 pm
Holmium
Ho
67
0.912 Å
91.2 pm
Dysprosium
Dy
66
0.923 Å
92.3 pm
Terbium
Tb
65
0.925 Å
92.5 pm
Einsteinium
Es
99
0.934 Å
93.4 pm
Californium
Cf
98
0.938 Å
93.8 pm
Gadolinium
Gd
64
0.947 Å
94.7 pm
Europium
Eu
63
0.949 Å
94.9 pm
Berkelium
Bk
97
0.964 Å
96.4 pm
Samarium
Sm
62
276
284
0.97 Å
97 pm
Curium
Cm
96
0.97 Å
97 pm
Tellurium
Te
52
0.97 Å
97 pm
Cadmium
Cd
48
0.972 Å
97.2 pm
Thorium
Th
90
0.979 Å
97.9 pm
Promethium
Pm
61
0.982 Å
98.2 pm
Americium
Am
95
0.99 Å
99 pm
Calcium
Ca
20
0.995 Å
99.5 pm
Neodymium
Nd
60
1.013 Å
101.3 pm
Praseodymium
Pr
59
1.02 Å
102 pm
Mercury
Hg
80
1.02 Å
102 pm
Sodium
Na
11
1.03 Å
103 pm
Bismuth
Bi
83
1.034 Å
103.4 pm
Cerium
Ce
58
1.061 Å
106.1 pm
Lanthanum
La
57
1.1 Å
110 pm
Nobelium
No
102
1.119 Å
111.9 pm
Actinium
Ac
89
1.12 Å
112 pm
Strontium
Sr
38
1.19 Å
119 pm
Lead
Pb
82
1.26 Å
126 pm
Silver
Ag
47
1.33 Å
133 pm
Fluorine
F
9
1.35 Å
135 pm
Barium
Ba
56
1.38 Å
138 pm
Potassium
K
19
1.4 Å
140 pm
Oxygen
O
8
1.43 Å
143 pm
Radium
Ra
88
1.5 Å
150 pm
Thallium
Tl
81
1.52 Å
152 pm
Rubidium
Rb
37
1.67 Å
167 pm
Cesium
Cs
55
1.8 Å
180 pm
Francium
Fr
87
1.81 Å
181 pm
Chlorine
Cl
17
1.84 Å
184 pm
Sulfur
S
16
1.96 Å
196 pm
Bromine
Br
35
2.2 Å
220 pm
Iodine
I
53
2.3 Å
230 pm
Polonium
Po
84
277
285
States of Matter and Appearance of Halogens at Room Temperature
States of Matter
Halogen
Appearance
Solid
Iodine
Violet
Solid
Astatine
Black/Metallic [Assumed]
Liquid
Bromine
Reddish-Brown
Gas
Fluorine
Pale Yellow-Brown
Gas
Chlorine
Pale Green
(at Room Temperature)
The gyromagnetic ratios for several common nuclei
Nuclei
1
H
13
C
31
P
27
Al
23
Na
7
Li
29
Si
17
O
Spin
Gyromagetic Ratio
Natural Abundance
(MHz/T)
(%)
1
2
42.576
99.9985
1
2
10.705
1.07
1
2
17.235
100
5
2
11.103
100
3
2
11.262
100
3
2
16.546
92.41
1
2
-8.465
4.68
5
2
5.772
0.038
278
286
1
2
15
N
-4.361
0.368
COMMON ISOTOPE PAIRS CHART
Isotope
Half-life of Parent
Effective Dating Range
(years)
(years)
Parent
Daughter
Uranium-238
Lead-206
4.5 billion
1 million to 4.5 billion
Potassium-40
Argon-40
1.3 billion
10 000 to 3 billion
Carbon-14
Nitrogen-14
5730
up to 50 000
Measurement
Absolute error = indicated value – true value
Absolute correction = true value – indicated value
Relative error =
Relative correction =
absolute error
true value
absolute correction
true value
Mechanical equations
axial stress =
axial strain =
axial force
cross sectional area
change in length
original length
279
287
shear force
shear stress =
Working or allowable stress =
Mechanical advantage (MA) =
Velocity ratio (VR) =
Velocity ratio =
Input speed × input size = output speed × output size
Gear systems
shear area
ultimate stress
Factor of Safety (FOS)
output force (or torque)
input force (or torque)
velocity of output from a mechanism
velocity of input to a mechanism
speed of input
speed of output
MA =
Number of teeth on output gear
VR =
Number of teeth on input gear
Number of teeth on input gear
Number of teeth on output gear
Belt and pulley systems
MA =
Diameter of output pulley
VR =
Diameter of input pulley
Diameter of input pulley
Diameter of output pulley
Fluid mechanics
Pressure due to a column of liquid = height of column × gravitational acceleration × density of liquid
Up-thrust force on a submerged body = volume of submerged body × gravitational acceleration × density of liquid
280
288
Energy equations
Non-flow energy equation
U1 + Q = U2 + W
where:
Q = energy entering the system
W = energy leaving the system
U1 = initial energy in the system
U2 = final energy in the system
Steady flow energy equation
Q = (W2 – W1) + W
where:
Q = heat energy supplied to the system
W1 = energy entering the system
W2 = energy leaving the system
W = work done by the system.
Principle of moments
Σ clockwise moments = Σ anti-clockwise moments
281
289
HYDRAULICS
Pressure loss due to Friction
𝑃𝑓 =
9000𝑓𝑙L2
d5
where:
Pf = Pressure loss due to friction in bar
f = Friction factor for the hose
l = Length of the hose in meters
L = Flow rate in liters per minute
d = Diameter of the hose in millimeters
Flow through a Nozzle
2
L = d2 √P
3
where:
L = Flow rate in liters per minute
d = Diameter of the nozzle in millimeters
P = Pressure in bar
Water power and Efficiency
WP =
100LP
60
where:
WP = Water Power in Watts
L = Flow rate in liters per minute
282
290
P = Pressure in bar
E=
where:
WP
BP
× 100
E = Efficiency of a pump (%)
WP = Water Power in Watts
BP = Brake Power of engine in Watts
Jet Reaction
R = 0.157Pd2
where:
R = Jet reaction in newtons
P = Pressure in bar
d = Diameter of the hose in millimeters
Effective Height of a Jet
He =
2
3
(H – 0.113
H2
d
)
where:
He = Effective height of jet in meters
H = Theoretical height to which water will rise when projected vertically from nozzle in meters
d = Diameter of nozzle in millimeters
283
291
E◦net = E◦red + E◦ox
E◦ net = net voltage of a cell (V)
E◦ red = voltage of the reduction half reaction (V)
E◦ ox = voltage of the oxidation half reaction (V)
NEWTON'S LAWS OF MOTION
Newton's First Law: An object continues in its state of rest or of uniform motion in a
straight line unless acted upon by an external force.
Newton's Second Law: A change in motion (acceleration) is proportional to the force
acting and takes place in the direction of the straight line along which the force acts.
Acting force = mass × acceleration caused
Newton's Third Law: To every action there is an equal and opposite reaction (or, if
object A exerts a force on object B, then object B exerts an equal, but oppositely-directed,
force on A).
284
292
The most abundant element in the universe is hydrogen.
The most abundant element on the Earth is Oxygen.
The idea of Friedrich August Kekule von Stradonitz's dream helped
form the benzene structure.
The density of ice is 10% lower than that of water.
Hydrofluoric acid (a solution of hydrogen fluoride in water) is so
corrosive that it can dissolve glass.
Helium (a colorless, odorless, tasteless, non-toxic, inert, monatomic gas) can
be frozen only through pressure; not by cooling.
Graphene (an allotrope of carbon) is the best conductor of electricity and heat.
Chalk is made of trillions of fossils of planktonic
microscopic skeleton.
285
Systematic Procedure for Inorganic Qualitative Analysis
Systematic Analysis of Anion
S.No
1
2
3
4
Experiment
Preliminary Reactions
Observation
Colourless
Inference
Absence of Fe2+, Fe3+, Ni2+,
Co2+.
Appearance
Green
May be Fe2+, Ni2+, Cu2+
Blue
Cu2+
Brown
May be Fe2+
Pink
May be Co2+, Mn2+
A colourless gas with a May be NH4+ salt
characteristic
pungent
odour turning moist red
Action of heat
litmus paper blue.
Take a small amount of
the given salt taken in a
Reddish brown vapours May be
dry test tube, heat it
turning acidified ferrous
gently; then strongly.
sulphate paper brown, are
obtained.
Substance is white when May be (Zn)2+
cold and yellow when hot.
Flame Test
(i) Bluish green flame
May be Cu2+
To a small amount of the (ii) Apple green
May be Ba2+
given salt taken in a (iii) Brick red
May be Ca2+
watch glass, add a drop (iv) Crimson red
May be Sr2+
of Con. HCl and make it
into a paste. Introduce
the paste with the help
of a glass rod to the base
of
the
non-luminous
bunsen burner.
Identification of Anions from Volatile Products:
Brisk
effervescence
of Anion is CO32colourless, odourless gas
turning lime water, milky is
obtained.
Colourless gas with a smell Anion is sulphide.
of rotten eggs, turning lead
acetate paper black is
obtained.
Colourless gas with smell of Anion is SO32burning sulphur turning
Action of dilute H2SO4:
acidified dichromatic green
To a small portion of the
is obtained.
given salt taken in a test
Reddish brown gas with Anion is
tube add 1 or 2ccs of
fishy
odour
turning
H2SO4 and gently warm
acidified ferrous sulphate
it.
brown is obtained.
Colourless gas with smell of Anion may be acetate.
vinegar is obtained.
No
characteristic Absence of CO32-,
, S2-,
2observation.
SO3 , CH3COO
286
293
5
6
7
8
Reddish brown vapours
turning moist fluorescent
paper red.
Colourless
gas
with
pungent smell giving dense
white fumes with a glass
Action of Con.H2SO4
rod dipped in NH4OH
To a small amount of
given salt taken in a test solution.
Violet coloured vapours
tube, add 2-3 ccs of
turning starch paper blue
Con.H2SO4 and gently
or violet.
heat it.
Reddish brown vapours
turning acidified ferrous
sulphate paper brown.
No
characteristic
observation.
Action of Con.H2SO4 with Copius evolution of reddish
Cu turnings:
brown gas turning acidified
Mix a small amount of ferrous
sulphate
paper
the given salt taken in a brown is observed.
test tube with a few Cu
bits, add 2 – 3 ccs of No reddish brown vapours.
H2SO4 and heat it.
A greenish yellow gas
Action of Con.H2SO4 with turning starch iodide paper
violet (or) blue is obtained.
MnO2
To a small amount of the Reddish brown vapours
given salt taken in a test turning moist fluorescent
paper red is obtained.
tube, add an equal
amount of MnO2 and
Violet
vapours
turning
add a few ccs of
starch paper blue (or) violet
Con.H2SO4 and gently
is obtained.
heat.
No characteristic coloured
vapours are obtained.
Action of NaOH
A colourless gas with a
To a pinch of the given pungent smell giving dense
salt taken in a test tube, white fumes with glass rod
add few ccs of 10% dipped in HCl is obtained.
NaOH
solution
and
gently warm it.
No characteristic gas is
Ammonium liberated.
Anion may be bromide.
Anion may be chloride.
Anion may be Iodide.
Anion may be nitrate.
Absence of
,
,
&
Anion is nitrate.
Absence of
Anion may be chloride.
Anion may be bromide.
Anion may be iodide
Absence of
,
,
Cation is ammonium.
Ammonium is absent.
Sodium Carbonate Extract
Identification of Anions in solution
Preparation of Extract:
Take about
or
of the given salt in a 50cc beaker.
Mix it well with about
thrice its amount of solid sodium carbonate. Add about 15 – 20ml of distilled
water. Mix well with neat glass rod. Boil contents of the beaker over Bunsen
flame. Cool and filter through filter assembly. Collect the clean filtrate in
another beaker. The Filtrate is called soda extract.
287
294
S.No
9
10
11
12
13
Experiment
Silver Nitrate Test:
To a portion of extract
add dilute HNO3 until
effervescence
ceases.
Add few drops in excess,
2 – 3nos of AgNO3
solution.
Observation
Inference
Curdy white precipitate Anion is Cl–
soluble in NH4OH.
–
Pale
yellow
precipitate Anion is Br
sparingly soluble in NH4OH.
Yellow precipitate insoluble Anion is
in NH4OH.
Absence of Br–, Cl–, I–
No precipitate is obtained.
Barium Chloride Test:
A
white
precipitate Anion is
To about one or two ccs insoluble in HCl.
of the extract, (after
neutralizing with acetic A white precipitate soluble Anion is
acid and boiling of CO2) in HCl.
add BaCl2 solution.
To a portion of the above No precipitate is obtained.
Absence of
ppt add dil. HCl.
Lead Acetate Test:
To about one or two ccs
of the extract (after
acidifying with acetic
acid, boiling off CO2 and
cooling) add lead acetate
solution.
Ferrous Sulphate Test:
(Brown Ring Test)
To about 1 or 2cc of
extract
add
dilute
H2SO4 in drops until the
effervescence
ceases.
And few drops in excess
add 2- 3 drops of freshly
prepared FeSO4 solution.
Keeping the test tube in
a slanting position, add
Con.
H2SO4
without
disturbing the solution.
Ferric Chloride Test:
Take about 1 or 2ccs of
the extract in a test tube
and add neutral FeCl3
solution.
Filter,
if
required, and divide the
solution or the filtrate in
two parts:
(i) To
dil.HCl
one
part
White ppt, soluble in excess
of
ammonium
acetate
solution.
A brown ring is obtained at Anion is
the junction of the liquid.
No brown ring is observed.
Deep
red
produced
colouration
add Red colouration disappears
(ii) To the second part
add water and boil
confirmed.
Reddish brown ppt.
288
295
Anion
is absent.
confirmed.
confirmed.
confirmed.
14
15
Calcium Chloride Test:
white precipitate
of Confirms Oxalate.
To a portion of the A
sodium
carbonate calcium oxalate is obtained
extract, taken in a test
tube add dil. Acetic acid
and boil off CO2. Then
add a few drops of
calcium
chloride
solution.
Add dil. HNO3 to the The precipitate dissolves.
white ppt and warm.
Ethyl Acetate Test:
To a pinch of given salt A pleasant fruity odor is
taken in a test tube, add obtained.
a few drops of ethanol
followed by 1 or 2ccs of
H2SO4. Gently heat and
cool it.
Pour into
Na2CO3.
The presence of anion acetate is
confirmed.
Diamond and graphite both are forms of pure carbon.
The chemical name for water (H2O) is dihydrogen monoxide.
The only 2 non-silvery metals are gold and copper.
Our body contains enough carbon to provide graphite for 9,000 pencils.
If we mix half a liter of alcohol and half a liter of water, the total
volume of the resultant liquid will be less than one liter.
289
296
Systematic Analysis of Cations
Preparation of Original solution:
Check solubility of the given salt in:
- Cold water (or) hot water (or) Dil HCl (or) Conc. HCl.
original solution.
Label this solution as
Procedure for Separation of Basic Radicals into Groups
To the original solution, add Dil. HCl.
White
ppt.
Group
I
2+
present (Pb
and
If no ppt. pass H2S through the given solution. If a coloured ppt. is formed,
group 2 cations are present (Cu2+), Pb2+.
If no ppt is obtained from the above, boil off H2s gas and add a
few drops of conc. HNO3 to the remaining solution. Cool, add
2-3g of solid NH4Cl. Boil again and add NH4OH solution till it
becomes alkaline.
If a ppt is formed, Group III cations are present. Reddish
brown ppt. Fe3+ Gelatinous white ppt. Al3+
If no ppt., pass H2S to the given solution.
If a ppt is formed Group IV cations are
present. Black ppt. (Co2+, Ni2+)
Flesh coloured ppt. Mn2+ white ppt. Zn2+.
If no ppt is formed, boil off
H 2S
gas
add
(NH4)2CO3
solution.
If a white ppt is formed Group
V cations are present (Ba2+,
Sr2+, Ca2+)
If
no
ppt.
Group
VI
cation
is
present (Mg2+
If none of the cations are present, check for Group 0 (
)
Cation Analysis
Group O (NH4+):
To a pinch of given salt add Yellowish brown precipitate Cation is ammonium.
some water and warm.
is obtained.
Then allow it to cool. Add
Nessler’s reagent and
No precipitate is obtained.
Cation is not ammonium.
excess of NaOH solution.
290
297
Group I (lead):
Group I precipitate is dissolved by heating the precipitate with dil.HNO3 or distilled
water. Divide the solution into 3 portions and carry out the following reactions.
Experiment
Observation
Inference
Pb2+
To one portion of the above A white precipitate
solution add dilute H2SO4. PbSO4 is obtained.
of
To another portion, add A
potassium
chromate
solution.
of Presence
confirmed.
yellow precipitate
is obtained.
Golden Spangles Test:
A yellow
To the 3rd portion, add KI obtained.
solution
precipitate
is present.
of
is The presence of
confirmed.
is
is
To above yellow precipitate, Precipitate dissolves and
add some H2O, boil and reappears in the form of
then cool.
golden spangles.
Group II (
:
The group 2 precipitate is dissolved by heating with dilute HCl. Precipitate dissolves.
Experiment
Test for
:
To one portion of the above
solution add drops of
NH4OH, until it is in
excess.
Observation
Inference
A pale blue precipitate The presence of Cu2+ is
which dissolves in excess confirmed.
NH4OH to give any inky
blue solution is obtained.
To another portion, add
dilute acetic acid and A chocolate brown ppt.
potassium
ferrocyanide
[K4(Fe(CN6))]
Confirms copper.
Group III:
Group III precipitate is heated with Con. HCl and water, cooled and filtered.
Reddish brown precipitate indicates Fe2+ (or) Fe3+
Gelatinous white indicates Al3+
Experiment
1.
Observation
Inference
To 1 cm3 OS, add a Formation of a deep Fe2+ confirmed.
few drops of dilute blue colour or ppt.
HCl and then add
291
298
2.
0.5 cm3 of potassium
ferricyanide solution.
White
gelatinous
precipitate dissolves
in minimum quantity
of dil. HCl. To this,
add a few drops of
blue litmus solution.
Formation of a blue Al3+ confirmed.
floating
ppt.
in
colourless
solution.
(This is known as Lake
test)
Add NH4OH solution A blue ppt., suspended
in excess.
in a colourless medium
(called a lake)
2B To one part of the White Precipitate soluble Al3+ confirmed
above solution add in excess of NaOH
NaOH solution
solution
3.
(i)
(ii)
Reddish brown ppt.
(Shows the presence
of Fe3+) Treat it with
minimum quantity of
dil. HCl solution to
dissolve the ppt. and
then heat. Divide the
solution
into
two
parts.
To one part, add few
drops of potassium
ferrocyanide solution.
A yellow
produced.
solution
is
may be present.
A deep blue colour or
ppt. is obtained.
confirmed.
To another portion A deep red colour is
add few drops of obtained.
potassium
sulphocyanide
solution.
confirmed.
Group IV :
Group IV precipitate is warmed with dilute HCl centrifugate
Black precipitate Ni2+
Ni is not soluble in dilute HCl. To residue A Red rosy precipitate
add Con.HCl, boil, cool. Divide the presence of Ni2+
solution into two parts and boil of H2S. To
one part add dimethyl glyoxime reagent.
Con.NH4OH, till the solution becomes
alikaline.
292
299
confirms
the
Sodium Hydroxide and Br2 – water test.
A black precipitate confirms the
To the second part of the above solution, of Ni2+.
add NaOH and Br2 water and then boil
Confirmation of Zn2+:
Dissolve a part of white ppt in dil. HCl.
Boil off H2S and divide the solution in two
Bluish White ppt confirms Zinc.
parts.
(i) To one part of solution add Pot.
ferrocyanide solution
White ppt soluble in excess of
(ii) To second part of solution add NaOH.
obtained.
Flesh (buff) colour precipitate indicates A white precipitate is formed.
Mn2+.
water to the white ppt it turns
Dissolve the precipitate in Dil. HCl and brown. Mn2+ confirmed.
boil off H2S then add NaOH solution.
Lead peroxide test
A pink colouration is produced.
To the second part of the flesh coloured confirmed.
ppt, add a little of PbO2 powder and
conc. HNO3.
Boil, cool and allow to
stand.
presence
NaOH is
Add Br
black or
Mn2+ is
Group V :
Take a small portion of Group V precipitate, carry out flame test. Take group V
precipitate, add dilute CH3COOH, warm. Boil of CO2 and divide the solution into
three parts.
Barium, Ba2+
1. Potassium chromate
test.
To one part of the above
solution, add a few drops of
K2CrO4 solution – Yellow
ppt. Ba2+ confirmed.
Stronium Sr2+
1. Ammonium sulphate
test.
To the second part of the
above solution add a few
drops
of
ammonium
sulphate solution – white
ppt. Sr2+ confirmed.
2. Dil. H2SO4 Test
Flame test
To another portion of the
above solution, add a few
drops of dil. H2SO4 – white
ppt. insoluble in HCl.
Ba2+ confirmed.
Calcium Ca2+
1. Ammonium oxalate test.
To the third portion of the
above
solution,
add
ammonium
oxalate
solution and then NH4OH
solution to make it alkaline
and scratch the sides of
the test tube – white ppt.
Ca2+ confirmed.
Flame test
293
300
Test for Mg2+:
1. Ammonium phosphate test.
White crystalline ppt.
To the original salt solution, add solid
NH4 Cl, warm to dissolve, cool and add
NH4 OH solution in slight excess. Then
add ammonium phosphate solution,
shake well and allow to stand
2. To the original sat solution, add White crystalline ppt confirms Mg2+
disodium hydrogen phosphate.
Additional Test:
Ash test for Al3+, Zn2+, Mg2+
To a pinch of given salt Blue tinted ash is obtained.
taken in a test tube, add a
Green tinted ash is
few drops of Con.H2SO4,
obtained.
Co(No3)2. Mix it well. Dip
one filter paper bit in a
Bunsen flame. After it burns Pink tinted ash is obtained.
remove it from flame. After
cooking observe the odor of
the ash formed.
The presence
confirmed.
of Al3+
is
The presence of Zn2+
confirmed.
is
The presence of Mg2+ is
confirmed.
Sound travels 4.3 times faster in water than in air
Urine glows under ultraviolet light
Apples produce a gas called ethylene on ripening.
We have lost about 1% of our body's water by the time we feel thirsty.
Warm water freezes more quickly than cold water.
294
301
Known ice ages
Name of ice age
Years BP
(Ma)
Geological
period
Era
Pongola
2900–2780
Huron
2400–2100
Siderian
Rhyacian
Paleoproterozoic
Sturt
Marino
Gaskiers
Baykonur
715–680
650–635
580
547
Cryogenian
Neoproterozoic
Andean-Saharan
(incl. Hirnantian and
Late Ordovician glaciation)
450–420
Late Ordovician
Silurian
Paleozoic
Karoo
360–260
Carboniferous
Permian
Paleozoic
Late Cenozoic Ice Age
(incl. Quaternary
glaciation)
34–present
Late Paleogene
Neogene
Quaternary
Cenozoic
Ediacaran
Binding Energy per nucleon =
Element
Mesoarchean
Binding Energy
Nucleon Number
Mass of
Nuclear mass
Binding energy
Binding energy
nucleons (u)
(u)
(MeV)
per nucleon
(MeV)
Deuterium
2.01594
2.01355
2.23
295
302
1.12
Helium 4
4.03188
4.00151
28.29
7.07
Lithium 7
7.05649
7.01336
40.15
5.74
Beryllium 9
9.07243
9.00999
58.13
6.46
Iron 56
56.44913
55.92069
492.24
8.79
Silver 107
107.86187
106.87934
915.23
8.55
Iodine 127
128.02684
126.87544
1072.53
8.45
Lead 206
207.67109
205.92952
1622.27
7.88
Polonium 210
211.70297
209.93683
1645.16
7.83
Uranium 235
236.90849
234.99351
1783.80
7.59
Uranium 238
239.93448
238.00037
1801.63
7.57
Viscosity of Water
Temperature
Dynamic Viscosity
Kinematic Viscosity
Density
°C
(centiPoise)
(centiPoise)
gm/cm3
2
1.6735
1.6736
0.9999
3
1.619
1.6191
1
4
1.5673
1.5674
1
5
1.5182
1.5182
1
6
1.4715
1.4716
0.9999
7
1.4271
1.4272
0.9999
8
1.3847
1.3849
0.9999
9
1.3444
1.3447
0.9998
10
1.3059
1.3063
0.9997
11
1.2692
1.2696
0.9996
12
1.234
1.2347
0.9995
13
1.2005
1.2012
0.9994
14
1.1683
1.1692
0.9992
296
303
15
1.1375
1.1386
0.9991
16
1.1081
1.1092
0.9989
17
1.0798
1.0811
0.9988
18
1.0526
1.0541
0.9986
19
1.0266
1.0282
0.9984
20
1.0016
1.0034
0.9982
21
0.9775
0.9795
0.998
22
0.9544
0.9565
0.9978
23
0.9321
0.9344
0.9975
24
0.9107
0.9131
0.9973
25
0.89
0.8926
0.997
26
0.8701
0.8729
0.9968
27
0.8509
0.8539
0.9965
28
0.8324
0.8355
0.9962
29
0.8145
0.8178
0.9959
30
0.7972
0.8007
0.9956
31
0.7805
0.7842
0.9953
32
0.7644
0.7682
0.995
33
0.7488
0.7528
0.9947
34
0.7337
0.7379
0.9944
35
0.7191
0.7234
0.994
36
0.705
0.7095
0.9937
37
0.6913
0.6959
0.9933
38
0.678
0.6828
0.993
39
0.6652
0.6702
0.9926
40
0.6527
0.6579
0.9922
45
0.5958
0.6017
0.9902
297
304
50
0.5465
0.5531
0.988
55
0.5036
0.5109
0.9857
60
0.466
0.474
0.9832
65
0.4329
0.4415
0.9806
70
0.4035
0.4127
0.9778
75
0.3774
0.3872
0.9748
80
0.354
0.3643
0.9718
Beer–Lambert law
The absorbance of a material that has only one attenuating species also depends on the pathlength and the
concentration of the species, according to the Beer–Lambert law:
A=ε×C×L
where:
ε is the molar attenuation coefficient of that material
C is the molar concentration of those species
L is the pathlength
Profitability ratios (SL/HL)
Gross profit margin =
Net profit margin =
gross profit
sales revenue
× 100
net profit before interest and tax
sales revenue
298
305
× 100
Liquidity ratios (SL/HL)
Current ratio =
current assets
current liabilities
Acid test (quick) ratio =
× 100
current assets − stock
current liabilities
× 100
Efficiency ratios (SL/HL)
Return on capital employed (ROCE) =
net profit before interest and tax
capital employed
× 100
where:
capital employed = loan capital (or long-term liabilities) + share capital + retained profit
Efficiency ratios (HL only)
Stock turnover (number of times) =
Stock turnover (number of days) =
cost of goods sold
average stock
average stock
cost of goods sold
× 365
where:
cost of goods sold is an approximation of total credit purchases and
average stock =
opening stock + closing stock
2
Debtor days ratio (number of days) =
299
306
debtors
total sales revenue
× 365
where total sales revenue is an approximation of total credit sales
Creditor days ratio (number of days) =
creditors
cost of goods sold
× 365
where cost of goods sold is an approximation of total credit purchases
Gearing ratio =
loan capital
capital employed
× 100
where capital employed = loan capital (or long-term liabilities) + share capital + retained profit
Investment appraisal (SL/HL)
Average rate of return (ARR) =
(total returns− capital cost)/ years of use
capital cost
× 100
Investment appraisal (HL only)
Net present value (NPV) = Σ present values of return − original cost
Capacity utilization and productivity (HL only)
Capacity utilization rate =
actual output
productive capacity
Productivity rate =
total output
total input
300
307
× 100
× 100
The Periodic Table of the Elements
1
2
H
He
Hydrogen
Helium
1.00794
3
4.003
4
5
6
7
8
9
10
Li
Be
B
C
N
O
F
Ne
Lithium
Beryllium
Boron
Carbon
Nitrogen
Oxygen
Fluorine
Neon
6.941
9.012182
10.811
12.0107
14.00674
11
12
13
14
15
15.9994 18.9984032 20.1797
16
17
18
Ar
Na
Mg
Al
Si
P
S
Cl
Sodium
Magnesium
Aluminum
Silicon
Phosphorus
Sulfur
Chlorine
Argon
22.989770
24.3050
26.981538
28.0855
30.973761
32.066
35.4527
39.948
19
20
31
32
33
34
35
36
21
22
23
24
25
26
27
28
29
30
K
Ca
Sc
Ti
V
Cr
Mn
Fe
Co
Ni
Cu
Zn
Ga
Ge
As
Se
Br
Kr
Potassium
Calcium
Scandium
Titanium
Vanadium
Chromium
Manganese
Iron
Cobalt
Nickel
Copper
Zinc
Gallium
Germanium
Arsenic
Selenium
Bromine
Krypton
39.0983
40.078
44.955910
47.867
50.9415
51.9961
54.938049
55.845
58.933200
58.6934
63.546
65.39
69.723
72.61
74.92160
78.96
79.904
83.80
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
Xe
Rb
Sr
Y
Zr
Nb
Mo
Tc
Ru
Rh
Pd
Ag
Cd
In
Sn
Sb
Te
I
Rubidium
Strontium
Yttrium
Zirconium
Niobium
Molybdenum
Technetium
Ruthenium
Rhodium
Palladium
Silver
Cadmium
Indium
Tin
Antimony
Tellurium
Iodine
Xenon
85.4678
87.62
88.90585
91.224
92.90638
95.94
(98)
101.07
102.90550
106.42
107.8682
112.411
114.818
118.710
121.760
127.60
126.90447
131.29
55
56
57
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
Rn
Cs
Ba
La
Hf
Ta
W
Re
Os
Ir
Pt
Au
Hg
Tl
Pb
Bi
Po
At
Cesium
Barium
Lanthanum
Hafnium
Tantalum
Tungsten
183.84
Rhenium
186.207
Osmium
190.23
Iridium
192.217
Platinum
195.078
Gold
196.96655
Mercury
200.59
Thallium
204.3833
Lead
207.2
Bismuth
Polonium
Astatine
(210)
(222)
106
107
108
109
110
111
112
113
114
66
67
68
69
70
71
132.90545
137.327
138.9055
178.49
180.9479
87
88
89
104
105
Fr
Ra
Ac
Rf
Db
Sg
Bh
Hs
Mt
Francium
Radium
Actinium
Rutherfordium
Dubnium
Seaborgium
Bohrium
Hassium
Meitnerium
(223)
(226)
(227)
(261)
(262)
(263)
(262)
(265)
(266)
(269)
(272)
(277)
58
59
60
61
62
63
64
65
208.98038
(209)
Radon
Ce
Pr
Nd
Pm
Sm
Eu
Gd
Tb
Dy
Ho
Er
Tm
Yb
Lu
Cerium
Praseodymium
Neodymium
Promethium
Samarium
150.36
Europium
151.964
Gadolinium
157.25
Terbium
158.92534
Dysprosium
162.50
Holmium
164.93032
Erbium
167.26
Thulium
168.93421
Ytterbium
173.04
Lutetium
174.967
90
91
92
93
94
95
96
97
98
99
100
101
102
103
140.116
140.90765
144.24
(145)
Th
Pa
U
Np
Pu
Am
Cm
Bk
Cf
Es
Fm
Md
No
Lr
Thorium
Protactinium
Uranium
Neptunium
Plutonium
Americium
Curium
Berkelium
Californium
Einsteinium
Fermium
Mendelevium
Nobelium
Lawrencium
232.0381 231.03588 238.0289
(237)
(244)
(243)
301
308
(247)
(247)
(251)
(252)
(257)
(258)
(259)
(262)
Sources of antioxidants
allium sulphur compounds – leeks, onions and garlic
anthocyanins – eggplant, grapes and berries
beta-carotene – pumpkin, mangoes, apricots, carrots, spinach and parsley
catechins – red wine and tea
copper – seafood, lean meat, milk and nuts
cryptoxanthins – red capsicum, pumpkin and mangoes
flavonoids – tea, green tea, citrus fruits, red wine, onion and apples
indoles – cruciferous vegetables such as broccoli, cabbage and cauliflower
isoflavonoids – soybeans, tofu, lentils, peas and milk
lignans – sesame seeds, bran, whole grains and vegetables
lutein – green, leafy vegetables like spinach, and corn
lycopene – tomatoes, pink grapefruit and watermelon
manganese – seafood, lean meat, milk and nuts
polyphenols – thyme and oregano
selenium – seafood, offal, lean meat and whole grains
vitamin A – liver, sweet potatoes, carrots, milk, and egg yolks
vitamin C – oranges, blackcurrants, kiwifruit, mangoes, broccoli, spinach, capsicum and strawberries
vitamin E – vegetable oils (such as wheatgerm oil), avocados, nuts, seeds and whole grains
zinc – seafood, lean meat, milk and nuts
zoochemicals – red meat, offal and fish.
309
302
Oxidation states of the elements
Element
Negative states
−5
−4
−3
−2
Positive states
−1
0
+1
+2
+3
+4
+5
+6
Group
+7
+8
+9
Z
1
hydrogen
H
2
helium
He
3
lithium
Li
4
beryllium
Be
5
boron
B
6
carbon
C
7
nitrogen
N
8
oxygen
O
9
fluorine
F
10
neon
Ne
11
sodium
Na
12
magnesium
Mg
13
aluminium
Al
14
silicon
Si
15
phosphorus
P
−1
1
+1
18
1
+1
−5
−4
0
+1
+2
−1
0
+1
+2
+3
0
+1
+2
+3
+4
+1
+2
+3
+4
+1
+2
−3
−2
−1
−3
−2
−1
−2
−1
0
2
13
14
+5
15
16
−1
17
18
−1
−4
1
+1
+1
+2
2
+1
+2
+3
−2
−1
−3
−2
−1
0
+1
+2
+3
+4
−3
−2
−1
0
+1
+2
+3
+4
310
303
13
14
+5
15
−2
16
sulfur
S
17
chlorine
Cl
18
argon
Ar
19
potassium
K
20
calcium
Ca
21
scandium
Sc
22
titanium
Ti
23
vanadium
V
24
chromium
Cr
25
manganese
Mn
26
iron
Fe
27
cobalt
Co
28
nickel
Ni
−2
29
copper
Cu
−2
30
zinc
Zn
−2
31
gallium
Ga
32
germanium
Ge
33
arsenic
As
34
selenium
Se
−1
0
−1
+1
+2
+3
+4
+5
+6
+1
+2
+3
+4
+5
+6
16
+7
0
−1
−4
0
+1
+2
+3
−1
0
+1
+2
+3
+4
−1
0
+1
+2
+3
+4
+5
−2
−1
0
+1
+2
+3
+4
+5
+6
−2
−1
0
+1
+2
+3
+4
+5
+6
+7
7
−2
−1
0
+1
+2
+3
+4
+5
+6
+7
8
−1
0
+1
+2
+3
+4
+5
−1
0
+1
+2
+3
+4
10
0
+1
+2
+3
+4
11
+1
+2
+1
+2
+3
−3
−5
1
+1
+2
−3
−3
18
+1
−2
−4
17
2
3
4
−3
−2
−1
−4
−3
−2
−1
0
+1
+2
+3
+4
−3
−2
−1
0
+1
+2
+3
+4
+5
−2
−1
+1
+2
+3
+4
+5
304
6
9
12
−4
311
5
13
14
15
+6
16
−1
35
bromine
Br
36
krypton
Kr
37
rubidium
Rb
38
strontium
Sr
39
yttrium
Y
40
zirconium
Zr
41
niobium
Nb
42
molybdenum
Mo
43
technetium
Tc
44
ruthenium
Ru
45
rhodium
Rh
46
palladium
Pd
47
silver
Ag
−2
48
cadmium
Cd
−2
49
indium
In
50
tin
Sn
51
antimony
Sb
52
tellurium
Te
53
iodine
I
+1
0
−1
−2
−4
−1
−2
−3
−4
−5
−4
+7
+5
18
1
+1
+2
2
+1
+2
+3
+1
+2
+3
+4
+1
+2
+3
+4
+5
3
4
5
0
+1
+2
+3
+4
+5
+6
−1
0
+1
+2
+3
+4
+5
+6
+7
0
+1
+2
+3
+4
+5
+6
+7
0
+1
+2
+3
+4
+5
+6
0
+1
+2
+3
+4
+1
+2
+3
+1
+2
+1
+2
+3
−1
17
+2
−1
−2
−3
+4
+1
0
−3
+1
+3
−1
+8
8
9
11
12
−1
−3
−2
−1
0
+1
+2
+3
+4
−3
−2
−1
0
+1
+2
+3
+4
+5
−2
−1
+1
+2
+3
+4
+5
+6
−1
+1
+3
+4
+5
+6
305
7
10
−2
312
6
13
14
15
16
+7
17
54
xenon
Xe
55
caesium
Cs
56
barium
Ba
57
lanthanum
La
58
cerium
Ce
59
praseodymium
Pr
0
60
neodymium
Nd
0
61
promethium
Pm
62
samarium
Sm
63
europium
Eu
64
gadolinium
Gd
0
65
terbium
Tb
0
66
dysprosium
Dy
67
holmium
68
0
−1
+1
+2
+4
+6
+8
18
1
+1
+1
+2
+1
+2
+3
+2
+3
+4
+2
+3
+4
+2
+3
+4
+2
+3
n/a
+2
+3
n/a
+2
+3
n/a
+1
+2
+3
n/a
+1
+2
+3
+4
n/a
0
+2
+3
+4
n/a
Ho
0
+2
+3
n/a
erbium
Er
0
+2
+3
n/a
69
thulium
Tm
+2
+3
n/a
70
ytterbium
Yb
+2
+3
n/a
71
lutetium
Lu
+2
+3
n/a
72
hafnium
Hf
+2
+3
0
+1
0
0
−2
+1
313
306
2
3
+4
n/a
+5
n/a
n/a
4
−3
73
tantalum
Ta
74
tungsten
W
75
rhenium
Re
76
osmium
Os
77
iridium
Ir
−3
78
platinum
Pt
−3
79
gold
Au
−3
80
mercury
Hg
81
thallium
Tl
82
lead
Pb
83
bismuth
Bi
84
polonium
Po
85
astatine
At
86
radon
Rn
87
francium
Fr
88
radium
Ra
89
actinium
Ac
90
thorium
Th
91
protactinium
Pa
−4
−1
−2
−3
+4
+5
5
+1
+2
+3
+4
+5
+6
−1
0
+1
+2
+3
+4
+5
+6
+7
−1
0
+1
+2
+3
+4
+5
+6
+7
+8
−1
0
+1
+2
+3
+4
+5
+6
+7
+8
−2
−1
0
+1
+2
+3
+4
+5
+6
−2
−1
0
+1
+2
+3
+1
+2
−2
−4
+3
0
−2
−5
+2
−1
−3
−4
+1
+1
+2
+3
−2
−1
+1
+2
+3
+4
−2
−1
+1
+2
+3
+4
+5
+4
+5
+2
15
+6
16
+7
+6
17
18
1
2
+2
3
+3
307
11
+5
+1
314
9
14
+2
+1
+9
13
+3
+1
8
12
−1
−1
7
10
+5
−2
−2
6
+2
+3
+4
+3
+4
n/a
+5
n/a
92
uranium
U
93
neptunium
94
+1
+2
+3
+4
+5
+6
n/a
Np
+2
+3
+4
+5
+6
+7
n/a
plutonium
Pu
+2
+3
+4
+5
+6
+7
n/a
95
americium
Am
+2
+3
+4
+5
+6
+7
n/a
96
curium
Cm
+3
+4
+5
+6
97
berkelium
Bk
+2
+3
+4
+5
n/a
98
californium
Cf
+2
+3
+4
+5
n/a
99
einsteinium
Es
+2
+3
+4
100
fermium
Fm
+2
+3
n/a
101
mendelevium
Md
+2
+3
n/a
102
nobelium
No
+2
+3
n/a
103
lawrencium
Lr
+3
n/a
104
rutherfordium
Rf
105
dubnium
Db
106
seaborgium
Sg
107
bohrium
Bh
108
hassium
Hs
109
meitnerium
Mt
9
110
darmstadtium
Ds
10
n/a
n/a
4
+4
5
+5
0
6
+6
7
+7
+8
315
308
8
111
roentgenium
Rg
11
112
copernicium
Cn
113
nihonium
Nh
13
114
flerovium
Fl
14
115
moscovium
Mc
15
116
livermorium
Lv
16
117
tennessine
Ts
17
118
oganesson
Og
18
+2
Factorial table
Number
Factorial
n
n!
0
1
1
1
2
2
3
6
4
24
5
120
6
720
7
5040
316
309
12
8
40320
9
362880
10
3628800
11
3.991680 × 107
12
4.790016 × 108
13
6.227021 × 109
14
8.717829 × 1010
15
1.307674 × 1012
16
2.092279 × 1013
17
3.556874 × 1014
18
6.402374 × 1015
19
1.216451 × 1017
20
2.432902 × 1018
Rocket Equations:
Thrust =
dM
dt
u
M → mass of the rocket
u → exhaust velocity in the rocket frame
(v − u) → exhaust velocity in the observer frame
v→ velocity of the rocket
Under the influence of the rocket thrust in a gravity-free environment, the resulting velocity can
be calculated from:
317
310
v = v0 + u ln
m0
m
velocity = initial velocity + exhaust velocity × ln
original mass
mass
Under the influence of the rocket thrust in a gravity environment, the resulting velocity can be
calculated from:
v = v0 + u ln
g→ gravitational acceleration
m0
m
− gt
t→ time
Power Table from 1 to 10
n
1
2
3
4
5
6
7
8
9
10
1n
1
1
1
1
1
1
1
1
1
1
2n
2
4
8
16
32
64
128
256
512
1024
3n
3
9
27
81
243
729
2187
6561
19683
59049
4n
4
16
64
256
1024
4096
16384
65536
262144
1048576
5n
5
25
125
625
3125
15625
78125
390625
1953125
9765625
318
311
6n
6
36
216
1296
7776
46656
279936
1679616
10077696
60466176
7n
7
49
343
2401
16807
117649
823543
5764801
40353607
282475249
8n
8
64
512
4096
32768
262144
2097152
16777216
134217728
1073741824
9n
9
81
729
6561
59049
531441
4782969
43046721
387420489
3486784401
10n
10
100
1000
10000
100000
1000000
10000000
100000000
1000000000
10000000000
Formulas of some saturated fatty acids
Common name Chemical structure
Caprylic acid
CH3(CH2)6COOH
Capric acid
CH3(CH2)8COOH
Lauric acid
CH3(CH2)10COOH
Myristic acid
CH3(CH2)12COOH
Palmitic acid
CH3(CH2)14COOH
Stearic acid
CH3(CH2)16COOH
Arachidic acid
CH3(CH2)18COOH
Behenic acid
CH3(CH2)20COOH
Lignoceric acid
CH3(CH2)22COOH
319
312
Cerotic acid
CH3(CH2)24COOH
Formulas of some Unsaturated Fatty Acids
Common name
Chemical structure
Myristoleic acid
CH3(CH2)3CH=CH(CH2)7COOH
Palmitoleic acid
CH3(CH2)5CH=CH(CH2)7COOH
Sapienic acid
CH3(CH2)8CH=CH(CH2)4COOH
Oleic acid
CH3(CH2)7CH=CH(CH2)7COOH
Elaidic acid
CH3(CH2)7CH=CH(CH2)7COOH
Vaccenic acid
CH3(CH2)5CH=CH(CH2)9COOH
Linoleic acid
CH3(CH2)4CH=CHCH2CH=CH(CH2)7COOH
Linoelaidic acid
CH3(CH2)4CH=CHCH2CH=CH(CH2)7COOH
α-Linolenic acid
CH3CH2CH=CHCH2CH=CHCH2CH=CH(CH2)7COOH
Arachidonic acid
CH3(CH2)4CH=CHCH2CH=CHCH2CH=CHCH2CH=CH(CH2)3COOH
Eicosapentaenoic acid
CH3CH2CH=CHCH2CH=CHCH2CH=CHCH2CH=CHCH2CH=CH(CH2)3COOH
Erucic acid
CH3(CH2)7CH=CH(CH2)11COOH
Docosahexaenoic acid
CH3CH2CH=CHCH2CH=CHCH2CH=CHCH2CH=CHCH2CH=CHCH2CH=CH(CH2)2COOH
320
313
Qualitative Analysis of the Phytochemicals
Test for Carbohydrates: The presence of carbohydrates is confirmed when 2 ml of
extract is treated with 1 ml of Molisch's reagent and few drops of concentrated sulphuric
acid which results in the formation of purple or reddish color.
Test for Tannins: To 1 ml of extract, 2 ml of 5% ferric chloride is added. Formation of
dark blue or greenish black indicates the presence of tannins.
Test for Saponins: 2 ml of extract, 2 ml of distilled water are added and shaken in a
graduated cylinder for 15 min lengthwise. It results in the formation of 1 cm layer of
foam that indicates the presence of saponins.
Test for Alkaloids: To 2 ml of extract, 2 ml of concentrated hydrochloric acid is added.
Then few drops of Mayer's reagent are added. Presence of green color or white
precipitate indicates the presence of alkaloids.
Test for Flavonoids: To 2 ml of extract, 1 ml of 2N sodium hydroxide is added.
Presence of yellow color indicates the presence of flavonoids.
Test for Glycosides: To 2 ml of extract, 3ml of chloroform and 10% ammonia solution is
added. Formation of pink color indicates presence of glycosides.
Test for Quinones: To 1 ml of extract, 1 ml of concentrated sulphuric acid is added.
Formation of red color indicates presence of quinones.
Test for Phenols: 2 ml of distilled water followed by few drops of 10% ferric chloride is
added to 1ml of the extract. Formation of blue or green color indicates presence of
phenols.
321
314
Test for Terpenoids: 0.5 ml of the extract is treated with 2 ml of chloroform and conc.
sulphuric acid. Formation of red brown colour at the interface indicates the presence of
terpenoids.
Test for Cardiac Glycosides: To 0.5 ml of the extract, 2 ml of glacial acetic acid and
few drops of ferric chloride are added. This is under layered with 1 ml of conc. sulphuric
acid. Formation of brown ring at the interface indicates the presence of cardiac
glycosides.
Ninhydrin Test: To 2 ml of the extract few drops of 0.2% ninhydrin reagent is added
and heated for 5 min. Formation of blue colour indicates the presence of amino acids.
Test for Coumarins: 1 ml of 10% sodium hydroxide is added to 1ml of the extract.
Formation of yellow colour indicates the presence of coumarins.
Anthraquinones: To 1 ml of extract few drops of 10% ammonia solution is added,
appearance of pink color precipitate indicates the presence of anthraquinones
Steroids: To 1 ml of extract equal volume of chloroform is added and a few drops of
concentrated sulphuric acid added appearance of brown ring indicates the presence of
steroids and appearance of bluish brown ring indicates the presence of phytosteroids.
Test for Phlobatannins: Few drops of 2% hydrochloric acid are added to 1ml of the
extract. Appearance of red colour precipitate indicates the presence of phlobatannins.
Anthracyanine: To 1 ml of the extract is added 1 mL 2N sodium hydroxide and heated
for 5 min at 100 °C. Formation of bluish green color indicates the presence of
anthocyanin.
322
315
Common names and IUPAC names of some carboxylic acids
Carbon atoms
Common name
IUPAC name
Chemical formula
1
Formic acid
Methanoic acid
HCOOH
2
Acetic acid
Ethanoic acid
CH3COOH
3
Propionic acid
Propanoic acid
CH3CH2COOH
4
Butyric acid
Butanoic acid
CH3(CH2)2COOH
5
Valeric acid
Pentanoic acid
CH3(CH2)3COOH
6
Caproic acid
Hexanoic acid
CH3(CH2)4COOH
7
Enanthic acid
Heptanoic acid
CH3(CH2)5COOH
8
Caprylic acid
Octanoic acid
CH3(CH2)6COOH
9
Pelargonic acid
Nonanoic acid
CH3(CH2)7COOH
10
Capric acid
Decanoic acid
CH3(CH2)8COOH
11
Undecylic acid
Undecanoic acid
CH3(CH2)9COOH
12
Lauric acid
Dodecanoic acid
CH3(CH2)10COOH
13
Tridecylic acid
Tridecanoic acid
CH3(CH2)11COOH
14
Myristic acid
Tetradecanoic acid
CH3(CH2)12COOH
15
Pentadecylic acid
Pentadecanoic acid
CH3(CH2)13COOH
323
316
16
Palmitic acid
Hexadecanoic acid
CH3(CH2)14COOH
17
Margaric acid
Heptadecanoic acid
CH3(CH2)15COOH
18
Stearic acid
Octadecanoic acid
CH3(CH2)16COOH
19
Nonadecylic acid
Nonadecanoic acid
CH3(CH2)17COOH
20
Arachidic acid
Icosanoic acid
CH3(CH2)18COOH
Magnetic properties of common nuclei
Isotope
Occurrence
Spin
Magnetic
Electric
Operating
Relative
in nature
number I
moment μ
quadrupole
frequency at 7 T
sensitivity
(μN)
moment
(MHz)
(%)
(e × 10
1
H
99.984
2
H
0.016
10
B
18.8
11
B
81.2
12
C
98.9
13
C
1.1
14
N
99.64
15
N
0.37
16
O
99.76
17
O
0.0317
19
28
F
100
Si
92.28
−24
2
cm )
1
2
2.79628
0
300.13
1
1
0.85739
0.0028
46.07
0.0964
3
1.8005
0.074
32.25
0.0199
3
2
2.6880
0.026
96.29
0.165
0
0
0
0
0
1
2
0.70220
0
75.47
0.0159
1
0.40358
0.071
21.68
0.00101
1
2
−0.28304
0
30.41
0.00104
0
0
0
0
0
5
2
1
2
−1.8930
−0.0040
40.69
0.0291
2.6273
0
282.40
0.834
0
0
0
0
0
324
317
29
Si
31
1
2
1
2
3
2
3
2
4.70
P
100
35
Cl
75.4
37
Cl
24.6
−0.5548
0
59.63
0.0785
1.1205
0
121.49
0.0664
0.92091
−0.079
29.41
0.0047
0.68330
−0.062
24.48
0.0027
List of plant hormones and their functions
Hormone
Function
Ethylene
Fruit ripening and abscission
Gibberellins
Break the dormancy of seeds and buds; promote
growth
Cytokinins
Promote cell division; prevent senescence
Abscisic Acid
Close the stomata; maintain dormancy
Auxins
Involved in tropisms and apical dominance
List of the Constellations
Constellation
Mythological Association
First
Genitive Form
Brightest Star
Ancient
Andromedae
Alpheratz
1756
Antliae
α-Ant
Appeared
Andromeda
The Princess Andromeda; in Greek
mythology, the daughter of
Cepheus and Cassiopeia and wife
of Perseus.
Antlia
The air pump; a southern
325
318
constellation introduced by
(Lacaille)
Lacaille in 1756, originally the
'pneumatic machine'.
Apus
Apodis
α-Aps
Ancient
Aquarii
Sadalsuud
Ancient
Aquilae
Altair
Ancient
Arae
α-Ara
Ancient
Arietis
Hamal
Ancient
Aurigae
Capella
Ancient
Bootis
Arcturus
The chisel; a southern
1756
Caeli
α-Cae
constellation introduced by
(Lacaille)
The bird of paradise; a southern
1598 (Keyser
constellation introduced by
& de Houtman)
Keyser & de Houtman in 1598.
Aquarius
The water bearer; in Greek
mythology, Ganymede, wine-waiter
to the Gods and lover of Zeus.
Aquila
The eagle; in Greek mythology,
the bird of Zeus and the
retriever of his thunderbolts.
Ara
The altar; in Greek mythology,
used by the Gods to vow
allegiance before their battle
with the Titans.
Aries
The ram; in Greek mythology, the
animal whose golden fleece was
recovered by Jason and the
Argonauts.
Auriga
The charioteer; in Greek
mythology, Erichthonius, son of
Vulcan, the first person to
attach four horses to a chariot.
Bootes
The herdsman; in Greek
mythology, Arcas, son of Zeus by
Callisto.
Caelum
Lacaille in 1756.
326
319
Camelopardalis
Camelopardalis
β-Cam
Ancient
Cancri
β-Cnc
The hunting dogs; introduced by
1687
Canum
Cor-Caroli
Johannes Hevelius in 1687, and
(Hevelius)
Venaticorum
Ancient
Canis Majoris
Sirius
Ancient
Canis Minoris
Procyon
Ancient
Capricorni
δ-Cap
The keel; a sub-division of the
1756
Carinae
Canopus
ancient constellation Argo – in
(Lacaille)
Ancient
Cassiopeiae
γ-Cas
Ancient
Centauri
Rigil-
The giraffe; a large but faint
1612
northern constellation
(Plancius)
introduced by Plancius in 1612.
Cancer
The crab; in Greek mythology, a
crab which bit Hercules's foot.
Canes Venatici
said to be held by the herdsman
Bootes.
Canis Major
The greater dog; in Greek
mythology, a hunting dog
belonging to Orion, depicted
pursuing the hare Lepus.
Canis Minor
The lesser dog; in Greek
mythology, a hunting dog
belonging to Orion, depicted
pursuing the hare Lepus.
Capricornus
The sea goat; associated with
Pan in Greek mythology, god of
the countryside.
Carina
Greek mythology, the ship of the
Argonauts.
Cassiopeia
Queen Cassiopeia; in Greek
mythology, wife of Cepheus and
mother of Andromeda.
Centaurus
The Centaur: half man and half
horse; in Greek mythology, the
wise centaur Chiron.
327
320
Kentaurus
Cepheus
King Cepheus of Ethiopeia; in
Ancient
Cephei
Alderamin
Ancient
Ceti
Diphda
The chameleon; introduced by
1598 (Keyser
Chamaeleontis
α-Cha
Keyser & de Houtman in 1598.
& de Houtman)
The pair of dividing compasses;
1756
Circini
α-Cir
a modern constellation
(Lacaille)
Columbae
Phact
Comae
β-Com
Greek mythology, the king of
Ethiopia, descended from Zeus
and Io.
Cetus
The sea monster, which in Greek
mythology attacked Cepheus's
territory and Andromeda, but
which was slain by Perseus.
Chamaeleon
Circinus
introduced by Lacaille in 1756.
Columba
The dove; introduced by Plancius
1592
in 1592. In Biblical history,
(Plancius)
said to be the dove of Noah.
Coma Berenices
The hair of Queen Berenice of
1536 (Vopel)
Egypt; introduced as a
Berenices
constellation by Vopel in 1536.
Corona
The southern crown, lying at the
Australis
feet of Sagittarius, and known
Ancient
Coronae
α-CrA
Australis
to the Greeks as a wreath.
Corona
The northern crown; in Greek
Borealis
mythology, worn by the Princess
Ancient
Coronae
Alphecca
Borealis
Ariadne on her wedding day.
Corvus
The crow; in Greek mythology,
Ancient
Corvi
Gienah
Ancient
Crateris
δ-Crt
sent by Apollo in search of
water.
Crater
The cup; in Greek mythology,
clutched by the crow Crater in
328
321
its search for water.
Crux
The southern cross; introduced
1598
Crucis
Acrux
as a constellation by Plancius
(Plancius)
Ancient
Cygni
Deneb
Ancient
Delphini
Rotanev
The goldfish; a constellation
1598 (Keyser
Doradus
α-Dor
introduced by Keyser & de
& de Houtman)
Ancient
Draconis
Eltanin
The little horse; a tiny yet
Ancient
Equulei
Kitalpha
ancient constellation with no
(Ptolemy)
Ancient
Eridani
Achernar
The furnace; originally a
1756
Fornacis
α-For
chemist's distillation furnace,
(Lacaille)
Ancient
Geminorum
Pollux
The crane; a constellation
1598 (Keyser
Gruis
Alnair
introduced by Keyser & de
& de Houtman)
Herculis
Kornephoros
in 1598.
Cygnus
The swan; in Greek mythology,
Zeus in disguise.
Delphinus
The dolphin; in Greek mythology,
the messenger of Poseidon.
Dorado
Houtman in 1598.
Draco
The dragon; in Greek mythology,
Ladon, guard of the tree on
which golden apples grew, slain
by Hercules.
Equuleus
mythological association.
Eridanus
The mythical river Eridanus;
associated variously with the
Nile or Po.
Fornax
introduced by Lacaille in 1756.
Gemini
The mythical twins Castor and
Pollux.
Grus
Houtman in 1598.
Hercules
Hercules; a large yet dark
329
322
Ancient
constellation representing the
greatest hero of Greek
mythology.
Horologium
Horologii
α-Hor
Ancient
Hydrae
Alphard
The lesser water snake;
1598 (Keyser
Hydri
β-Hyi
introduced as a constellation by
& de Houtman)
Indi
α-Ind
Lacertae
α-Lac
Ancient
Leonis
Regulus
The lion cub; introduced as a
1687
Leonis Minoris
46-LMi
constellation by Johannes
(Hevelius)
Ancient
Leporis
Arneb
The balance; a zodiacal
Ancient
Librae
Zubeneschamali
constellation introduced by the
(Roman)
The pendulum clock; a modern
1756
constellation introduced by
(Lacaille)
Lacaille in 1756.
Hydra
The multi-headed water snake,
slain by Hercules in Greek
mythology.
Hydrus
Keyser & de Houtman in 1598.
Indus
The Indian; introduced as a
1598 (Keyser
constellation by Keyser & de
& de Houtman)
Houtman in 1598.
Lacerta
The lizard; introduced as a
1690
constellation by Johannes
(Hevelius)
Hevelius in 1690.
Leo
The lion of Nemea; in Greek
mythology, a monster slain by
Hercules.
Leo Minor
Hevelius in 1687.
Lepus
The hare; often depicted being
chased by Orion and his two
dogs.
Libra
Romans.
330
323
Lupus
Ancient
Lupi
α-Lup
The lynx; a faint constellation
1687
Lyncis
α-Lyn
introduced by Johannes Hevelius
(Hevelius)
Ancient
Lyrae
Vega
Table Mountain, South Africa; a
1756
Mensae
α-Men
modern constellation introduced
(Lacaille)
Microscopii
γ-Mic
Monocerotis
α-Mon
Muscae
α-Mus
Normae
γ²-Nor
Octantis
ν-Oct
Ophiuchi
Rasalhague
The wolf; an ancient
constellation, but without
mythological association.
Lynx
in 1687.
Lyra
The lyre; often said to be
played by Orpheus, the greatest
musician of his age.
Mensa
by Lacaille in 1756, celebrating
his southern-hemisphere
observing site.
Microscopium
The microscope; a modern
1756
constellation introduced by
(Lacaille)
Lacaille in 1756.
Monoceros
Musca
The unicorn; a constellation
1612
introduced by Plancius in 1612.
(Plancius)
The fly; a constellation
1598 (Keyser
introduced by Keyser & de
& de Houtman)
Houtman in 1598.
Norma
The set square; a modern
1756
constellation introduced by
(Lacaille)
Lacaille in 1756.
Octans
The octant, a navigational
1756
instrument invented in the
(Lacaille)
1730s. A modern constellation
introduced by Lacaille in 1756.
Ophiuchus
The serpent bearer; in Greek
331
324
Ancient
mythology, Asclepius, the god of
medicine, depicted in the sky
holding the snake Serpens.
Orion
The hunter; associated in Greek
Ancient
Orionis
Rigel
The peacock; a constellation
1598 (Keyser
Pavonis
Peacock
introduced by Keyser & de
& de Houtman)
Ancient
Pegasi
Enif
Ancient
Persei
Mirfak
The phoenix; a constellation
1598 (Keyser
Phoenicis
Ankaa
introduced by Keyser & de
& de Houtman)
Pictoris
α-Pic
Ancient
Piscium
η-Psc
Ancient
Piscis
Fomalhaut
mythology with a son of
Poseidon, but associated by the
Sumerians with their great hero
Gilgamesh.
Pavo
Houtman in 1598.
Pegasus
The winged horse; in Greek
mythology, used by Zeus to carry
thunder and lightning.
Perseus
Perseus; in Greek mythology, the
husband of Andromeda, also known
for slaying Medusa the Gorgon.
Phoenix
Houtman in 1598.
Pictor
The painter's easel; a modern
1756
constellation introduced by
(Lacaille)
Lacaille in 1756.
Pisces
Two fishes, swimming in opposite
directions with their tails
connected by a cord.
Piscis
The southern fish; the parent of
Austrinus
the two fish depicted by Pisces.
Puppis
The poop deck of the Argo Navis;
1756
a sub-division of the ancient
(Lacaille)
332
325
Austrini
Puppis
Naos
constellation Argo – in Greek
mythology, the ship of the
Argonauts.
Pyxis
Pyxidis
α-Pyx
Reticuli
α-Ret
Ancient
Sagittae
γ-Sge
Ancient
Sagittarii
Kaus-Australis
Ancient
Scorpii
Antares
The sculptor – originally, the
1756
Sculptoris
α-Scl
sculptor's studio; a modern
(Lacaille)
Scuti
α-Sct
Serpentis
Unukalhai
The compass; a southern
1756
constellation introduced by
(Lacaille)
Lacaille in 1756.
Reticulum
The net; a southern
1756
constellation introduced by
(Lacaille)
Lacaille in 1756, commemorating
the cross-hair in his telescope.
Sagitta
The arrow; in Greek mythology,
perhaps the arrow that Apollo
used to kill the Cyclopes.
Sagittarius
The archer; usually drawn as a
centaur – half man, half horse
Scorpius
The scorpion; said to have stung
the hunter Orion to death in
Greek mythology.
Sculptor
constellation introduced by
Lacaille in 1756.
Scutum
The shield; a constellation
1684
honouring King John III Sobieski
(Hevelius)
of Poland – the only politically
inspired constellation still in
use.
Serpens Caput
The serpent's head; held by
Ophiuchus and part of the same
constellation as Serpens Cauda.
333
326
Ancient
Caput
Serpens Cauda
The serpent's tail; held by
Ancient
Ophiuchus and part of the same
Serpentis
η-Ser
Cauda
constellation as Serpens Caput.
Sextans
Sextantis
α-Sex
Ancient
Tauri
Aldebaran
The telescope; a modern
1756
Telescopii
α-Tel
constellation introduced by
(Lacaille)
Ancient
Trianguli
β-Tri
Atria
The sextant; a constellation
1687
introduced by Johannes Hevelius
(Hevelius)
in 1687, celebrating an
instrument used to measure star
positions.
Taurus
The bull; said by the Sumerians
to be charging at Orion the
hunter, but in Greek mythology
said to be Zeus in disguise.
Telescopium
Lacaille in 1756.
Triangulum
The triangle; appearing similar
to a capital delta in the Greek
alphabet.
Triangulum
The southern triangle; a
1598 (Keyser
Trianguli
Australe
constellation introduced by
& de Houtman)
Australe
The toucan; a constellation
1598 (Keyser
Tucanae
α-Tuc
introduced by Keyser & de
& de Houtman)
Ancient
Ursae Majoris
Alioth
Ancient
Ursae Minoris
Polaris
Keyser & de Houtman in 1598.
Tucana
Houtman in 1598.
Ursa Major
The great bear, also known as
the Big Dipper or the Plough. In
Greek mythology, Callisto, lover
of Zeus.
Ursa Minor
The lesser bear; in Greek
mythology, one of the nymphs
334
327
that nursed Zeus as an infant.
Vela
Velorum
γ²-Vel
Ancient
Virginis
Spica
The flying fish; a constellation
1598 (Keyser
Volantis
γ²-Vol
introduced by Keyser & de
& de Houtman)
Vulpeculae
α-Vul
The sail; a sub-division of the
1756
ancient constellation Argo – in
(Lacaille)
Greek mythology, the ship of the
Argonauts.
Virgo
The virgin; in Greek mythology,
the goddess of justice.
Volans
Houtman in 1598, celebrating the
family Exocoetidae.
Vulpecula
The fox; a constellation
1687
introduced by Johannes Hevelius
(Hevelius)
in 1687.
List of superconductors
Substance
Al
Class
Element
Transition
Critical magnetic
Type
temperature (K)
field (T)
1.20
0.01
I
5.3×10−4
5.2×10−6
I
Bi
Element
Cd
Element
0.52
0.0028
I
Diamond:B
Element
11.4
4
II
Ga
Element
1.083
0.0058
I
Hf
Element
0.165
α-Hg
Element
4.15
335
328
I
0.04
I
β-Hg
Element
3.95
0.04
I
In
Element
3.4
0.03
I
Ir
Element
0.14
0.0016
I
α-La
Element
4.9
β-La
Element
6.3
I
I
−4
Li
Element
4×10
Mo
Element
0.92
0.0096
I
Nb
Element
9.26
0.82
II
Os
Element
0.65
0.007
I
Pa
Element
1.4
Pb
Element
7.19
Re
Element
2.4
3.25×10
I
I
0.08
I
0.03
−4
Rh
Element
Ru
Element
0.49
0.005
I
Si:B
Element
0.4
0.4
II
Sn
Element
3.72
0.03
I
Ta
Element
4.48
0.09
I
Tc
Element
7.46–11.2
0.04
II
α-Th
Element
1.37
0.013
I
Ti
Element
0.39
0.01
I
Tl
Element
2.39
0.02
I
α-U
Element
0.68
I
β-U
Element
1.8
I
V
Element
5.03
1
II
α-W
Element
0.015
0.00012
I
β-W
Element
1–4
Zn
Element
0.855
0.005
I
Zr
Element
0.55
0.014
I
Ba8Si46
Compound
8.07
0.008
II
C6Ca
Compound
11.5
0.95
II
C6Li3Ca2
Compound
11.15
II
C8K
Compound
0.14
II
C8KHg
Compound
1.4
II
336
329
4.9×10
I
−6
I
C6K
Compound
1.5
II
C3K
Compound
3.0
II
C3Li
Compound
<0.35
II
C2Li
Compound
1.9
II
C3Na
Compound
2.3–3.8
II
C2Na
Compound
5.0
II
C8Rb
Compound
0.025
II
C6Sr
Compound
1.65
II
C6Yb
Compound
6.5
II
C60Cs2Rb
Compound
33
II
C60K3
Compound
19.8
C60RbX
Compound
28
II
FeB4
Compound
2.9
II
InN
Compound
3
II
In2O3
Compound
3.3
LaB6
Compound
0.45
MgB2
Compound
39
Nb3Al
Compound
18
NbC1-xNx
Compound
17.8
12
II
Nb3Ge
Compound
23.2
37
II
NbO
Compound
1.38
II
NbN
Compound
16
II
Nb3Sn
Compound
18.3
30
II
NbTi
Compound
10
15
II
SiC:B
Compound
1.4
0.008
I
SiC:Al
Compound
1.5
0.04
II
TiN
Compound
5.6
5
I
V3Si
Compound
17
YB6
Compound
8.4
ZrN
Compound
10
ZrB12
Compound
6.0
YBCO
Cuprate
95
GdBCO
Cuprate
91
337
330
0.013
II
~3
II
74
II
II
II
II
120–250
II
II
BSCCO
Cuprate
104
HBCCO
Cuprate
135
SmFeAs(O,F)
Iron-based
55
CeFeAs(O,F)
Iron-based
41
LaFeAs(O,F))
Iron-based
26
LaFePO
Iron-based
4
FeSe
Iron-based
65
(Ba,K)Fe2As2
Iron-based
38
NaFeAs
Iron-based
20
List of vitamins and their functions
Water-soluble vitamins
Vitamin
Function
Sources
Thiamine
Part of an enzyme needed for energy
Found in all nutritious foods in moderate
(vitamin B1)
metabolism; important to nerve function
amounts: pork, whole-grain or enriched breads
and cereals, legumes, nuts and seeds
Riboflavin
Part of an enzyme needed for energy
Milk and milk products; leafy green vegetables;
(vitamin B2)
metabolism; important for normal vision
whole-grain, enriched breads and cereals
and skin health
Niacin
(vitamin B3)
Part of an enzyme needed for energy
Meat, poultry, fish, whole-grain or enriched
metabolism; important for nervous
breads and cereals, vegetables (especially
mushrooms, asparagus, and leafy green
338
331
system, digestive system, and skin health
vegetables), peanut butter
Pantothenic
Part of an enzyme needed for energy
Widespread in foods
acid
metabolism
Biotin
Part of an enzyme needed for energy
Widespread in foods; also produced in intestinal
metabolism
tract by bacteria
Part of an enzyme needed for protein
Meat, fish, poultry, vegetables, fruits
Pyridoxine
(vitamin B6)
Folic acid
metabolism; helps make red blood cells
Part of an enzyme needed for
Leafy green vegetables and legumes, seeds,
making DNA and new cells, especially
orange juice, and liver; now added to most refined
red blood cells
grains
Part of an enzyme needed for making
Meat, poultry, fish, seafood, eggs, milk and milk
new cells; important to nerve function
products; not found in plant foods
Ascorbic acid
Antioxidant; part of an enzyme needed
Found only in fruits and vegetables, especially
(vitamin C)
for protein metabolism; important for
citrus fruits, vegetables in the cabbage family,
immune system health; aids in iron
cantaloupe, strawberries, peppers, tomatoes,
absorption
potatoes, lettuce, papayas, mangoes, kiwifruit
Cobalamin
(vitamin B12)
339
332
Fat-soluble vitamins
Vitamin
Function
Sources
Vitamin A (and its
Needed for vision, healthy skin
Vitamin A from animal sources (retinol): fortified
precursor*, beta-
and mucous membranes, bone
milk, cheese, cream, butter, fortified margarine,
carotene)
and tooth growth, immune
eggs, liver
*A precursor is
system health
Beta-carotene (from plant sources): Leafy, dark
converted by the
green vegetables; dark orange fruits (apricots,
body to the vitamin.
cantaloupe) and vegetables (carrots, winter squash,
sweet potatoes, pumpkin)
Vitamin D
Needed for proper absorption
Egg yolks, liver, fatty fish, fortified milk, fortified
of calcium; stored in bones
margarine. When exposed to sunlight, the skin can
make vitamin D.
Vitamin E
Antioxidant; protects cell walls
Polyunsaturated plant oils (soybean, corn,
cottonseed, safflower); leafy green vegetables;
wheat germ; whole-grain products; liver; egg yolks;
nuts and seeds
Vitamin K
Needed for proper blood clotting
Leafy green vegetables such as kale, collard greens,
and spinach; green vegetables such as broccoli,
Brussels sprouts, and asparagus; also produced
in intestinal tract by bacteria
340
333
Surface tension for some interfaces
Interface
Temperature
Surface tension
(mN/m)
Water–air
20 °C
72.86 ± 0.05
Water–air
21.5 °C
72.75
Water–air
25 °C
71.99±0.05
Methylene iodide–air
20 °C
67.00
Methylene iodide–air
21.5 °C
63.11
Ethylene glycol–air
25 °C
47.3
Ethylene glycol–air
40 °C
46.3
Dimethyl sulfoxide–air
20 °C
43.54
Propylene carbonate–air
20 °C
41.1
Benzene–air
20 °C
28.88
Benzene–air
30 °C
27.56
341
334
Toluene–air
20 °C
28.52
Chloroform–air
25 °C
26.67
Propionic acid–air
20 °C
26.69
Butyric acid–air
20 °C
26.51
Carbon tetrachloride–air
25 °C
26.43
Butyl acetate–air
20 °C
25.09
Diethylene glycol–air
20 °C
30.09
Nonane–air
20 °C
22.85
Methanol–air
20 °C
22.50
Ethanol–air
20 °C
22.39
Ethanol–air
30 °C
21.55
Octane–air
20 °C
21.61
Heptane–air
20 °C
20.14
Ether–air
25 °C
20.14
342
335
Mercury–air
20 °C
486.5
Mercury–air
25 °C
485.5
Mercury–air
30 °C
484.5
NaCl–air
1073 °C
115
KClO3–air
20 °C
81
Water–1-Butanol
20 °C
1.8
Water–Ethyl acetate
20 °C
6.8
Water–Heptanoic acid
20 °C
7.0
Water–Benzaldehyde
20 °C
15.5
Water–transformer oil
20 °C
37.2
Water–Mercury
20 °C
415
Ethanol–Mercury
20 °C
389
Water–1,2-Dichloroethane
20 °C
30.5 ± 0.3
Water–α,α,α-trifluorotoluene
20 °C
38.0 ± 0.5
343
336
Water–nitrobenzene
20 °C
24.4 ± 0.2
Water–nitromethane
20 °C
16.0 ± 0.2
Water–propylene carbonate
20 °C
2.9 ± 0.1
List of inorganic and organic reagents commonly used in chemistry
Name
General Description
Acetic acid
an organic acid; is one of the simplest carboxylic acids
Acetone
an organic compound; simplest example of the ketones
Acetylene
a hydrocarbon and the simplest alkyne; widely used as a
fuel and chemical building block
Ammonia
inorganic; the precursor to most nitrogen-containing
compounds; used to make fertilizer
Ammonium hydroxide
aqueous ammonia; used in traditional qualitative
inorganic analysis
Azobisisobutyronitrile
organic compound; often used as a foamer in plastics
and rubber and as a radical initiator
344
337
Baeyer's reagent
is an alkaline solution of potassium permanganate; used
in organic chemistry as a qualitative test for the presence
of unsaturation, such as double bonds;
N-Bromosuccinimide
used in radical substitution and electrophilic
addition reactions in organic chemistry
Butanone (methyl ethyl ketone)
organic compound; similar solvent properties to acetone
but has a significantly slower evaporation rate
Butylated hydroxytoluene
a fat-soluble organic compound that is primarily used as
an antioxidant food additive
n-Butyllithium
an organolithium reagent; used as
a polymerization initiator in the production
of elastomers such as polybutadiene or styrenebutadiene-styrene (SBS)
Carbon disulfide
a non-polar solvent; used frequently as a building block
in organic chemistry
Carbon tetrachloride
toxic, and its dissolving power is low; consequently, it
has been largely superseded by deuterated solvents
Carbonyldiimidazole
often used for the coupling of amino
acids for peptide synthesis and as a reagent in organic
synthesis
Ceric ammonium nitrate
an inorganic compound; used as an oxidising agent in
organic synthesis and as a standard oxidant in
345
338
quantitative analysis
Chloridotris(triphenylphosphine) rhodium (I)
Coordination complex; used in
homogeneous catalysis of alkenes to alkanes
Chloroform
organic compound; often used as CHCl3 (deuterated
chloroform) as a solvent for NMR spectroscopy and as a
general solvent.
Chromic acid
a strong and corrosive oxidising agent; an intermediate
in chromium plating
Chromium trioxide
the acidic anhydride of chromic acid; mainly used in
chrome-plating
Collins reagent
used to selectively oxidize primary alcohols to
an aldehyde
Copper(I) iodide
useful in a variety of applications ranging from organic
synthesis to cloud seeding
Dess–Martin periodinane
chemical reagent used to oxidize primary alcohols to
aldehydes and secondary alcohols to ketones
Diborane
the central organic synthesis reagent for hydroboration
Dicyclohexylcarbodiimide
an organic compound; primary use is to couple amino
acids during artificial peptide synthesis
Diethyl azodicarboxylate
a valuable reagent but also quite dangerous and explodes
346
339
upon heating
Diethyl ether
organic compound; a common laboratory solvent
Dihydropyran
a heterocyclic compound; used as a protecting
group for alcohols in organic synthesis.
Diisobutylaluminium hydride
an organoaluminium compound ; a reducing agent;
converts esters and nitriles to aldehydes
Diisopropyl azodicarboxylate
the diisopropyl ester of azodicarboxylic acid; a reagent
in the production of many organic compounds
Dimethyl ether
the simplest ether; a useful precursor to other organic
compounds and an aerosol propellant
Dimethylformamide
organic compound; a common solvent for chemical
reactions
Dimethylsulfide
organosulfur compound; used in petroleum refining and
in petrochemical production processes; a reducing agent
in ozonolysis reactions
Dimethyl sulfoxide
an organosulfur compound; an important polar aprotic
solvent that dissolves both polar and nonpolar
compounds
Dioxane
a heterocyclic organic compound; classified as an ether
Ethanol
a powerful psychoactive drug; used in alcoholic
347
340
beverages, in thermometers, as a solvent, and as a fuel
Fehling's reagent
used to differentiate between water-soluble aldehyde and
ketone functional groups
Fenton's reagent
a solution of hydrogen peroxide and an iron catalyst that
is used to oxidize contaminants or waste waters
Formaldehyde
the simplest aldehyde; an important precursor to many
other chemical compounds, such as polymers and
polyfunctional alcohols
Formic acid
the simplest carboxylic acid; often used as a source of
the hydride ion
Grignard reagents
the most common application is for alkylation of
aldehydes and ketones
Hexamethylphosphoramide
a phosphoramide; useful polar aprotic solvent and
additive in organic synthesis
Hydrazine
It's a good reducing agent and is used in the WolffKishner reaction for reducing carbonyls to its
corresponding alkanes. used as a foaming agent in
preparing polymer foams; also a precursor to
polymerization catalysts and pharmaceuticals; also as an
Oxygen scavenger in Power Plants
Hydrazoic acid
used primarily for preservation of stock solutions, and as
a reagent
348
341
Hydrochloric acid
a highly corrosive, strong mineral acid with many
industrial uses
Hydrofluoric acid
valued source of fluorine, precursor to numerous
pharmaceuticals; highly corrosive
Hydrogen peroxide
an oxidizer commonly used as a bleach
Imidazole
an organic compound; this aromatic heterocyclic is
a diazole and is classified as an alkaloid
Isopropyl alcohol
simplest example of a secondary alcohol; dissolves a
wide range of non-polar compounds
Lime
used in Flue Gas Desulphurisation in Power Plants
Limestone
used in Flue Gas Desulphurisation in Power Plants
Lithium aluminium hydride
a reducing agent in organic synthesis; used to prepare
main group and transition metal hydrides from the
corresponding metal halides
Lithium diisopropylamide
strong base used in organic chemistry for the
deprotonation of weakly acidic compounds
Manganese dioxide
used as a pigment and as a precursor to other manganese
compounds; used as a reagent in organic synthesis for
the oxidation of allylic alcohols
349
342
Meta-Chloroperoxybenzoic acid
used as an oxidant in organic synthesis
Methyl tert-butyl ether
a gasoline additive; also used in organic chemistry as a
relatively inexpensive solvent
Millon's reagent
an analytical reagent used to detect the presence of
soluble proteins
Nitric acid
highly corrosive and toxic strong acid; used for the
production of fertilizers, production of explosives, and
as a component of aqua regia
Osmium tetroxide
in organic synthesis, is widely used to oxidise alkenes to
the vicinal diols
Oxalyl chloride
used in organic synthesis for the preparation of acid
chlorides from the corresponding carboxylic acids
Palladium(II) acetate
a catalyst for many organic reactions by combining with
many common classes of organic compounds to form
reactive adduct
Perchloric acid
a powerful oxidizing agent; readily forms explosive
mixtures; mainly used in the production of rocket fuel
Phosphoric acid
a mineral acid with many industrial uses; commonly
used in the laboratory preparation of hydrogen halides
Phosphorus pentachloride
one of the most important phosphorus chlorides; a
chlorinating reagent. Also used as a dehydrating agent
350
343
for oximes which turn them into nitriles.
Phosphorus tribromide
used for the conversion of alcohols to alkyl bromides
Phosphorus trichloride
most important of the three phosphorus chlorides; used
to manufacture organophosphorus compounds; used to
convert primary and secondary alcohols into alkyl
chlorides, or carboxylic acids into acyl chlorides
Phosphoryl chloride
used to make phosphate esters such as tricresyl
phosphate
Potassium dichromate
a common inorganic chemical reagent, most commonly
used as an oxidizing agent in various laboratory and
industrial applications
Potassium hydroxide
a strong base; precursor to most soft and liquid soaps as
well as numerous potassium-containing chemicals
Potassium permanganate
a strong oxidizing agent; can be used to quantitatively
determine the total oxidisable organic material in an
aqueous sample; a reagent for the synthesis of organic
compounds
Pyridinium chlorochromate
used to oxidize primary alcohols to aldehydes and
secondary alcohols to ketones
Pyridinium dichromate (Cornforth reagent)
converts primary and secondary alcohols to ketones
Raney nickel
an alternative catalyst for the hydrogenation of vegetable
351
344
oils; in organic synthesis, used for desulfurization
Sakaguchi's Reagent
Detects the presence of arginine
Samarium(II) iodide (Kagan Reagent)
a powerful reducing agent
Silver oxide
used to prepare other silver compounds; in organic
chemistry, used as a mild oxidizing agent
Silver nitrate
precursor to many other silver compounds; commonly
used in inorganic chemistry to abstract halides
Sodium amide
used in the industrial production of indigo, hydrazine,
and sodium cyanide; used for the drying of ammonia;
used as a strong base in organic chemistry
Sodium azide
gas-forming component in airbag systems; used in
organic synthesis to introduce the azide functional group
by displacement of halides
Sodium bis(trimethylsilyl)amide
a strong base; deprotonates ketones and esters to
generate enolate derivative
Sodium borohydride
a versatile reducing agent; converts ketones and
aldehydes to alcohols
Sodium chlorite
in organic synthesis, used for the oxidation of aldehydes
to carboxylic acids
Sodium hydride
a strong base used in organic synthesis
352
345
Sodium hydroxide
strong base with many industrial uses; in the laboratory,
used with acids to produce the corresponding salt, also
used as an electrolyte
Sodium hypochlorite
frequently used as a disinfectant or a bleaching agent
Sodium nitrite
used to convert amines into diazo compounds
Sulfuric acid
strong mineral acid; major industrial use is the
production of phosphoric acid
tert-Butyl hydroperoxide
used in a variety of oxidation processes; industrially, is
used as a starter of radical polymerization
Tetrahydrofuran
one of the most polar ethers; a useful solvent; its main
use is as a precursor to polymers
Tetrakis(triphenylphosphine)palladium(0)
a catalyst for palladium-catalyzed coupling reactions
Tetramethylammonium hydroxide
a quaternary ammonium salt; used as an anisotropic
etchant of silicon; used as a basic solvent in the
development of acidic photoresist in
the photolithography process
Tetramethylsilane
the simplest tetraorganosilane; a building block
in organometallic chemistry
Thionyl chloride
an inorganic compound; used in chlorination reactions;
converts carboxylic acids to acyl chlorides
353
346
Thiophenol
an organosulfur compound; the simplest aromatic thiol
Titanium tetrachloride
an intermediate in the production of titanium metal and
titanium dioxide
Tollens' reagent
a chemical test most commonly used to determine
whether a known carbonyl-containing compound is an
aldehyde or a ketone
Triphenylphosphine
used in the synthesis of organic and organometallic
compounds
The Four Fundamental Interactions of Nature
Interaction
Current theory
Mediators
Relative strength
Range (m)
Weak
Electroweak theory (EWT) W and Z bosons
1025
10−18
Strong
Quantum chromodynamics
gluons
1038
10−15
photons
1036
∞
gravitons
1
∞
(QCD)
Electromagnetic
Quantum electrodynamics
(QED)
Gravitation
General relativity
(GR)
(hypothetical)
354
347
Table of liquid–vapor critical temperature and pressure for selected substances
Substance
Critical temperature
Critical pressure (absolute)
Argon
−122.4 °C (150.8 K)
48.1 atm (4,870 kPa)
Ammonia (NH3)
132.4 °C (405.5 K)
111.3 atm (11,280 kPa)
R-134a
101.06 °C (374.21 K)
40.06 atm (4,059 kPa)
R-410A
72.8 °C (345.9 K)
47.08 atm (4,770 kPa)
Bromine
310.8 °C (584.0 K)
102 atm (10,300 kPa)
Caesium
1,664.85 °C (1,938.00 K)
94 atm (9,500 kPa)
Chlorine
143.8 °C (416.9 K)
76.0 atm (7,700 kPa)
Ethanol (C2H5OH)
241 °C (514 K)
62.18 atm (6,300 kPa)
Fluorine
−128.85 °C (144.30 K)
51.5 atm (5,220 kPa)
Helium
−267.96 °C (5.19 K)
2.24 atm (227 kPa)
Hydrogen
−239.95 °C (33.20 K)
12.8 atm (1,300 kPa)
Krypton
−63.8 °C (209.3 K)
54.3 atm (5,500 kPa)
Methane (CH4)
−82.3 °C (190.8 K)
45.79 atm (4,640 kPa)
355
348
Neon
−228.75 °C (44.40 K)
27.2 atm (2,760 kPa)
Nitrogen
−146.9 °C (126.2 K)
33.5 atm (3,390 kPa)
Oxygen (O2)
−118.6 °C (154.6 K)
49.8 atm (5,050 kPa)
Carbon dioxide (CO2)
31.04 °C (304.19 K)
72.8 atm (7,380 kPa)
Nitrous oxide (N2O)
36.4 °C (309.5 K)
71.5 atm (7,240 kPa)
Sulfuric acid (H2SO4)
654 °C (927 K)
45.4 atm (4,600 kPa)
Xenon
16.6 °C (289.8 K)
57.6 atm (5,840 kPa)
Lithium
2,950 °C (3,220 K)
652 atm (66,100 kPa)
Mercury
1,476.9 °C (1,750.1 K)
1,720 atm (174,000 kPa)
Sulfur
1,040.85 °C (1,314.00 K)
207 atm (21,000 kPa)
Iron
8,227 °C (8,500 K)
Gold
6,977 °C (7,250 K)
Aluminum
7,577 °C (7,850 K)
Water (H2O)
373.946 °C (647.096 K)
356
349
5,000 atm (510,000 kPa)
217.7 atm (22,060 kPa)
List of Natural Satellites
Name of Natural Satellite
Planet of Origin
Moon
Earth
Mimas
Saturn
Enceladus
Saturn
Tethys
Saturn
Rhea
Saturn
Dione
Saturn
Titan
Saturn
Hyperion
Saturn
Iapetus
Saturn
Phobos
Mars
Deimos
Mars
Metis
Jupiter
Adrastea
Jupiter
Amalthea
Jupiter
Thebe
Jupiter
Io
Jupiter
Europa
Jupiter
Ganymede
Jupiter
Callisto
Jupiter
Themisto
Jupiter
Leda
Jupiter
Himalia
Jupiter
Lysithea
Jupiter
Elara
Jupiter
Dia
Jupiter
Carpo
Jupiter
357
350
S/2003 J 12
Jupiter
Euporie
Jupiter
S/2003 J 3
Jupiter
S/2011 J 1
Jupiter
S/2003 J 18
Jupiter
S/2010 J 2
Jupiter
Thelxinoe
Jupiter
Euanthe
Jupiter
Helike
Jupiter
Orthosie
Jupiter
S/2016 J 1
Jupiter
Iocaste
Jupiter
S/2003 J 16
Jupiter
Praxidike
Jupiter
Harpalyke
Jupiter
Mneme
Jupiter
Hermippe
Jupiter
Thyone
Jupiter
Ananke
Jupiter
Herse
Jupiter
Aitne
Saturn
Kale
Jupiter
Taygete
Jupiter
S/2003 J 19
Jupiter
Chaldene
Jupiter
S/2003 J 15
Jupiter
S/2003 J 10
Jupiter
S/2003 J 23
Jupiter
Erinome
Jupiter
Aoede
Jupiter
358
351
Kallichore
Jupiter
Kalyke
Jupiter
Carme
Jupiter
Callirrhoe
Jupiter
Eurydome
Jupiter
Pasithee
Jupiter
S/2010 J 1
Jupiter
Kore
Jupiter
Cyllene
Jupiter
S/2011 J 2
Jupiter
Eukelade
Jupiter
S/2017 J 1
Jupiter
S/2003 J 4
Jupiter
Pasiphae
Jupiter
Hegemone
Jupiter
Arche
Jupiter
Isonoe
Jupiter
S/2003 J 9
Jupiter
S/2003 J 5
Jupiter
Sinope
Jupiter
Sponde
Jupiter
Autonoe
Jupiter
Megaclite
Jupiter
S/2003 J 2
Jupiter
S/2009 S 1
Saturn
Pan
Saturn
Daphnis
Saturn
Atlas
Saturn
Peggy
Saturn
Prometheus
Saturn
359
352
Pandora
Saturn
Epimetheus
Saturn
Janus
Saturn
Aegaeon
Saturn
Mimas
Saturn
Methone
Saturn
Anthe
Saturn
Pallene
Saturn
Enceladus
Saturn
Tethys
Saturn
Telesto
Saturn
Calypso
Saturn
Dione
Saturn
Helene
Saturn
Polydeuces
Saturn
Rhea
Saturn
Titan
Saturn
Hyperion
Saturn
Iapetus
Saturn
Kiviuq
Saturn
Ijiraq
Saturn
Phoebe
Saturn
Paaliaq
Saturn
Skathi
Saturn
Albiorix
Saturn
S/2007 S 2
Saturn
Bebhionn
Saturn
Erriapus
Saturn
Skoll
Saturn
Siarnaq
Saturn
360
353
Tarqeq
Saturn
S/2004 S 13
Saturn
Greip
Saturn
Hyrrokkin
Saturn
Jarnsaxa
Saturn
Tarvos
Saturn
Mundilfari
Saturn
S/2006 S 1
Saturn
S/2004 S 17
Saturn
Bergelmir
Saturn
Narvi
Saturn
Suttungr
Saturn
Hati
Saturn
S/2004 S 12
Saturn
Farbauti
Saturn
Thrymr
Saturn
Aegir
Saturn
S/2007 S 3
Saturn
Bestla
Saturn
S/2004 S 7
Saturn
S/2006 S 3
Saturn
Fenrir
Saturn
Surtur
Saturn
Kari
Saturn
Ymir
Saturn
Loge
Saturn
Fornjot
Saturn
Themis (Destroyed)
Saturn
Chiron (Destroyed)
Saturn
Cordelia
Uranus
361
354
Ophelia
Uranus
Bianca
Uranus
Cressida
Uranus
Desdemona
Uranus
Juliet
Uranus
Portia
Uranus
Rosalind
Uranus
Cupid
Uranus
Belinda
Uranus
Perdita
Uranus
Puck
Uranus
Mab
Uranus
Miranda
Uranus
Ariel
Uranus
Umbriel
Uranus
Titania
Uranus
Oberon
Uranus
Francisco
Uranus
Caliban
Uranus
Stephano
Uranus
Trinculo
Uranus
Sycorax
Uranus
Margaret
Uranus
Prospero
Uranus
Setebos
Uranus
Ferdinand
Uranus
Naiad
Neptune
Thalassa
Neptune
Despina
Neptune
Galatea
Neptune
362
355
Larissa
Neptune
Hippocamp
Neptune
Proteus
Neptune
Triton
Neptune
Nereid
Neptune
Halimede
Neptune
Sao
Neptune
Laomedeia
Neptune
Psamathe
Neptune
Neso
Neptune
Charon
Pluto
Styx
Pluto
Nix
Pluto
Kerberos
Pluto
Hydra
Pluto
MK 2
Makemake
Namaka
Haumea
Hi'laka
Dysnomia
Eris
Dactyl
243 Ida
Skamandrios
624 Hektor
Remus
87 Sylvia
Romulus
87 Sylvia
S/2001 (107) 1
107 Camilla
S/2016 (107) 1
107 Camilla
Petit-Prince
45 Eugenia
S/2004 (45) 1
45 Eugenia
S/2007 (225088) 1
Snow-White
S/2013 (285263) 1
(285263) 1998 QE2
Alexhelios
216 Kleopatra
363
356
Cleoselene
216 Kleopatra
Weywot
50000 Quaoar
Didymoon
65803 Didymos
Groups
Neurotransmitter
Function
Acetylcholine
Acetylcholine
Excitatory
Amines
Epinephrine
Excitatory
Norephinephrine
Excitatory
Dopamine
Excitatory and Inhibitory
Serotonin
Excitatory
Glutamate
Excitatory
Glycine
Mainly inhibitory
g-Aminobutiric acid (GABA)
Inhibitory
Amino Acids
Binary star
Orbital period
AM Canum Venaticorum
17.146 minutes
Beta Lyrae AB
12.9075 days
Alpha Centauri AB
79.91 years
Proxima Centauri – Alpha Centauri AB 500,000 years or more
364
357
Properties of Ionic Diatomic Molecules
Molecule Dissociation Energy(eV) Equilibrium Separation (nm)
(Bond length)
NaCl
4.26
0.236
NaF
4.99
0.193
NaBr
3.8
0.250
NaI
3.1
0.271
NaH
2.08
0.189
LiCl
4.86
0.202
LiH
2.47
0.239
LiI
3.67
0.238
KCl
4.43
0.267
KBr
3.97
0.282
RbF
5.12
0.227
RbCl
4.64
0.279
CsI
3.57
0.337
Properties of Heteronuclear Diatomic Molecules
Molecule Dissociation Energy(eV) Equilibrium Separation (nm)
(Bond length)
BN
4.0
0.128
CO
11.2
0.113
HBr
...
0.141
HCl
4.4
0.127
HF
5.8
0.092
NO
7.0
0.115
PbO
4.1
0.192
PbS
3.3
0.239
365
358
Thermal Conductivity and Debye Temperature
Li
Be
Debye temperature and thermal conductivity
B
C
N
O
F
Ne
344
1440
Low temperature limit of Debye temperature in Kelvin
...
2230
...
...
...
75
0.85
2.00
Thermal conductivity at 300K, in W/cmK
0.27
1.29
...
...
...
...
Na
Mg
...
Al
Si
P
S
Cl
Ar
158
400
428
645
...
...
...
92
1.41
1.56
2.37
1.48
...
...
...
...
K
Ca
Sc
Ti
V
Cr
Mn
Fe
Co
Ni
Cu
Zn
Ga
Ge
As
Se
Br
Kr
91
230
360
420
380
630
410
470
445
450
343
327
320
374
282
90
...
72
1.02
...
0.16
0.22
0.31
0.94
0.08
0.80
1.00
0.91
4.01
1.16
0.41
0.6
0.50
0.02
...
...
Rb
Sr
Y
Zr
Nb
Mo
Tc
Ru
Rh
Pd
Ag
Cd
In
Sn
Sb
Te
I
Xe
56
147
280
291
275
450
...
600
480
274
225
209
108
200
211
153
...
64
0.58
...
0.17
0.23
0.54
1.38
0.51
1.17
1.50
0.72
4.29
0.97
0.82
0.67
0.24
0.02
...
...
Cs
Ba
La
Hf
Ta
W
Re
Os
Ir
Pt
Au
Hg
Tl
Pb
Bi
Po
At
Rn
38
110
142
252
240
400
430
500
420
240
165
71.9
78.5
105
119
...
...
64
0.36
...
0.14
0.23
0.58
1.74
0.48
0.88
1.47
0.72
3.17
...
0.46
0.35
0.08
...
...
...
Fr
Ra
Ac
...
...
...
...
...
...
...
...
...
...
Ce
Pr
Nd
Pm
Sm
Eu
Gd
Tb
Dy
Ho
Er
Tm
Yb
Lu
...
...
...
...
...
...
200
...
210
...
...
...
120
210
0.11
0.13
0.16
...
0.13
...
0.11
0.11
0.11
0.16
0.14
0.17
0.35
0.16
Th
Pa
U
Np
Pu
Am
Cm
Bk
Cf
Es
Fm
Md
No
Lr
163
...
207
...
...
...
...
...
...
...
...
...
...
...
0.54
...
0.28
0.06
0.07
...
...
...
...
...
...
...
...
...
366
359
...
Vibrational frequencies of diatomic molecules
Molecule Frequency (1013 Hz)
HH
13
NN
7.0
CO
6.4
NO
5.7
OO
4.7
Superconductor coherence lengths and penetration depths
Material Coherence length London penetration depth
Ratio
𝛌𝐋
𝛏𝟎
ξ0(nm)
λL(nm)
Sn
230
34
0.16
Al
1600
16
0.010
Pb
83
37
0.45
Cd
760
110
0.14
Nb
38
39
1.02
Semiconductor Band Gaps
367
360
Material Energy gap (eV)
0K
300K
Si
1.17
1.11
Ge
0.74
0.66
InSb
0.23
0.17
InAs
0.43
0.36
InP
1.42
1.27
GaP
2.32
2.25
GaAs
1.52
1.43
GaSb
0.81
0.68
CdSe
1.84
1.74
CdTe
1.61
1.44
ZnO
3.44
3.2
ZnS
3.91
3.6
Quarks
Generation
1
Name
up
down
Symbol Antiparticle Spin Charge
(e)
u
d
Mass
(MeV/c2)
u̅
1
+
2
2.2+0.6
−0.4
d̅
1
−
1
4.6+0.5
−0.4
368
361
2
2
3
3
2
charm
strange
3
top
bottom
c
s
t
b
c̅
1
+
2
1,280±30
s̅
1
−
1
96+8
−4
t̅
1
+
2
173,100±600
̅
b
1
−
1
4,180+40
−30
2
2
2
2
3
3
3
3
Leptons
Generation
Name
Symbol Antiparticle Spin Charge
(e)
1
Electron
e−
e+
2
νe
ν̅e
Muon
Muon neutrino
μ−
μ+
νμ
νμ
̅̅̅
369
362
(MeV/c2)
1
−1
0.511
1
0
< 0.0000022
1
−1
105.7
1
0
< 0.170
2
Electron neutrino
Mass
2
2
2
3
Tau
Tau neutrino
τ−
τ+
1
−1
1,776.86±0.12
ντ
ν̅τ
1
0
< 15.5
2
2
Bosons
Name
Symbol
Antiparticle
Spin
Charge
Mass
(e)
Interaction
Observed
mediated
(GeV/c2)
Photon
γ
Self
W−
W+
1
0
0
Electromagnetism
Yes
1
−1
80.385±0.015
Weak interaction
Yes
Self
1
0
91.1875±0.0021
Weak interaction
Yes
Self
1
0
0
Strong interaction
Yes
Self
0
0
125.09±0.24
Mass
Yes
Self
2
2
0
Gravitation
No
W boson
Z boson
Z
Gluon
g
Higgs
boson
H
Graviton
G
0
370
363
Low-frequency dielectric constants of some common solvents
Solvent
Dielectric constant Temperature (K)
benzene
2.3
298
diethyl ether
4.3
293
tetrahydrofuran (THF)
7.6
298
dichloromethane
9.1
293
liquid ammonia
17
273
ethanol
24.3
298
methanol
32.7
298
nitromethane
35.9
303
dimethyl formamide (DMF)
36.7
298
acetonitrile
37.5
293
water
78.4
298
formamide
109
293
371
364
Poisson's ratio values for different materials
Material
Poisson's ratio
rubber
0.4999
gold
0.42–0.44
saturated clay
0.40–0.49
magnesium
0.252–0.289
titanium
0.265–0.34
copper
0.33
aluminium-alloy
0.32
clay
0.30–0.45
stainless steel
0.30–0.31
steel
0.27–0.30
cast iron
0.21–0.26
sand
0.20–0.455
concrete
0.1–0.2
glass
0.18–0.3
372
365
Material
metallic glasses
0.276–0.409
foam
0.10–0.50
cork
0.0
Typical values for shear modulus (GPa)
(at room temperature)
Diamond
478.0
Steel
79.3
Iron
52.5
Copper
44.7
Titanium
41.4
Glass
26.2
Aluminium
25.5
Polyethylene
0.117
Rubber
0.0006
Granite
24
Shale
1.6
Limestone
24
Chalk
3.2
Sandstone
0.4
Wood
4
373
366
Thermal diffusivity of selected materials and substances
Material
Thermal diffusivity
(mm²/s)
Wood (Yellow Pine)
0.082
Water vapour (1 atm, 400 K)
23.38
Water at 25 °C
0.143
Tin
40
Steel, stainless 310 at 25 °C
3.352
Steel, stainless 304A at 27 °C
4.2
Steel, AISI 1010 (0.1% carbon)
18.8
Steel, 1% carbon
11.72
Silver, pure (99.9%)
165.63
Silicon Dioxide (Polycrystalline)
0.83
Silicon
88
Si3 N4 with CNTs 26 °C
9.142
Si3 N4 without CNTs 26 °C
8.605
Sandstone
1.15
374
367
Rubber
0.089 - 0.13
Quartz
1.4
Pyrolytic graphite, parallel to layers
1220
Pyrolytic graphite, normal to layers
3.6
PVC (Polyvinyl Chloride)
0.08
PTFE (Polytetrafluorethylene) at 25 °C
0.124
PP (Polypropylene) at 25 °C
0.096
PC (Polycarbonate) at 25 °C
0.144
Paraffin at 25 °C
0.081
Oil, engine (saturated liquid, 100 °C)
0.0738
Nylon
0.09
Nitrogen (300 K, 1 atm)
22
Molybdenum (99.95%) at 25 °C
54.3
Iron
23
Inconel 600 at 25 °C
3.428
Ice at 0 °C
1.02
375
368
Hydrogen (300 K, 1 atm)
160
Helium (300 K, 1 atm)
190
Gold
127
Glass, window
0.34
Copper at 25 °C
111
Carbon/carbon composite at 25 °C
216.5
Brick, common
0.52
Brick, adobe
0.27
Argon (300 K, 1 atm)
22
Aluminium oxide (polycrystalline)
12.0
Aluminium 6061-T6 Alloy
64
Aluminium
97
Alcohol
0.07
Al-10Si-Mn-Mg (Silafont 36) at 20 °C
74.2
Al-5Mg-2Si-Mn (Magsimal-59) at 20 °C
44.0
Air (300 K)
19
376
369
Substance
Vapor pressure
Temperature
(°C)
(Pa)
(bar)
(mmHg)
Tungsten
100 Pa
0.001
0.75
3203
Ethylene glycol
500 Pa
0.005
3.75
20
Xenon difluoride
600 Pa
0.006
4.50
25
Water (H2O)
2.3 kPa
0.023
17.5
20
Propanol
2.4 kPa
0.024
18.0
20
Methyl isobutyl ketone
2.66 kPa
0.0266
19.95
25
Ethanol
5.83 kPa
0.0583
43.7
20
Freon 113
37.9 kPa
0.379
284
20
Acetaldehyde
98.7 kPa
0.987
740
20
Butane
220 kPa
2.2
1650
20
Formaldehyde
435.7 kPa
4.357
3268
20
Propane
997.8 kPa
9.978
7584
26.85
Carbonyl sulfide
1.255 MPa
12.55
9412
25
Nitrous oxide
5.660 MPa
56.60
42453
25
Carbon dioxide
5.7 MPa
57
42753
20
377
370
Antibody isotypes of mammals
Class Subclasses
IgA
2
Description
Found in mucosal areas, such as the gut, respiratory
tract and urogenital tract, and prevents colonization
by pathogens. Also found in saliva, tears, and breast milk.
IgD
1
Functions mainly as an antigen receptor on B cells that have not
been exposed to antigens. It has been shown to
activate basophils and mast cells to produce antimicrobial factors.
IgE
1
Binds to allergens and triggers histamine release from mast
cells and basophils, and is involved in allergy. Also protects
against parasitic worms.
IgG
4
In its four forms, provides the majority of antibody-based immunity
against invading pathogens. The only antibody capable of crossing
the placenta to give passive immunity to the fetus.
IgM
1
Expressed on the surface of B cells (monomer) and in a secreted
form (pentamer) with very high avidity. Eliminates pathogens in the
early stages of B cell-mediated (humoral) immunity before there is
sufficient IgG.
378
371
Antibody isotypes not found in mammals
Class Types
Description
IgY
Found in birds and reptiles; related to mammalian IgG.
IgW
Found in sharks and skates; related to mammalian IgD.
The luminosity L of a star is related to its apparent brightness b and its distance d to us by:
b=
L
4πd2
The luminosity L of a star is related to its radius R and its temperature T by:
L = 4πR2σT4
where σ is Stefan–Boltzmann constant.
Helmholtz free energy:
F = U − TS
Gibbs free energy:
G = H − TS
Enthalpy:
H = U + PV
379
372
where: H → enthalpy, P → pressure, V → volume, T → temperature, S → entropy and U →
internal energy.
Limiting Magnitudes for Visual Observation at High Magnification
Telescope aperture
Limiting
(mm)
Magnitude
35
11.3
60
12.3
102
13.3
152
14.1
203
14.7
305
15.4
406
15.7
508
16.4
380
373
Neutron energy range names
Neutron energy
Energy range
0.0–0.025 eV
Cold neutrons
0.025 eV
Thermal neutrons
0.025–0.4 eV
Epithermal neutrons
0.4–0.5 eV
Cadmium neutrons
0.5–1 eV
EpiCadmium neutrons
1–10 eV
Slow neutrons
10–300 eV
Resonance neutrons
300 eV–1 MeV
Intermediate neutrons
1–20 MeV
Fast neutrons
> 20 MeV
Ultrafast neutrons
381
374
Black hole Equations:
Rs =
2GM
T=
ħc3
P=
tev =
S=
c2
8πGMkB
ħc6
15360πG2M2
5120πG2 M3
ħc4
kB A
dE =
dA
ρ=
ħG
16πG2 M2
A=
480c2 V
4L2Planck
dt
=
κ
c4
8π
dA + ΩdJ + ϕdQ
≥0
3c6
32πG3 M2
where: M is the Mass, G is the gravitational constant, S is the Entropy, A is the Horizon area, t ev
is the evaporation time, T is the temperature, kB is the Boltzmann constant, ρ is the density, c is
Għ
the speed of light, LPlanck = √ 3 is the Planck length, V is the volume, Rs is the Schwarzschild
c
radius, E = Mc2 is the energy, κ is the surface gravity, Ω is the angular velocity, J is the angular
momentum, ϕ is the electrostatic potential and Q is the electric charge.
382
375
Thermodynamics of the universe:
0 = dQ = dU + PdV
dU = − PdV
where Q is the total heat which is assumed to be constant, U is the internal energy of the matter
and radiation in the universe, P is the pressure and V the volume.
Energy density u =
For radiation, p =
U
u
3
V
du = − (P + u)
dV
V
= − 3(P + u)
d𝑎
𝑎
whereas for matter p << u and the pressure can be neglected. Thus we get:
For radiation
du = − 4u
d𝑎
thus u is proportional to a−4
du = − 3u
d𝑎
thus u is proportional to a−3
For matter
𝑎
𝑎
a being the scale factor of the universe.
Redshift
λnow
λthen
383
376
=
𝑎now
𝑎then
1+z=
𝑎now
𝑎then
If the source moves away from the observer with velocity v, which is much less than the speed of
light (v ≪ c), the redshift is given by:
z=
v
c
Gravitational redshift:
1
1+ z =
2GM
rc2
√1−
where
G is the gravitational constant,
M is the mass of the object creating the gravitational field,
r is the radial coordinate of the source (which is analogous to the classical distance from the
center of the object, but is actually a Schwarzschild coordinate), and
c is the speed of light.
Hubble's law:
v = HD
where
v is the recessional velocity, typically expressed in km/s.
H is the Hubble parameter
D is the proper distance from the galaxy to the observer, measured in mega parsecs
(Mpc)
384
377
Hubble Distance =
Hubble Time =
dH
c
H
1
H
= −H2 (1+ q)
dt
q being the deceleration parameter.
Critical density of the universe:
ρc =
3H2
8πG
Density parameter:
Ω=
ρ
ρc
=
8πGρ
3H2
Ω = 0: empty universe
Ω < 1: expansion overcomes gravity; universe expands forever
Ω = 1: critical density; mass is just enough to stop it expanding but not enough to make it
recollapse
Ω > 1 : gravity overcomes expansion; universe recollapse
General relativity: Ω determines the curvature (k), or "shape", of the universe:
Ω = 1: flat universe, k = 0
385
378
Ω > 1: closed (or bound) universe, k = +1
Ω < 1: open (or unbound) universe, k = −1
The virial theorem relates the total kinetic energy of a self-gravitating body due to the motions
of its constituent parts, T to the gravitational potential energy, U of the body.
2T + U = 0
Chandrasekhar limit:
Mlimit =
ѡ03 √3π
2
×
1
μe
×
(Planck mass)3
(proton mass)2
μe is the average molecular weight per electron, which depends upon the chemical
composition of the star.
ω03 ≈ 2.018236 is a constant connected with the solution to the Lane–Emden equation.
Schönberg–Chandrasekhar limit:
Mcore
M
μ2env
≈ 0.37 2
μ
core
Mcore − mass of the core.
M − mass of the whole star.
μcore − mean molecular mass of the core.
μenv − mean molecular mass of the envelope.
Eddington luminosity:
LEdd =
4πGMmp c
σT
379
386
Eddington Parameter
A=
Luminosity of the star
Eddington Luminosity
where M is the mass of the star, G is the gravitational constant, mp is the proton mass, c is the
speed of light and σT is the Thomson cross section.
σT =
8πr2e
3
Classical electron radius
re =
e2
4πε0 me c2
where e is the elementary charge, me is the electron rest mass, c is the speed of light, and ε0 is the
permittivity of free space.
Fine-structure constant
α=
where ħ =
h
2π
is the reduced Planck constant.
e2
4πε0 ħc
Gravitational coupling constant
αG =
(electron rest mass)2
(Planck mass)2
387
380
αG =
(proton rest mass)2
(Planck mass)2
Compton scattering
λ'–λ=
h
me c
(1− cosθ)
where
λ is the initial wavelength,
λ' is the wavelength after scattering,
h is the Planck constant,
me is the electron rest mass,
c is the speed of light, and
θ is the scattering angle.
Photoelectric effect
Energy of the photon = Work function of the surface + Kinetic energy of the emitted electron
E = W + KE
hυ = hυ0 +
υ < υ0 → no photoelectric emission
388
381
m0 v2
2
hυ = hυ0 + eVstop
where e is the electron charge and Vstop is the stopping voltage (or stopping potential).
Photoemission from atoms:
hυ = electron's binding energy + KE
Photoemission from solids:
hυ = W + electron's binding energy + KE
Photon gas
4σT4
U=
μ=0
c
U
P=
S=
H=
A=−
G=0
3V
=
4U
×V
4σT4
3c
3T
4U
3
U
3
where U is the internal energy, Gibbs free energy, H is the Enthalpy, A is the Helmholtz free
energy, S is the entropy, T is the temperature, V is the volume, μ is the chemical potential, c is
the speed of light and σ =
π2 k2B
60ħ3 c2
is the Stefan's constant.
389
382
Poynting–Robertson effect
The Poynting–Robertson force is equal to:
FPR =
v
c2
W=
r2 Lsun
4c2
GMsun
√
R5
where v is the grain's velocity, c is the speed of light, W is the power of the incoming radiation, r
the grain's radius, G is the universal gravitational constant, Msun the Sun's mass, Lsun is the solar
luminosity and R the grain's orbital radius.
The ratio of the force due to radiation pressure to the force of gravity on the particle:
β=
FR
FG
=
3Lsun QPR
16πGMsun cρr
where QPR is the Mie scattering coefficient and ρ is the density and r is the radius of the dust
grain.
The scale height is related to the temperature (T) and mean molecular mass (m) of the atmosphere
kB T
by the formula H =
where kB is Boltzmann's constant and g is the gravitational acceleration of
mg
the body.
390
383
If electrons are accelerated to a velocity v by a potential difference V and then allowed to collide
with a metal target, the maximum frequency of the X-rays emitted is given by the equation:
Therefore:
m0 v2
2
= eV = hυmax
υmax =
eV
h
This shows that the maximum frequency is directly proportional to the accelerating voltage.
Fermi energy
1
The Fermi energy for a non-interacting ensemble of identical spin- fermions in a three2
dimensional (non-relativistic) system is given by:
EF =
ħ2
2m0
( 3π2
N 2/3
)
V
where N is the number of particles, m0 the rest mass of each fermion, V the volume of the
system, and ħ the reduced Planck constant.
EF = k B TF
vF =
pF
m0
pF = ħkF
where TF is the Fermi temperature, vF is the Fermi velocity, pF is the Fermi momentum and kF is
Fermi wave-vector.
391
384
Heat capacity ratio for various gases
Temp.
Gas
γ
Temp.
Gas
γ
−181 °C
H2
1.597
200 °C
Dry air 1.398
20 °C
NO
1.400
−76 °C
1.453
400 °C
1.393
20 °C
N2O
1.310
20 °C
1.410
1000 °C
1.365
−181 °C
N2
1.470
100 °C
1.404
15 °C
1.404
400 °C
1.387
0 °C
1.310
20 °C
Cl2
1.340
1000 °C
1.358
20 °C
1.300
−115 °C
CH4
1.410
2000 °C
1.318
100 °C
1.281
−74 °C
1.350
1.660
400 °C
1.235
20 °C
1.320
1000 °C
1.195
15 °C
NH3
1.310
20 °C
20 °C
He
Water vapour 1.330
Gas
CO2
γ
Temp.
100 °C
1.324
20 °C
CO
1.400
19 °C
Ne
1.640
200 °C
1.310
−181 °C
O2
1.450
19 °C
Xe
1.660
1.760
−76 °C
1.415
19 °C
Kr
1.680
1.670
20 °C
1.400
15 °C
SO2
1.290
1.403
100 °C
1.399
360 °C
Hg
1.670
20 °C
1.400
200 °C
1.397
15 °C
C2H6 1.220
100 °C
1.401
400 °C
1.394
16 °C
C3H8 1.130
−180 °C
Ar
20 °C
0 °C
Dry air
392
385
The acid in our stomach is strong enough to dissolve razor blades
An average cumulus cloud weighs over a million pounds.
There are more trees on Earth than stars in our galaxy
Cold water heats up faster than hot water
Water can exist in all three states: solid (ice), liquid and gas
(vapor) at the same time at a temperature called triple point.
Men are more likely to be colorblind than women
Sound waves almost always generate a little bit of heat when they
travel and are absorbed by materials.
According to Albert Einstein's theory of Relativity, the farther you are from
the earth's surface, the faster time passes.
386
Gravitational waves
P=−
−
dE
dt
dr
dt
=
=
tlife =
32G4(m1 m2 )2
5c5
64G3(m1 m2 )
5c5
×
5c5 r4
×
(m1 +m2 )
r5
(m1 +m2 )
r3
256G3 (m1 m2 )(m1 +m2 )
where:
P is the rate of loss of energy from the binary system through gravitational radiation.
m1, m2 = masses of the orbiting bodies.
tlife is the lifetime of distance "r" between the masses orbiting each other in highly circular
orbit about their center of mass.
Relative size of a scattering particle is defined by size parameter which is the ratio of its
characteristic dimension and wavelength of incident radiation
α=
2πr
λ
α ≪ 1: Rayleigh scattering (small particle compared to wavelength of light)
α ≈ 1: Mie scattering (particle about the same size as wavelength of light, valid only for
spheres)
α ≫ 1: geometric scattering (particle much larger than wavelength of light).
393
387
Laws of reflection:
The incident ray, the reflected ray and the normal ray at the point of incidence, lie in the
same plane.
The angle of incidence is equal to the angle of reflection
Laws of refraction:
The incident ray refracted ray, and the normal to the interface of two media at the point of
incidence all lie on the same plane.
The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a
constant.
sin i
sin r
= constant
Zeroth Law of Thermodynamics:
C
A
B
If two bodies A and B are in thermal equilibrium with third body C, then body A and B are also
in thermal equilibrium with each other.
Tyndall effect
The scattering of light by very small particles suspended in a gas or liquid
388
Wiedemann-Franz Law:
Thermal conductivity of the material
Electrical conductivity of the material
Thermal conductivity of the material
Electrical conductivity of the material
Plant Cell
∝ Temperature
= Lorenz number × Temperature
Animal Cell
Cell Shape
Square or rectangular in shape
Irregular or round in shape
Cell Wall
Present
Absent
Cell Membrane
Present
Present
Endoplasmic Reticulum
Present
Present
Nucleus
Present and lies on one side of the cell
Present and lies in the centre of the cell
Lysosomes
Present but are very rare
Present
Centrosomes
Absent
Present
Golgi Apparatus
Present
Present
Cytoplasm
Present
Present
Ribosomes
389
Present
Present
Plastids
Present
Absent
Vacuoles
Few large or a single, centrally positioned vacuole
Usually small and numerous
Cilia
Absent
Present in most of the animal cells
Mitochondria
Present but fewer in number
Present and are numerous
Mode of Nutrition
Primarily autotrophic
Heterotrophic
Mitosis
Meiosis
It takes place in both Haploid cells and diploid cells
It takes place only in diploid cells.
It takes place in all body cells or vegetative cells or
It takes place in reproductive cells or germinal cells.
somatic.
Nucleus divides once
Nucleus divides twice to produce 4 nuclei.
Daughter cells are identical to mother cells
Daughter cells are not identical.
Chromosomes do not pair
Homologous chromosomes (similar) pair to form
bivalent ones.
Chiasmata is absent, Also there is no crossing over
Chiasmata present. Crossing over between non-sister
chromatids occurs.
The chromosome number in the daughter cell is
Chromosome number is reduced to half of the parent cell.
unchanged.
The entire cell division is short comparatively.
The duration of cell division is very large as it involves
many steps.
It helps for the growth of the body and in lower forms
It helps in gamete formation for sexual reproduction.
like bacteria, to multiply organism numbers.
390
Soap
Detergent
Sodium salt of Carboxylic acids
Sodium salts of benzene sulphonic acids.
Soaps are bio-degradable
Some detergents are non- biodegradable
Soaps do not lather in hard water
Detergent lather well in hard water
Weak cleansing action
Have strong cleansing action
Photosynthesis
Respiration
It is the process by which plants use sunlight, water,
It refers to a metabolic pathway that breaks down
and carbon dioxide to create oxygen and energy in the
glucose and produces ATP.
form of sugar.
Occurs in plants containing chlorophyll and some
Occurs in all living organisms
bacteria
It takes place in chloroplasts
It takes place in mitochondria
Anabolic process
Catabolic process
Endothermic reaction because it needs energy
Exergonic reaction because it releases energy
Produces food and captures the energy
Takes in oxygen and liberates out carbon dioxide
Requires sunlight because it is mandatory
Does not require sunlight as it takes place all the
time
Absorbs carbon dioxide and water
Releases carbon dioxide and water
6CO2 + 6H2O → C6H12O6 + 6O2
C6H12O6 + 6O2 → 6CO2 + 6H2O
391
Bragg's Law
n λ = 2 d sin θ
where λ is the wavelength of the radiation used, d is the inter-planar spacing involved and θ is
the angle between the incident (or diffracted) ray and the relevant crystal planes; n is an integer,
referred to as the order of diffraction.
The Nuclear radius is given by the following relation:
R = R0 A1/3
where R0 is constant for all nuclei and its value is 1.2 × 10−15 m and A = Mass number of nucleus
(the number of protons Z, plus the number of neutrons N).
Moore's law → the number of transistors in a dense integrated circuit (IC) doubles about every
two years.
In a medium of constant refractive index, n, the Optical path length for a path of geometrical
length L is just
OPL = nL
Optical depth = ln10 × Absorbance
394
392
Refractive index
n=
c
v
where c is the speed of light in vacuum and v is the phase velocity of light in the medium. For
example, the refractive index of water is 1.333, meaning that light travels 1.333 times as fast in
c
vacuum as in water. The speed of light in a medium is v = , and similarly the wavelength in that
n
medium is λ =
λ0
n
, where λ0 is the wavelength of that light in vacuum.
Refractivity = (n – 1)
Specific refractivity =
Refractivity of the medium
Density of the medium
Eyring equation
∆G0∗
k=κ
exp (−
)
h
RT
kB T
where
∆G∗0 is the standard Gibbs free energy of activation, κ is the transmission coefficient, kB
is Boltzmann's constant, T is the absolute temperature, k is the reaction rate constant, R is the gas
constant and h is Planck's constant.
Michaelis–Menten equation
395
393
The Michaelis–Menten kinetics takes the form of an equation describing the rate of enzymatic
reactions, by relating reaction rate v (rate of formation of product, [P]) to [S], the concentration
of a substrate S. Its formula is given by:
v=
d[P]
dt
=
vmax [S]
Km + [S]
This equation is called the Michaelis–Menten equation. Here, vmax represents the maximum rate
achieved by the system, happening at saturating substrate concentration. The value of the
Michaelis constant Km is numerically equal to the substrate concentration at which the reaction
rate is half of vmax.
k1
E + S → ES
k2
ES → E + S
k3
ES → P + E
Km =
(k2 + k3 )
k3
k1
(catalytic efficiency) is a measure of how efficiently an enzyme converts a
Km
substrate into product.
The ratio
396
394
Monod equation
μ = μmax
S
Ks + S
where:
μ is the specific growth rate of the microorganisms
μmax is the maximum specific growth rate of the microorganisms
S is the concentration of the limiting substrate for growth
Ks is the "half-velocity constant" or the value of S when
Nernst Equation
0
Ecell = Ecell
−
RT
nF
lnQ
where:
Ecell = cell potential of the cell
0
Ecell
= cell potential under standard conditions
R = universal gas constant
T = temperature
n = number of electrons transferred in the redox reaction
F = Faraday constant
Q = reaction quotient
397
395
μ
μmax
= 0.5
Faraday's law of electrolysis
The mass m of elements deposited at an electrode in g is directly proportional to the Charge Q in
Coulombs.
m=Z×Q
Here, the constant of proportionality Z is called the Electro-Chemical Equivalent of the
substance.
Chemical equivalent of a substance =
atomic weight
valency
Activity of sample at instant t is given by A = A0 eλt where λ is the Decay constant
Activity per unit mass → Specific activity
Half life: T1 =
2
0.693
Average life: Tav =
398
396
λ
T1
2
0.693
Quantum numbers
Principal Quantum Number (n) = 1, 2, 3, …, ∞
Orbital angular momentum of electron in any orbit =
Angular Momentum (Secondary, Azimuthal) Quantum Number ( l ) = 0,1, ..., (n −1).
Number of orbitals in a subshell = 2l + 1
Maximum number of electrons in particular subshell = 2 × (2l +1)
Orbital angular momentum (L) =
Name
Symbol
h
2π
𝑛ℎ
2π
√𝑙 (𝑙 + 1)
Orbital meaning
Range of
Value examples
values
Principal quantum number
n
shell
1≤n
n = 1, 2, 3, …
Azimuthal quantum
l
subshell (s orbital is listed as 0, p
0≤l≤n−1
for n = 3:
number (angular momentum)
Magnetic quantum number
orbital as 1 etc.)
ml
energy shift (orientation of the
l = 0, 1, 2 (s, p, d)
−l ≤ ml ≤ l
ml = −2, −1, 0, 1, 2
subshell's shape)
(projection of angular momentum)
spin of the electron
Spin quantum number
ms
1
(− = "spin down",
2
1
2
= "spin up")
399
397
for l = 2:
−s ≤ ms ≤ s
for an electron
1
s= ,
2
1
1
so ms = −2, +2
Nuclide Ratio of atomic mass to mass number
1
H
1.00782505
2
H
1.0070508885
3
H
1.0053497592
3
He
1.0053431064
4
He
1.0006508135
6
Li
12
1.0025204658
C
1
14
N
1.0002195718
16
O
0.9996821637
Fe
0.9988381696
56
210
232
Po
0.9999184462
Th
1.0001640315
238
U
1.0002133958
400
398
Equivalent weight of acid =
Molar mass
Basicity
Basicity → The number of hydrogen atoms replaceable by a base in a particular acid
Equivalent weight of base =
Molar mass
Acidity
Acidity → The number of ionizable hydrogen ions (OH−) present in one molecule of a base
Oxidation number = number of electrons in the valence shell – number of electrons left after bonding
Hardness in ppm =
mass of CaCO3
Total mass of water
× 106
Thermodynamic processes
Isothermal process:
Temperature = constant
Isochoric process:
Volume = constant
Isobaric process:
Pressure = constant
Adiabatic process:
Heat exchange with the surroundings = 0
401
399
Work done on the system = positive
Work done by the system = negative
Law of Equipartition Energy
Internal energy =
N
2
× number of moles × universal gas constant × absolute temperature
where: N = number of active degrees of freedom (Translational + Rotational)
N = 3 for monoatomic gas
N=5 for diatomic or linear polyatomic gas
N=6 for non-linear polyatomic gas
Second law of Thermodynamics
∆Suniverse = ∆Ssystem + ∆Ssurrounding > 0 for a spontaneous process
Third law of thermodynamics
The entropy change associated with any condensed system undergoing a reversible isothermal
process approaches zero as the temperature at which it is performed approaches 0 K.
Criteria of spontaneity:
∆G = ∆H − T∆S
402
400
If ∆G is negative (< 0), the process is spontaneous.
If ∆G is positive (> 0), the process is non spontaneous.
Endothermic → absorbs heat
Exothermic → releases heat
Degree of dissociation
α=
number of moles dissociated
initial number of moles
% Dissociation = α × 100
Relative humidity =
partial pressure of water vapor
equilibrium vapor pressure of water at a given temperature
The quantum yield for the decomposition of a reactant molecule in a decomposition reaction is
defined as:
Φ=
number of molecules decomposed
number of photons absorbed
Quantum yield can also be defined for other events, such as fluorescence:
Φ=
number of photons emitted
number of photons absorbed
403
401
Simple buffering agents
Buffering agent
pKa
pH range
Citric acid
3.13, 4.76, 6.40
2.1–7.4
Acetic acid
4.8
3.8–5.8
KH2PO4
7.2
6.2–8.2
CHES
9.3
8.3–10.3
Borate
9.24
8.25–10.25
Acid Buffer: CH3COOH and CH3COONa (weak acid and salt of its conjugate base).
pH = pKa + log
[Salt]
[Acid]
(Henderson–Hasselbalch equation)
Basic Buffer: NH4OH and NH4Cl (weak base and salt of its conjugate acid).
pH = pKb + log
[Salt]
[Base]
Buffer capacity:
β=
dCb
d(pH)
where dCb is an infinitesimal amount of added base
404
402
β=−
dCa
d(pH)
where dCa is an infinitesimal amount of added acid. pH is defined as −log10[H+], and d(pH) is an
infinitesimal change in pH.
van 't Hoff factor
i =
Observed value of colligative property
Theoretical value of colligative property
Steric Number = (number of lone electron pairs on the central atom) + (number of atoms bonded to the central atom)
Steric Number
Predicted Shape
Bond angle (Degrees)
2
Linear
180
3
Trigonal Planar
120
4
Tetrahedral
109.5
5
Trigonal Bipyramidal
90,120
6
Octahedral
90
Table of Common Ligands
Type
monodentate
Charge
neutral
Name in
Ligand
Formula
ammonia
NH3
ammine
water
H2O
aqua
carbon monoxide
CO
carbonyl
405
403
Complexes
pyridine
pyr
pyridine
azide
N3
azido
bromide
Br
bromido
chloride
Cl
chlorido
cyanide
CN
cyanido
fluoride
F
fluorido
hydroxide
OH
hydroxido
nitrite
NO2
nitrito
thiocyanate
SCN or NCS
thiocyanato
bipyridine
bipy
bipyridine
ethylenediamine
en
ethylenediamine
carbonate
CO32
carbonato
oxide
O2
oxo
oxalate
C2O42
oxolato
sulfate
SO42
sulfato
minus one
neutral
bidentate
minus two
Hybridisation
Geometry
Coordination number
sp
linear
2
sp2
Trigonal planar
3
sp3
Tetrahedral
4
dsp2
Square planar
4
dsp3
Trigonal bipyramidal
5
406
404
dsp3
Square-based pyramid
5
d2sp3
Octahedral
6
Bead test
Metal
Color in Oxidizing flame
Color in Reducing flame
Aluminum
colorless (hot and cold), opaque
colorless, opaque
Antimony
colorless, yellow or brown (hot)
gray and opaque
Barium
colorless
Bismuth
colorless, yellow or brownish (hot)
gray and opaque
Cadmium
colorless
gray and opaque
Calcium
colorless
Cerium
red (hot)
colorless (hot and cold)
Copper
sky blue (hot and cold), opaque
red, opaque
Iron
yellow (hot and cold), opaque
bottle-green, opaque
Manganese
pink (hot and cold), opaque
colorless, opaque
407
405
Cobalt
deep blue (hot and cold), opaque
deep blue, opaque
Nickel
yellow-brown (hot and cold), opaque
grey, opaque
Silver
colourless (hot and cold), opaque
grey, opaque
Vanadium
colourless (hot and cold), opaque
green, opaque
Uranium
yellow-brown (hot and cold), opaque
green, opaque
Chromium
green (hot and cold), opaque
green, opaque
Platinum
colourless (hot and cold), opaque
grey, opaque
Gold
yellow-brown (hot and cold), opaque
grey, opaque
Tin
colourless (hot and cold), opaque
colourless, opaque
Titanium
colourless (hot and cold), opaque
yellow, opaque (hot) violet (cold)
Tungsten
colourless (hot and cold), opaque
brown, opaque
Magnesium
colourless (hot and cold), opaque
colourless, opaque
Molybdenum
colourless (hot and cold), opaque
yellow or brown, opaque
Strontium
colourless (hot and cold), opaque
colourless, opaque
Thorium
colourless (hot and cold), opaque
colourless, opaque
408
406
Yttrium
colourless (hot and cold), opaque
colourless, opaque
Neodymium
colourless (hot and cold), opaque
colourless, opaque
Praseodymium
colourless (hot and cold), opaque
colourless, opaque
Silicon
colourless (hot and cold), opaque
colourless, opaque
Germanium
colourless (hot and cold), opaque
colourless, opaque
List of oncogenic bacteria
Species or genera
Possibly associated cancers
Bacteroides fragilis
Colon cancer.
Borrelia burgdorferi
MALT lymphoma.
Campylobacter jejuni
Immunoproliferative small intestinal disease
(IPSID), which is rare a type of MALT lymphoma.
Chlamydia pneumonia
Lung MALT lymphoma.
Chlamydia trachomatis (chlamydia)
Cervical cancer.
Chlamydophila psittaci
Ocular/adnexal lymphoma (forms of eye cancer).
Clostridium ssp
Colon cancer.
Helicobacter bilis
Biliary cancers (such as gallbladder and biliary tract
cancers).
Helicobacter bizzozeronii
Gastric MALT lymphoma.
Helicobacter felis
Gastric MALT lymphoma.
Helicobacter heilmannii
Marginal zone B-cell lymphoma of the stomach.
Helicobacter hepaticus
Biliary cancer.
Helicobacter pylori
Stomach cancer, Marginal zone B-cell lymphoma
409
407
of the stomach, and bile duct cancer
Helicobacter salomonis
Gastric MALT lymphoma.
Helicobacter suis
Gastric MALT lymphoma.
Mycoplasma spp
Stomach, colon, ovarian, and lung
cancers (particularly M. fermentans, M.
penetrans, M. hyorhinis).
Neisseria gonorrhoeae (gonorrhea)
Bladder cancer and possibly prostate cancer.
Cutibacterium acnes
Bladder and prostate cancer.
Salmonella enterica serovar Paratyphi
Biliary cancer.
Salmonella enterica serovar Typhimurium
Biliary cancer.
Treponema pallidum (syphilis)
Bladder cancer and possibly prostate cancer.
List of infectious diseases
Infectious agent
Common name
Acinetobacter baumannii
Acinetobacter infections
Actinomyces israelii, Actinomyces
Actinomycosis
gerencseriae and Propionibacterium propionicus
Trypanosoma brucei
African sleeping sickness (African
trypanosomiasis)
HIV (Human immunodeficiency virus)
AIDS (acquired immunodeficiency
syndrome)
Entamoeba histolytica
Amoebiasis
Anaplasma species
Anaplasmosis
Angiostrongylus
Angiostrongyliasis
Anisakis
Anisakiasis
Bacillus anthracis
Anthrax
Arcanobacterium haemolyticum
Arcanobacterium
haemolyticum infection
410
408
Junin virus
Argentine hemorrhagic fever
Ascaris lumbricoides
Ascariasis
Aspergillus species
Aspergillosis
Astroviridae species
Astrovirus infection
Babesia species
Babesiosis
Bacillus cereus
Bacillus cereus infection
multiple bacteria
Bacterial meningitis
multiple bacteria
Bacterial pneumonia
List of bacterial vaginosis microbiota
Bacterial vaginosis
Bacteroides species
Bacteroides infection
Balantidium coli
Balantidiasis
Bartonella
Bartonellosis
Baylisascaris species
Baylisascaris infection
BK virus
BK virus infection
Piedraia hortae
Black piedra
Blastocystis species
Blastocystosis
Blastomyces dermatitidis
Blastomycosis
Machupo virus
Bolivian hemorrhagic fever
Clostridium botulinum; Note: Botulism is not an
Botulism (and Infant botulism)
infection by Clostridium botulinum but caused by the
intake of botulinum toxin.
Sabiá virus
Brazilian hemorrhagic fever
Brucella species
Brucellosis
Yersinia pestis
Bubonic plague
usually Burkholderia cepacia and
Burkholderia infection
other Burkholderia species
Mycobacterium ulcerans
Buruli ulcer
Caliciviridae species
Calicivirus infection
(Norovirus and Sapovirus)
Campylobacter species
Campylobacteriosis
411
409
usually Candida albicans and other Candida species
Candidiasis (Moniliasis; Thrush)
Intestinal disease by Capillaria philippinensis, hepatic
Capillariasis
disease by Capillaria hepatica and pulmonary disease
by Capillaria aerophila
Bartonella bacilliformis
Carrion's disease
Bartonella henselae
Cat-scratch disease
usually Group A Streptococcus and Staphylococcus
Cellulitis
Trypanosoma cruzi
Chagas disease (American
trypanosomiasis)
Haemophilus ducreyi
Chancroid
Varicella zoster virus (VZV)
Chickenpox
Alphavirus
Chikungunya
Chlamydia trachomatis
Chlamydia
Chlamydophila pneumoniae
Chlamydophila pneumoniae infection
(Taiwan acute respiratory agent or
TWAR)
Vibrio cholerae
Cholera
usually Fonsecaea pedrosoi
Chromoblastomycosis
Batrachochytrium dendrabatidis
Chytridiomycosis
Clonorchis sinensis
Clonorchiasis
Clostridium difficile
Clostridium difficile colitis
Coccidioides immitis and Coccidioides posadasii
Coccidioidomycosis
Colorado tick fever virus (CTFV)
Colorado tick fever (CTF)
usually rhinoviruses and coronaviruses
Common cold (Acute viral
rhinopharyngitis; Acute coryza)
Severe acute respiratory syndrome coronavirus
Coronavirus disease 2019 (COVID-
2 (SARS-CoV-2)
19)
PRNP
Creutzfeldt–Jakob disease (CJD)
Crimean-Congo hemorrhagic fever virus
Crimean-Congo hemorrhagic
fever (CCHF)
412
410
Cryptococcus neoformans
Cryptococcosis
Cryptosporidium species
Cryptosporidiosis
usually Ancylostoma braziliense; multiple other
Cutaneous larva migrans (CLM)
parasites
Cyclospora cayetanensis
Cyclosporiasis
Taenia solium
Cysticercosis
Cytomegalovirus
Cytomegalovirus infection
Dengue viruses (DEN-1, DEN-2, DEN-3 and DEN-4) –
Dengue fever
Flaviviruses
Green algae Desmodesmus armatus
Desmodesmus infection
Dientamoeba fragilis
Dientamoebiasis
Corynebacterium diphtheriae
Diphtheria
Diphyllobothrium
Diphyllobothriasis
Dracunculus medinensis
Dracunculiasis
Ebolavirus (EBOV)
Ebola hemorrhagic fever
Echinococcus species
Echinococcosis
Ehrlichia species
Ehrlichiosis
Enterobius vermicularis
Enterobiasis (Pinworm infection)
Enterococcus species
Enterococcus infection
Enterovirus species
Enterovirus infection
Rickettsia prowazekii
Epidemic typhus
Parvovirus B19
Erythema infectiosum (Fifth disease)
Human herpesvirus 6 (HHV-6) and human herpesvirus
Exanthem subitum (Sixth disease)
7 (HHV-7)
Fasciola hepatica and Fasciola gigantica
Fasciolasis
Fasciolopsis buski
Fasciolopsiasis
PRNP
Fatal familial insomnia (FFI)
Filarioidea superfamily
Filariasis
Clostridium perfringens
Food poisoning by Clostridium
perfringens
413
411
multiple
Free-living amebic infection
Fusobacterium species
Fusobacterium infection
usually Clostridium perfringens;
Gas gangrene (Clostridial
other Clostridium species
myonecrosis)
Geotrichum candidum
Geotrichosis
PRNP
Gerstmann-Sträussler-Scheinker
syndrome (GSS)
Giardia lamblia
Giardiasis
Burkholderia mallei
Glanders
Gnathostoma spinigerum and Gnathostoma hispidum
Gnathostomiasis
Neisseria gonorrhoeae
Gonorrhea
Klebsiella granulomatis
Granuloma inguinale (Donovanosis)
Streptococcus pyogenes
Group A streptococcal infection
Streptococcus agalactiae
Group B streptococcal infection
Haemophilus influenzae
Haemophilus influenzae infection
Enteroviruses, mainly Coxsackie
Hand, foot and mouth
A virus and enterovirus 71 (EV71)
disease (HFMD)
Sin Nombre virus
Hantavirus Pulmonary Syndrome
(HPS)
Heartland virus
Heartland virus disease
Helicobacter pylori
Helicobacter pylori infection
Escherichia coli O157:H7, O111 and O104:H4
Hemolytic-uremic syndrome (HUS)
Bunyaviridae species
Hemorrhagic fever with renal
syndrome (HFRS)
Hendra virus
Hendra virus infection
Hepatitis A virus
Hepatitis A
Hepatitis B virus
Hepatitis B
Hepatitis C virus
Hepatitis C
Hepatitis D Virus
Hepatitis D
Hepatitis E virus
Hepatitis E
414
412
Herpes simplex virus 1 and 2 (HSV-1 and HSV-2)
Herpes simplex
Histoplasma capsulatum
Histoplasmosis
Ancylostoma duodenale and Necator americanus
Hookworm infection
Human bocavirus (HBoV)
Human bocavirus infection
Ehrlichia ewingii
Human ewingii ehrlichiosis
Anaplasma phagocytophilum
Human granulocytic
anaplasmosis (HGA)
Human metapneumovirus (hMPV)
Human metapneumovirus infection
Ehrlichia chaffeensis
Human monocytic ehrlichiosis
One of the human papillomaviruses
Human papillomavirus (HPV)
infection
Human parainfluenza viruses (HPIV)
Human parainfluenza virus infection
Hymenolepis nana and Hymenolepis diminuta
Hymenolepiasis
Epstein–Barr virus (EBV)
Epstein–Barr virus infectious
mononucleosis (Mono)
Orthomyxoviridae species
Influenza (flu)
Isospora belli
Isosporiasis
unknown; evidence supports that it is infectious
Kawasaki disease
multiple
Keratitis
Kingella kingae
Kingella kingae infection
PRNP
Kuru
Lassa virus
Lassa fever
Legionella pneumophila
Legionellosis (Legionnaires' disease)
Legionella pneumophila
Pontiac fever
Leishmania species
Leishmaniasis
Mycobacterium leprae and Mycobacterium
Leprosy
lepromatosis
Leptospira species
Leptospirosis
Listeria monocytogenes
Listeriosis
Borrelia burgdorferi, Borrelia garinii, and Borrelia
Lyme disease (Lyme borreliosis)
415
413
afzelii
Wuchereria bancrofti and Brugia malayi
Lymphatic filariasis (Elephantiasis)
Lymphocytic choriomeningitis virus (LCMV)
Lymphocytic choriomeningitis
Plasmodium species
Malaria
Marburg virus
Marburg hemorrhagic fever (MHF)
Measles virus
Measles
Middle East respiratory syndrome coronavirus
Middle East respiratory
syndrome (MERS)
Burkholderia pseudomallei
Melioidosis (Whitmore's disease)
multiple
Meningitis
Neisseria meningitidis
Meningococcal disease
usually Metagonimus yokagawai
Metagonimiasis
Microsporidia phylum
Microsporidiosis
Molluscum contagiosum virus (MCV)
Molluscum contagiosum (MC)
Monkeypox virus
Monkeypox
Mumps virus
Mumps
Rickettsia typhi
Murine typhus (Endemic typhus)
Mycoplasma pneumoniae
Mycoplasma pneumonia
Mycoplasma genitalium
Mycoplasma genitalium infection
numerous species of bacteria (Actinomycetoma)
Mycetoma
and fungi (Eumycetoma)
parasitic dipterous fly larvae
Myiasis
most commonly Chlamydia trachomatis and Neisseria
Neonatal conjunctivitis (Ophthalmia
gonorrhoeae
neonatorum)
Nipah virus
Nipah virus infection
Norovirus
Norovirus (children and babies)
PRNP
(New) Variant Creutzfeldt–Jakob
disease (vCJD, nvCJD)
usually Nocardia asteroides and other Nocardia species
Nocardiosis
Onchocerca volvulus
Onchocerciasis (River blindness)
416
414
Opisthorchis viverrini and Opisthorchis felineus
Opisthorchiasis
Paracoccidioides brasiliensis
Paracoccidioidomycosis (South
American blastomycosis)
usually Paragonimus westermani and
Paragonimiasis
other Paragonimus species
Pasteurella species
Pasteurellosis
Pediculus humanus capitis
Pediculosis capitis (Head lice)
Pediculus humanus corporis
Pediculosis corporis (Body lice)
Pthirus pubis
Pediculosis pubis (pubic lice, crab
lice)
multiple
Pelvic inflammatory disease (PID)
Bordetella pertussis
Pertussis (whooping cough)
Yersinia pestis
Plague
Streptococcus pneumoniae
Pneumococcal infection
Pneumocystis jirovecii
Pneumocystis pneumonia (PCP)
multiple
Pneumonia
Poliovirus
Poliomyelitis
Prevotella species
Prevotella infection
usually Naegleria fowleri
Primary amoebic
meningoencephalitis (PAM)
JC virus
Progressive multifocal
leukoencephalopathy
Chlamydophila psittaci
Psittacosis
Coxiella burnetii
Q fever
Rabies virus
Rabies
Borrelia hermsii, Borrelia recurrentis, and
Relapsing fever
other Borrelia species
Respiratory syncytial virus (RSV)
Respiratory syncytial virus infection
Rhinosporidium seeberi
Rhinosporidiosis
Rhinovirus
Rhinovirus infection
417
415
Rickettsia species
Rickettsial infection
Rickettsia akari
Rickettsialpox
Rift Valley fever virus
Rift Valley fever (RVF)
Rickettsia rickettsii
Rocky Mountain spotted
fever (RMSF)
Rotavirus
Rotavirus infection
Rubella virus
Rubella
Salmonella species
Salmonellosis
SARS coronavirus
SARS (severe acute respiratory
syndrome)
Sarcoptes scabiei
Scabies
Group A Streptococcus species
Scarlet fever
Schistosoma species
Schistosomiasis
multiple
Sepsis
Shigella species
Shigellosis (bacillary dysentery)
Varicella zoster virus (VZV)
Shingles (Herpes zoster)
Variola major or Variola minor
Smallpox (variola)
Sporothrix schenckii
Sporotrichosis
Staphylococcus species
Staphylococcal food poisoning
Staphylococcus species
Staphylococcal infection
Strongyloides stercoralis
Strongyloidiasis
Measles virus
Subacute sclerosing panencephalitis
Treponema pallidum
Bejel, Syphilis, and Yaws
Taenia species
Taeniasis
Clostridium tetani
Tetanus (lockjaw)
usually Trichophyton species
Tinea barbae (barber's itch)
usually Trichophyton tonsurans
Tinea capitis (ringworm of the scalp)
usually Trichophyton species
Tinea corporis (ringworm of the body)
usually Epidermophyton floccosum, Trichophyton
Tinea cruris (Jock itch)
rubrum, and Trichophyton mentagrophytes
418
416
Trichophyton rubrum
Tinea manum (ringworm of the hand)
usually Hortaea werneckii
Tinea nigra
usually Trichophyton species
Tinea pedis (athlete’s foot)
usually Trichophyton species
Tinea unguium (onychomycosis)
Malassezia species
Tinea versicolor (Pityriasis versicolor)
Toxocara canis or Toxocara cati
Toxocariasis (ocular larva migrans
(OLM))
Toxocara canis or Toxocara cati
Toxocariasis (visceral larva migrans
(VLM))
Toxoplasma gondii
Toxoplasmosis
Chlamydia trachomatis
Trachoma
Trichinella spiralis
Trichinosis
Trichomonas vaginalis
Trichomoniasis
Trichuris trichiura
Trichuriasis (whipworm infection)
usually Mycobacterium tuberculosis
Tuberculosis
Francisella tularensis
Tularemia
Salmonella enterica subsp. enterica, serovar typhi
Typhoid fever
Rickettsia
Typhus fever
Ureaplasma urealyticum
Ureaplasma urealyticum infection
Coccidioides immitis or Coccidioides posadasii.
Valley fever
Venezuelan equine encephalitis virus
Venezuelan equine encephalitis
Guanarito virus
Venezuelan hemorrhagic fever
Vibrio vulnificus
Vibrio vulnificus infection
Vibrio parahaemolyticus
Vibrio parahaemolyticus enteritis
multiple viruses
Viral pneumonia
West Nile virus
West Nile fever
Trichosporon beigelii
White piedra (tinea blanca)
Yersinia pseudotuberculosis
Yersinia pseudotuberculosis infection
Yersinia enterocolitica
Yersiniosis
Yellow fever virus
Yellow fever
419
417
Zeaspora fungus
Zeaspora
Zika virus
Zika fever
Mucorales order (Mucormycosis)
Zygomycosis
and Entomophthorales order (Entomophthoramycosis)
Pharmacokinetics
Volume of Distribution =
Volume of Distribution =
Total Dose
Drug Concentration
clearance
elimination rate constant
0.693
Half Life = elimination rate constant
𝐁𝐢𝐨𝐚𝐯𝐚𝐢𝐥𝐚𝐛𝐢𝐥𝐢𝐭𝐲 ×Dose
Clearance =
Dose Rate = Desired concentration of drug in plasma at steady state × Clearance
Adjusted Dose Rate = Initial Dose Rate ×
area under curve
Desired concentration of drug in plasma at steady state
Measured concentration of drug in plasma at steady state
420
418
Molecularity of Reaction
The molecularity of an elementary reaction is defined as the number of reactant molecules taking
part in the chemical reaction.
Chemical Reaction
Molecularity
PCl5 → PCl3 + Cl2
Unimolecular
2HI → H2 + I2
Bimolecular
2SO2 + O2 → 2SO3
Trimolecular
NO + O3 → NO2 + O2
Bimolecular
2CO + O2 → 2CO2
Trimolecular
2FeCl3 + SnCl2 → SnCl2 + 2FeCl2
Trimolecular
Common Multiferroic Materials
Material
Ferroelectric TC [K] magnetic TN or TC [K] Type of Ferroelectricity
BiFeO3
1100
HoMn2O5
39
TbMnO3
27
Ni3V2O8
6.5
653
lone pair
magnetically driven
42
421
419
magnetically driven
MnWO4
13.5
magnetically driven
CuO
230
230
ZnCr2Se4
110
20
magnetically driven
Ranges of the Trig Functions
−1 ≤ sinθ ≤ 1
−1 ≤ cosθ ≤ 1
−∞ ≤ tanθ ≤ ∞
cscθ ≥ 1 and cscθ ≤ −1
secθ ≥ 1 and secθ ≤ −1
−∞ ≤ cotθ ≤ ∞
Periods of the Trig Functions
The period of a function is the number, T, such that f (θ + T) = f (θ).
So, if ω is a fixed number and θ is any angle we have the following periods.
sin(ωθ) → T =
cos(ωθ) → T =
tan(ωθ) → T =
422
420
2π
ω
2π
ω
π
ω
csc(ωθ) → T =
sec(ωθ) → T =
cot(ωθ) → T =
2π
ω
2π
ω
π
ω
If n is an integer
sin(θ+ 2πn) = sinθ
cos(θ + 2πn) = cosθ
tan(θ + πn) = tanθ
csc(θ + 2πn) = cscθ
sec(θ + 2πn) = secθ
cot(θ + πn) = cotθ
Degrees to Radians Formulas
If x is an angle in degrees and t is an angle in radians then:
x=
180o t
π
Conic Sections
Circle
Standard Form: (x − h) 2 + (y − k) 2 = r2
423
421
where (h, k) = center and r = radius
Ellipse
Standard Form for Horizontal Major Axis:
Standard Form for Vertical Major Axis:
(x − h)2
a2
(x − h)2
b2
+
+
(y − k)2
b2
(y − k)2
a2
=1
=1
where (h, k) = center
2a=length of major axis
2b=length of minor axis
(0 < b < a)
Foci can be found by using c2 = a2 − b2
where c = foci length
Hyperbola
Standard Form for Horizontal Transverse Axis:
Standard Form for Vertical Transverse Axis:
(x − h)2
a2
(y − k)2
a2
−
−
(y − k)2
b2
(x − h)2
b2
where (h, k) = center
a=distance between center and either vertex
Foci can be found by using b2 = c2 − a2
where c is the distance between center and either focus. (b > 0)
424
422
=1
=1
Parabola
Vertical axis: y = a(x − h) 2 + k
Horizontal axis: x = a(y − k) 2 + h
where (h, k) = vertex
a=scaling factor
Range of Trigonometric Expression:
− √a2 + b 2 ≤ asinθ +bcosθ ≤ √a2 + b 2
Coefficient of Determination Formula
r=
n(Σxy)−(Σx) (Σy)
√[nΣx2 −(Σx2 )][nΣy2 −(Σy2 )]
where,
r = Correlation coefficient
x = Values in first set of data
y = Values in second set of data
n = Total number of values.
Formula for Conditional Probability
Conditional Probability of A given B
Conditional Probability of B given A
425
423
P (A|B) =
P(A ∩ B)
P (B|A) =
P(B ∩ A)
P(B)
P(A)
Covariance Formula
Population Covariance Formula
Sample Covariance Formula
Cov(x, y) =
∑(xi −x̅ )(yi −y
̅)
Cov(x, y) =
∑(xi −x̅ )(yi −y
̅)
N
N−1
xi = data value of x
yi = data value of y
x̄ = mean of x
ȳ = mean of y
N = number of data values.
Correlation =
Cov(x,y)
σx σy
where: Cov(x, y) is the covariance between x and y while σx and σy are the standard deviations of
x and y.
Anova Formula
Mean Square Factor =
Mean Square Error =
sum of squares factor
degrees of freedom factor
sum of squares error
degrees of freedom error
Degrees of freedom factor = number of factor levels – 1
426
424
Degrees of freedom error = total number of observations − number of factor levels
F-value =
R2 =
R2 (adjusted) = 1 –
Mean square factor
Mean square error
sum of squares error
sum of squares total
Mean Square error
Sum of Squares total / degrees of freedom total
R2 (predicted) = 1 −
Predicted Residual Sum of squares
Sum of Squares total
Process capability Formula
Process capability =
upper specification limit − lower specification limit
6 × standard deviation
Effect Size Formula
Cohen's index =
Mean of first observation−Mean of second observation
√(Standard deviation of first observation)
2 + (Standard deviation of second observation)2
Effect-size coefficient =
where: d denote the Cohen's index
427
425
2
d
√d2 + 4
Euler's Formula Equation
eix = cos x + i sin x
Exponential Equation Formula
y = abx
x and y are the variables
a and b are constants
Fibonacci Formula
Fn = Fn – 1 + Fn – 2
where,
Fn = nth term of the series
Fn – 1 and Fn – 2 are the (n −1) th and (n – 2) th terms respectively
Gaussian Distribution Formula
The probability density function formula for Gaussian distribution is given by:
f (x, μ, σ) =
where,
1
σ√2π
x is the variable
μ is the mean
σ is the standard deviation
428
426
exp (
−(x−μ)2
2σ2
)
Infinite Series Formula
n
∑∞
0 r =
1
1− r
Linear Interpolation Formula
y = y1 +
(x−x1 )
(x2 −x1 )
× (y2 − y1)
Percent Decrease Formula
Percent Decrease =
Decreased Value
× 100
Original Value
Percentage Increase Formula
Percent Increase =
Increased Value
Original Value
× 100
Percentile Formula
Percentile =
Number of Values Below "x"
Total Number of Values
Perfect Square Trinomial Formula
429
427
× 100
(ax)2 + 2abx + b2 = (ax + b)2
(ax)2 − 2abx + b2 = (ax − b)2
Poisson Distribution Formula
Suppose we conduct a Poisson experiment, in which the average number of successes within a
given region is μ. Then, the Poisson probability is:
P(x, μ) =
e−μ μx
x!
where x is the actual number of successes that result from the experiment, and e is approximately
equal to 2.71828.
Quartile Formula
When the set of observation is arranged in an ascending order, then the lower percentile is given
by:
Q1 = (
N+1
) th Term
Q2 = (
N+1
) th Term
The middle quartile is given by:
The upper quartile is given by:
Q3 = (
4
2
3(N+1)
4
430
428
) th Term
inter quartile range = Q3 – Q1
N → number of observations
Ratio Analysis Formula
Liquidity Ratios
Current Ratio =
Quick Ratio =
Current Liabilities
(Total Current Ratio − Inventory)
Total Current Liabilities
Profitability Ratios
Net Profit Ratio =
Net profit after tax
NetSales
Gross Profit Ratio =
Operating Ratio =
Earnings per share =
Current Asset
GrossProfit
NetSales
× 100
Operating Cost
NetSales
× 100
× 100
Net Income – Preferred Dividends
average outstanding common shares
Activity Ratios
431
429
Inventory Turnover Ratio =
Receivables Turnover Ratio =
Cost of goods sold
Average Inventory
Net Credit Sales
Average Trade Receivable
Solvency Ratios
Debt Equity Ratio =
Proprietary Ratio =
Total Liabilities
Stakeholder Equity
Stakeholder Equity
Total Assets
×100
Relative frequency formula
relative frequency =
number of times the data occurred in an observation
total frequencies
Sampling Error Formula
Sampling Error = Z ×
σ
√n
where,
Z is the Z score value based on the confidence interval (approx = 1.96)
σ is the population standard deviation
n is the size of the sample
432
430
Stirling Formula
n! ≈ (
n n
)
e √2πn
Annulus Formula
A = π (R2 − r2)
where,
A = Area of Annulus
R = Outer radius
r = Inner radius
(Pi) π = is approximately 3.142
Bayes' theorem
P(A | B) =
P(B |
A) P(A)
P(B)
where A and B are events and P(B) ≠ 0.
P(A | B) is a conditional probability: the likelihood of event A occurring given that B is
true.
P(B | A) is also a conditional probability: the likelihood of event B occurring given that A
is true.
P(A) and P(B) are the probabilities of observing A and B respectively; they are known as
the marginal probability.
433
431
32 × 31 = ?
35 × 11
9 × 1 = 09
3
+
5
3
8
5
9 × 2 = 18
9 × 3 = 27
9 × 4 = 36
9 × 5 = 45
35 × 11 = 385
9
9 × 6 = 54
6 +3 = 9
2
9 × 7 = 63
992
9 × 8 = 72
32 × 11
9 × 9 = 81
32 × 31 = 992
9 × 10 = 90
19
=
1❾
=
1
16
=
1❻
=
1
95
64
26
65
=
❾5
❻4
2❻
❻5
=
3
+
2
3
5
2
32 × 11 = 352
374 × 43 = ?
374 = 300 + 70 + 4
43 = 40 + 3
5
4
1
5
300
70
4
40
12000
2800
160
3
900
210
12
12000 + 2800 + 160 + 900 + 210 + 12 =16082
374 × 43 = 16082
432
Central Limit Theorem Formula
Central limit theorem is applicable for a sufficiently large sample sizes (n ≥ 30). The formula for
central limit theorem can be stated as follows:
Sample mean = Population mean
and
Sample standard deviation =
Population standard deviation
√Sample size
Coefficient of Variation Formula
Coefficient of variation =
Standard Deviation
Mean
×100%
Process capability index (Cpk) Formula
Cpk = min(
upper specification limit − mean
3 × standard deviation
,
mean− lower specification limit
3 × standard deviation
Signal to Noise Ratio Formula
signal to noise ratio =
standard deviation
mean of the given data
Uniform Distribution Formula
Theoretical Mean =
434
433
x+y
2
)
(y−x)2
Standard Deviation = √
12
Z Score Formula
Z Score =
Standardized random variable − mean
Standard deviation
Inductance Formula
The total series inductance is
L=L1 + L2 + L3 +…. + Ln
The parallel inductance is
1
L
=
1
L1
+
1
L2
+
1
L3
+….+
1
Ln
where, L1, L2, L3….. Ln denotes the inductance values.
Soil Erosion Formula
The universal soil loss equation predicts the annual soil loss per unit area. The universal soil loss
equation is given by:
A = R × K × L× S × CP
where,
435
434
A is the estimated annual soil loss
R is the rainfall and runoff factor representing the summed erosive potential of all rainfall
events in a year.
L is the slope length
S is the slope steepness
K is the soil erodibility factor representing units of soil loss per unit of soil erosivity
CP characterizes conservation management and land cover practices.
Critical Velocity Formula
Critical velocity of a liquid flowing through a tube =
where:
K is the Reynold's number
η is the coefficient of the viscosity of the liquid
r is the radius of the tube through which the liquid flows
ρ is the density of the liquid
Horsepower Formula
One Horsepower equals to 33,000 lb. ft/min
Horsepower (HP) =
Torque × Speed
5252
Horsepower (HP) = Weight × (
436
435
velocity
234
)2
K× η
ρ×r
Beat Frequency Formula
The formula for beat frequency is the difference in frequency of the two superimposed waves.
fb = f2−f1
f1 and f2 are the frequency of two waves
Voltage Drop Formula
voltage drop across the circuit = Current in amperes × impedance in Ω
Brewster's law Formula
µ = tanθp
where,
µ is the refractive index of the medium
θp is the polarizing angle
Hagen–Poiseuille equation
Δp =
8πμLQ
A2
where:
Δp is the pressure difference between the two ends,
L is the length of pipe,
μ is the dynamic viscosity,
Q is the volumetric flow rate,
437
436
R is the pipe radius,
A is the cross section of pipe.
Pressure Drop Formula
J = fLv2 / 2gD
where:
J = pressure drop
f = friction factor
L = length of the tube
v = velocity of the fluid
g = acceleration due to gravity
D = inner diameter of the tube
Strain Energy Formula
strain energy =
F×δ
strain energy =
1
where,
δ = compression,
F = force applied.
where,
σ = stress
ε= strain
V = volume of body
438
437
2
2
Vσε
strain energy =
where,
σ = stress,
E = Young's modulus,
V = volume of body.
2E × V
Rate Law
Zero order
−
dC
=k
dt
t1 =
2
2k
dC
dt = kC
t1 =
2
C0
First order
−
ln2
2k
Second
−
dC
= kC2
dt
439
438
σ2
t1 =
2
kC0
nth order
−
n → order of the reaction
C → reactant concentration
C0 → initial reactant concentration
t 1 → Half life period
1
dC
n
dt = kC
2
k → rate constant
List of ester odorants
Ester name
Odor or occurrence
Allyl hexanoate
pineapple
Benzyl acetate
pear, strawberry, jasmine
Bornyl acetate
pine
Butyl acetate
apple, honey
Butyl butyrate
pineapple
440
439
Butyl propanoate
pear drops
Ethyl acetate
nail polish remover, model paint, model airplane glue
Ethyl benzoate
sweet, wintergreen, fruity, medicinal, cherry, grape
Ethyl butyrate
banana, pineapple, strawberry
Ethyl hexanoate
pineapple, waxy-green banana
Ethyl cinnamate
cinnamon
Ethyl formate
lemon, rum, strawberry
Ethyl heptanoate
apricot, cherry, grape, raspberry
Ethyl isovalerate
apple
Ethyl lactate
butter, cream
Ethyl nonanoate
grape
Ethyl pentanoate
apple
Geranyl acetate
geranium
Geranyl butyrate
cherry
Geranyl pentanoate
apple
Isobutyl acetate
cherry, raspberry, strawberry
Isobutyl formate
raspberry
441
440
Isoamyl acetate
pear, banana (flavoring in Pear drops)
Isopropyl acetate
fruity
Linalyl acetate
lavender, sage
Linalyl butyrate
peach
Linalyl formate
apple, peach
Methyl acetate
glue
Methyl anthranilate
grape, jasmine
Methyl benzoate
fruity, ylang ylang, feijoa
Methyl butyrate
pineapple, apple, strawberry
(methyl butanoate)
Methyl cinnamate
strawberry
Methyl pentanoate
flowery
(methyl valerate)
Methyl phenylacetate
honey
Methyl salicylate
Modern root beer, wintergreen,
(oil of wintergreen)
Germolene and Ralgex ointments (UK)
Nonyl caprylate
orange
Octyl acetate
fruity-orange
442
441
Octyl butyrate
parsnip
Amyl acetate
apple, banana
(pentyl acetate)
Pentyl butyrate
apricot, pear, pineapple
(amyl butyrate)
Pentyl hexanoate
apple, pineapple
(amyl caproate)
Pentyl pentanoate
apple
(amyl valerate)
Propyl acetate
pear
Propyl hexanoate
blackberry, pineapple, cheese, wine
Propyl isobutyrate
rum
Terpenyl butyrate
cherry
List of dyes with Colour Index International generic names and numbers
Common name
Synonyms
C.I. generic name
C.I. number
Alcian Blue 8GX
Alcian Blue
Ingrain Blue
74240
Alcian yellow GXS
Sudan orange
Ingrain yellow 1
12840
443
442
Alizarin
Mordant red 11
58000
Alizarin Red S
Mordant red 3
58005
Alizarin yellow GG
Mordant yellow 1
14025
Alizarin yellow R
Mordant orange 1
14030
Azophloxin
Azogeranin B
Acid red 1
18050
Bismarck brown R
Vesuvine brown
Basic brown 4
21010
Bismarck brown Y
Vesuvine
Phenylene brown
Basic brown 1
21000
Brilliant cresyl blue
Cresyl blue BBS
Basic dye
51010
Chrysoidine R
Basic orange 1
11320
Chrysoidine Y
Basic orange 2
11270
Congo red
Direct red 28
22120
Crystal violet
Basic violet 3
42555
Ethyl Green
42590
Fuchsin acid
Acid violet 19
42685
Gentian violet
Basic violet 1
42535
Janus green
Basic dye
11050
Acid yellow 17
18965
Lissamine fast yellow
Yellow 2G
444
443
Malachite green
Martius yellow
Acid yellow 24
10315
Basic blue 6
51175
Metanil yellow
Acid yellow 36
13065
Methyl orange
Acid orange 52
13025
Methyl red
Acid red 2
13020
Acid black 1
20470
Naphthol green B
Acid green 1
10020
Naphthol yellow S
Acid yellow 1
10316
Orange G
Acid orange 10
16230
Purpurin
Verantin
Rose bengal
Acid red 94
45440
Sudan II
Solvent orange 7
12140
Titan yellow
Direct yellow 9
19540
Acid orange 6
14270
Acid orange 5
13080
Acid orange 7
15510
Meldola blue
Naphthalene black 12B
Tropaeolin O
Phenylene blue
Amido black 10B
Sulpho orange
Tropaeolin OO
Tropaeolin OOO
Orange II
445
444
Victoria blue 4R
Basic blue 8
42563
Victoria blue B
Basic blue 26
44045
Victoria blue R
Basic blue 11
44040
Xylene cyanol FF
Acid blue 147
42135
List of copper salts
Name
Chemical Formula
Anion
Copper silicide
Cu5Si
Silicide (silane)
Copper(I) oxide
Cu2O
Oxide (oxygen)
Copper(I) chloride
CuCl
Chloride (hydrochloric acid)
Copper(I) iodide
CuI
Iodide (hydroiodic acid)
Copper(I) cyanide
CuCN
Cyanide (hydrocyanic acid)
Copper(I) thiocyanate
CuSCN
Thiocyanate (thiocyanic acid)
Copper(I) sulfate
Cu2SO4
Sulfate (sulfuric acid)
Copper(I) sulfide
Cu2S
Sulfide (hydrogen sulfide)
Copper(I) acetylide
Cu2C2
Acetylide (acetylene)
Copper(I) bromide
CuBr
Bromide (hydrobromic acid)
Copper(I) fluoride
CuF
Fluoride (hydrofluoric acid)
Copper(I) hydroxide
CuOH
Hydroxide (water)
Copper(I) hydride
CuH
Hydride (hydrogen gas)
Copper(I) nitrate
CuNO3
Nitrate (nitric acid)
Copper(I) phosphide
Cu3P
Phosphide (phosphine)
Copper(I) thiophene-2-
C5H3CuO2S
thiophene-2-carboxylate (thiophene-2-
carboxylate
carboxylic acid)
Copper(I) t-butoxide
C16H36Cu4O4
t-butoxide (t-butyl alcohol)
Copper(II) sulfate
CuSO4
Sulfate (sulfuric acid)
446
445
Copper(II) chloride
CuCl2
Chloride (hydrochloric acid)
Copper(II) hydroxide
Cu(OH)2
Hydroxide (water)
Copper(II) nitrate
Cu(NO3)2
Nitrate (nitric acid)
Copper(II) oxide
CuO
Oxide (oxygen)
Copper(II) acetate
Cu(OAc)2
Acetate (acetic acid)
Copper(II) fluoride
CuF2
Fluoride (hydrofluoric acid)
Copper(II) bromide
CuBr2
Bromide (bromine)
Copper(II) carbonate
CuCO3
Carbonate (carbonic acid)
Copper(II) carbonate
Cu2CO3(OH)2
Hydroxide (water)
hydroxide
Carbonate (carbonic acid)
Copper(II) chlorate
Cu(ClO3)2
Chlorate (chloric acid)
Copper(II) arsenate
Cu3(AsO4)2
Arsenate (arsenic acid)
Copper(II) azide
Cu(N3)2
Azide (hydrazoic acid)
Copper(II)
Cu(O2C5H7)2
Acetylacetonate (acetylacetone)
Copper(II) aspirinate
C36H28Cu2O16
Acetylsalicylate (acetylsalicylic acid)
Copper(II) cyanurate
CuC3HN3O3
Cyanurate (cyanuric acid)
Copper(II) glycinate
Cu(H2NCH2CO2)2
Glycinate (glycine)
Copper(II) phosphate
Cu3(PO4)2
Phosphate (phosphoric acid)
Copper(II) perchlorate
Cu(ClO4)2
Perchlorate (perchloric acid)
Copper(II) selenite
CuSeO3
Selenite (selenous acid)
Copper(II) sulfide
CuS
Sulfide (hydrogen sulfide)
Copper(II) thiocyanate
Cu(SCN)2
Thiocyanate (thiocyanic acid)
Copper(II) triflate
Cu(OSO2CF3)2
Triflate (triflic acid)
Copper(II)
Cu(BF4)2
Tetrafluoroborate (tetrafluoroboric acid)
acetylacetonate
tetrafluoroborate
447
446
Copper(II) acetate
Cu(C2H3O2)2·3Cu(AsO2)2
Acetate (acetic acid)
triarsenite
Triarsenite
(Paris Green)
(1,3,5,2,4,6-Trioxatriarsinane-2,4,6-triol)
Copper(II) benzoate
Cu(C6H5CO2)2
Benzoate (benzoic acid)
Copper(II) arsenite
AsCuHO3
Arsenite (Arsenous acid)
Copper(II) chromite
Cu2Cr2O5
Chromite (chromic acid)
Copper(II) gluconate
C12H22CuO14
Gluconate (gluconic acid)
Copper(II) peroxide
CuO2
Peroxide (hydrogen peroxide)
Copper(II) usnate
C18H14CuO7
Usnate (usnic acid)
Copper(III) oxide
Cu2O3
Oxide (oxygen)
(Scheele's Green)
List of purification methods in chemistry
Affinity purification purifies proteins by retaining them on a column through their affinity
to antibodies, enzymes, or receptors that have been immobilised on the column.
Filtration is a mechanical method to separate solids from liquids or gases by passing the feed stream
through a porous sheet such as a cloth or membrane, which retains the solids and allows the liquid to
pass through.
Centrifugation is a process that uses an electric motor to spin a vessel of fluid at high speed to make
heavier components settle to the bottom of the vessel.
Evaporation removes volatile liquids from non-volatile solutes, which cannot be done through
filtration due to the small size of the substances.
Liquid–liquid extraction removes an impurity or recovers a desired product by dissolving the crude
material in a solvent in which other components of the feed material are soluble.
Crystallization separates a product from a liquid feed stream, often in extremely pure form, by
cooling the feed stream or adding precipitants that lower the solubility of the desired product so that it
forms crystals. The pure solid crystals are then separated from the remaining liquor by filtration or
centrifugation.
Recrystallization: In analytical and synthetic chemistry work, purchased reagents of doubtful purity
may be recrystallized, e.g. dissolved in a very pure solvent, and then crystallized, and the crystals
recovered, in order to improve and/or verify their purity.
448
447
Trituration removes highly soluble impurities from usually solid insoluble material by rinsing it
with an appropriate solvent.
Adsorption removes a soluble impurity from a feed stream by trapping it on the surface of a solid
material, such as activated carbon, that forms strong non-covalent chemical bonds with the impurity.
Chromatography employs continuous adsorption and desorption on a packed bed of a solid to purify
multiple components of a single feed stream. In a laboratory setting, mixture of dissolved materials
are typically fed using a solvent into a column packed with an appropriate adsorbent, and due to
different affinities for solvent (moving phase) versus adsorbent (stationary phase) the components in
the original mixture exit the column in the moving phase at different rates, which thus allows to
selectively collect desired materials out of the initial mixture.
Smelting produces metals from raw ore, and involves adding chemicals to the ore and heating it up to
the melting point of the metal.
Refining is used primarily in the petroleum industry, whereby crude oil is heated and separated into
stages according to the condensation points of the various elements.
Distillation is widely used in petroleum refining and in purification of ethanol separates volatile
liquids on the basis of their relative volatilities. There is several type of distillation: simple
distillation, steam distillation etc.
Water purification combines a number of methods to produce potable or drinking water.
Downstream processing refers to purification of chemicals, pharmaceuticals and food ingredients
produced by fermentation or synthesized by plant and animal tissues, for example antibiotics, citric
acid, vitamin E, and insulin.
Fractionation refers to a purification strategy in which some relatively inefficient purification
method is repeatedly applied to isolate the desired substance in progressively greater purity.
Electrolysis refers to the breakdown of substances using an electric current. This removes impurities
in a substance that an electric current is run through
Sublimation is the process of changing of any substance (usually on heating) from a solid to a gas
(or from gas to a solid) without passing through liquid phase. In terms of purification - material is
heated, often under vacuum, and the vapors of the material are then condensed back to a solid on a
cooler surface. The process thus in its essence is similar to distillation, however the material which is
condensed on the cooler surface then has to be removed mechanically, thus requiring different
laboratory equipment.
Bioleaching is the extraction of metals from their ores through the use of living organisms.
449
448
Physics Glossary
Absolute zero: The lowest possible temperature T, at which substances contain no heat energy
Q.
Acceleration: The rate at which the speed of an object is changing and it is given by the
equation a =
𝐝𝐯
𝐝𝐭
.
Anthropic principle: We see the universe the way it is because if it were different we would not
be here to observe it through a gigantic telescopes pointing deep into the immense sky – merely
stating that the constants of nature must be tuned to allow for intelligence (otherwise we would
not be here). Some believe that this is the sign of a cosmic creator. Others believe that this is a
sign of the multiverse.
Antiparticle: Each type of matter particle has a corresponding antiparticle – first predicted to
exist by P. A. M. Dirac. When a particle collides with its antiparticle, they annihilate, leaving
only pure energy in the form of discrete bundle (or quantum) of electromagnetic (or light) energy
called photons.
Atom: The basic unit of ordinary matter, made up of a tiny nucleus (consisting of positively
charged protons and electrically neutral neutrons – which obey the strong interactions)
surrounded by orbiting negatively charged weakly interacting particles called the electrons.
Big Bang: The singularity at the beginning of the universe. The titanic explosion that created the
universe, sending the galaxies hurtling in all directions. When the universe was created, the
temperature was extremely hot, and the density of material was enormous i.e., infinite. The big
bang took place 13.7 billion years ago, according to the WMAP satellite. The afterglow of the
big bang is seen today as the cosmic background microwave radiation (of temperature 2.7 degrees
above absolute zero). There are three experimental "proofs" of the big bang: the redshift of
the galaxies, the cosmic background microwave radiation, and nucleosynethsis of the elements.
Big crunch: The singularity at the end of the universe i.e., The final collapse of the universe. If
the density of matter is large enough (Omega – The parameter that measures the average density
of matter in the universe – being larger than 1), then there is enough matter in the universe to
reverse the original expansion and cause the universe to recollapse. Temperatures rise to infinity
at the instant of the big crunch.
Big freeze: The end of the universe when it reaches near absolute zero. The big freeze is probably
the final state of our universe, because the sum of Omega and Lambda is believed to be 1.0, and
450
449
hence the universe is in a state of inflation. There is not enough matter and energy to reverse the
original expansion of the universe, so it will probably expand forever.
Big Bang nucleosynthesis: The production of deuterium, Helium-3 and Helium-4 (the latter to
about 25% mass fraction) in the first 500 to 1000 sec of the early universe. These light isotopes,
plus measurable amounts of lithium-7 and trace amounts of elements B, Be, are the result of nonequilibrium nuclear reactions as the universe cooled to about 10 to the power of 8 K. Heavier
isotopes were produced in stellar nucleosynthesis.
Black hole: A region of space-time from which nothing, not even light, can escape, because
gravity is so strong and escape velocity equals the speed of light. Because the speed of light is the
ultimate velocity in the universe, this means that nothing can escape a black hole, once an object
has crossed the event horizon. Black holes can be of various sizes. Galactic black holes, lurking
in the center of galaxies and quasars, can weight millions to billions of solar masses. Stellar black
holes are the remnant of a dying star, perhaps originally up to forty times the mass of our Sun.
Both of these black holes have been identified with our instruments. Mini–black holes may also
exist, as predicted by theory, but they have not yet been seen in the laboratory conditions.
Black Hole Escape Velocity: It is widely held by astrophysicists and astronomers that a black
hole has an escape velocity c (or c, the speed of light in Vacuum). Chandrasekhar [Nobel
laureate] remarked,
"Let me be more precise as to what one means by a black hole. One says that a black hole is
formed when the gravitational forces on the surface become so strong that light cannot escape
from it. ... A trapped surface is one from which light cannot escape to infinity."
According to Hawking,
"Eventually when a star has shrunk to a certain critical radius, the gravitational field at the surface
becomes so strong that the light cones are bent inward so much that the light can no longer
escape. According to the theory of relativity, nothing can travel faster than light. Thus, if light
cannot escape, neither can anything else. Everything is dragged back by the gravitational field. So
one has a set of events, a region of space-time from which it is not possible to escape to reach a
distant observer. Its boundary is called the event horizon. It coincides with the paths of the light
rays that just fail to escape from the black hole."
A neutron star has a radius of about ten miles, only a few times the critical radius at which a star
becomes a black hole.
451
450
"I had already discussed with Roger Penrose the idea of defining a black hole as a set of events
from which it is not possible to escape to a large distance. It means that the boundary of the black
hole, the event horizon, is formed by rays of light that just fail to get away from the black hole.
Instead, they stay forever hovering on the edge of the black hole."
However, according to the alleged properties of a black hole, nothing at all can even leave the
black hole. In the very same paper Chandrasekhar made the following quite typical
contradictory assertion:
"The problem we now consider is that of the gravitational collapse of a body to a volume so small
that a trapped surface forms around it; as we have stated, from such a surface no light can
emerge."
Hughes reiterates,
"Things can go into the horizon (from r > 2M to r < 2M), but they cannot get out; once inside, all
causal trajectories (time-like or null) take us inexorably into the classical singularity at r = 0."
The defining property of black holes is their event horizon. Rather than a true surface, black holes
have a 'one-way membrane' through which stuff can go in but cannot come out.
Taylor and Wheeler assert,
"... Einstein predicts that nothing, not even light, can be successfully launched outward from the
horizon ... and that light launched outward EXACTLY at the horizon will never increase its radial
position by so much as a millimeter."
Zero point Energy: an intrinsic and unavoidable part of quantum physics. The ZPE has been
studied, both theoretically and experimentally, since the discovery of quantum mechanics in the
1920s and there can be no doubt that the ZPE is a real physical effect.
Casimir effect: The attractive pressure between two flat, parallel metal plates placed very near to
each other in a vacuum. The pressure is due to a reduction in the usual number of virtual
particles in the space between the plates. This tiny effect has been measured in the laboratory.
The Casimir effect may be used as the energy to drive a time machine or wormhole, if its
energy is large enough.
Chandrasekhar limit: The maximum possible mass of a stable cold star (i.e., 1.4 solar masses),
above which it must collapse into a black hole.
452
451
Conservation of energy: The law of science that states that energy (or its equivalent in mass) can
neither be created nor destroyed i.e., they never change with time. For example, the conservation
of matter and energy posits that the total amount of matter and energy in the universe is a
constant.
Coordinates: Numbers that specify the position of a point in 4 dimensional space-time.
Cosmological constant: A mathematical parameter (which measures the amount of dark energy
in the universe) introduced by Albert Einstein to give space-time an inbuilt tendency to expand.
At present, the data supports density parameter + cosmological constant = 1, which fits the
prediction of inflation for a flat universe. Cosmological constant, which was once thought to be
zero, is now known to determine the ultimate destiny of the universe.
Cosmology: The study of the universe as a whole.
COBE: The Cosmic Observer Background Explorer satellite.
Dark matter: Invisible Matter usually found in a huge halo around galaxies, clusters, and
possibly between clusters, that cannot be observed directly but can be detected by its gravitational
effect and they does not interact with light. As much as 90 percent of the mass of the universe
may be in the form of dark matter and they makes up 23 percent of the total matter/energy content
of the universe. According to string theory, dark matter may be made of subatomic particles, such
as the neutralino, which represent higher vibrations of the superstring.
Duality: A correspondence between apparently different theories that lead to the same physical
results.
Einstein-Rosen bridge: A thin tube of space-time linking two black holes.
Electric charge: A property of a particle by which it may repel (or attract) other particles that
have a charge of similar (or opposite) sign.
Electromagnetic force: The force of electricity and magnetism that arises between particles
with electric charge; the second strongest of the four fundamental forces – which
obeys Maxwell's equations.
Electron: A negatively charged subatomic particle with negative electric charge that orbits
the nucleus of an atom and determines the chemical properties of the atom.
Electroweak unification energy: The energy (around 100 GeV) above which the distinction
between the electromagnetic force and the weak force disappears.
Elementary particle: A particle that, it is believed fundamental building block of Nature, cannot
be subdivided and are not composed of other simpler particles.
453
452
Event: A point in space-time, specified by its time and place.
Event horizon: The boundary of a black hole. The point of no return, often called the horizon.
Exclusion principle: The idea that two identical spin-1/2 particles cannot have (within the limits
set by the uncertainty principle) both the same position and the same velocity. This means that
two electrons cannot occupy precisely the same point with the same properties, so that there is a
net force pushing the electrons apart (in addition to electrostatic repulsion).
Field: Something that exists throughout 4 dimensional fabric of space -time, as opposed to a
particle that exists at only one point at a time.
Frequency: For a wave, the number of complete cycles per second.
Gamma rays: Electromagnetic rays of very short wavelength, produced in radio-active
decay or by collisions of elementary particles.
General relativity: Einstein's theory of gravity based on the idea that the laws of science
should be the same for all observers, no matter how they are moving. It explains the force of
gravity in terms of the curvature of a four dimensional space-time; so that the curvature of spacetime gives the illusion that there is a force of attraction called gravity. It has been verified
experimentally to better than 99.7 percent accuracy and predicts the existence of black holes and
the expanding universe. The theory, however, break down at the center of a black hole or the
instant of creation, where the theory predicts nonsense. To explain these phenomena, one must
resort to a theory of subatomic physics.
Geodesic: The shortest (or longest) path between two points.
Grand unification energy: The energy above which, it is believed, the electromagnetic force,
weak force, and strong force become indistinguishable from each other.
Grand unified theory (GUT): A theory which unifies the electromagnetic, strong, and weak
forces (but not gravity). The proton is not stable in these theories and can decay into
positrons. GUT theories are inherently unstable (unless one adds super symmetry). GUT theories
also lack gravity. (Adding gravity to GUT theories makes them diverge with infinities.)
Imaginary time: Time measured using imaginary numbers.
Inflation: The theory which states that the universe underwent an incredible amount
of superliminal expansion at the instant of its birth i.e., A distance of one nanometer was
enlarged to a quarter of a billion light-years.
Hyperspace: Dimensions higher than four.
454
453
Light cone: A surface in space-time that marks out the possible directions for light rays passing
through a given event.
Light year: The distance light travels in one year, or approximately 5.88 trillion miles (9.46
trillion kilometers).
LIGO: The Laser Interferometry Gravitational-Wave Observatory, based in Washington state
and Louisiana,which is the world’s largest gravity wave detector.
LISA: The Laser Interferometry Space Antenna- which is a series of three space satellites using
laser beams to measure gravity waves. It is sensitive enough to confirm or disprove the
inflationary theory and possibly even string theory.
Magnetic field: The field responsible for magnetic forces, now incorporated along with
the electric field, into the electromagnetic field.
Muon: A subatomic particle identical to the electron but with a much larger mass. It belongs to
the second redundant generation of particles found in the Standard Model.
Mass: The quantity of matter in a body; its inertia, or resistance to acceleration.
Microwave background radiation: The remnant radiation (with a temperature of about 2.7
degrees K) from the glowing of the hot early universe (big bang), now so greatly red-shifted that
it appears not as light but as microwaves (radio waves with a wavelength of a few centimeters).
Tiny deviations in this background radiation give scientists valuable data that can verify or rule
out many cosmological theories.
Naked singularity: A space-time singularity not surrounded by a black hole.
Neutrino: An extremely light (possibly massless) subatomic particle that react very weakly with
other particles and may penetrate several light-years of lead without ever interacting with
anything and is affected only by the weak force and gravity.
Neutron: A neutral subatomic particle, very similar to the proton, which accounts for roughly
half the particles in an atomic nucleus.
Neutron star: A cold collapsed star consisting of a solid mass of neutrons — which is usually
about 10 to 15 miles across — supported by the exclusion principle repulsion between neutrons.
If the mass of the neutron stars exceeds (3- 4 solar masses) i.e., if the number of neutrons
becomes ≥ 5.9 × 10 57, then the degenerate neutron pressure will not be large enough to overcome
the gravitational contraction and the star collapses into the next stage called black holes.
No boundary condition: The idea that the universe is finite but has no boundary (rooted in
the Euclidean formalism) to account for the initial conditions in the big bang.
455
454
Nuclear fusion: The process by which two nuclei collide and coalesce to form a single, heavier
nucleus.
Nucleus: The tiny core of an atom, which is roughly 10
−13
cm across, consisting only of protons
and neutrons, held together by the strong force.
Particle accelerator: A machine — based in Geneva, Switzerland — that, using electromagnets,
can accelerate moving charged particles, giving them more energy.
Phase: For a wave, the position in its cycle at a specified time: a measure of whether it is at a
crest, a trough, or somewhere in between.
Photon: A quantum of light (which was first proposed by Einstein to explain the photoelectric
effect—that is, the fact that shining light on a metal results in the ejection of electrons).
Planck's quantum principle: The idea that light (or any other classical waves) can be emitted or
absorbed only in discrete quanta, whose energy E is proportional to their wavelength λ (i.e., E =
hc
).
λ
Positron: The (positively charged) antiparticle of the electron.
Primordial black hole: A black hole created in the very early universe.
Negative energy: Energy that is less than zero.
Proton: A positively charged subatomic particle, very similar to the neutron, that accounts for
roughly half the particles in the nucleus of most atoms. They are stable, but Grand Unification
theory predicts that they may decay over a long period of time.
Pulsar: A rotating neutron star that emits regular pulses of radio waves.
Quantum: The indivisible unit in which waves may be emitted or absorbed.
Quark: A subatomic particle that makes up the proton and neutron and feels the strong force.
Three quarks make up a proton or neutron, and a quark and antiquark pair makes up a meson.
Quantum chromodynamics (QCD): The theory that describes the interactions of quarks
and gluons.
Quantum mechanics: The theory developed from wave equations, Planck's quantum principle
and Heisenberg's uncertainty principle. No deviation from quantum mechanics has ever been
found in the laboratory. Its most advanced version today is called quantum field theory, which
combines special relativity and quantum mechanics. A fully quantum mechanical theory of
gravity, however, is exceedingly difficult.
456
455
Quasar: Quasi-stellar object. They are huge galaxies that were formed shortly after the gigantic
explosion called the big bang.
Quantum foam: Tiny, foam like distortions of 4 dimensional fabric of space-time at the level of
the Planck length.
Radioactivity: The spontaneous breakdown of one type of atomic nucleus into another.
Red shift: The reddening or decrease in frequency of light from a star that is moving away from
us, due to the Doppler effect.
Singularity: A point in space-time at which the space-time curvature becomes infinite – which
represent a breakdown of general relativity, forcing the introduction of a quantum theory of
gravity.
Singularity theorem: A theorem that states that the universe must have started with a singularity.
Space-time: The four-dimensional space whose points are events.
Spatial dimension: Any of the three dimensions that are space like – that is, any except
the time dimension.
Special relativity: Einstein's 1905 theory based on the idea that the laws of science should be the
same for all observers, no matter how they are moving, in the absence of gravitational
phenomena. Consequences include: time slows down, mass increases, and distances shrink the
faster you move. Also, matter and energy are related via E = mc2. One consequence of special
relativity is the atomic bomb.
Spectrum: The different colors or component frequencies that make up a wave. By analyzing the
spectrum of starlight, one can determine that stars are mainly made of hydrogen and helium.
Spin: An internal property of elementary particles.
Stationary state: One that is not changing with time.
Supernova: An exploding star. They are so energetic that they can sometimes outshine a galaxy.
String theory: A theory of physics based on tiny vibrating strings, such that each particle is
described as a wave on a string. It is the only theory that can combine gravity with the quantum
theory, making it the leading candidate for a theory of everything.
Strong force: The strongest of the four fundamental forces, with the shortest range of all. It holds
the quarks together within protons and neutrons, and holds the protons and neutrons together to
form atoms.
Steady state theory: The theory which states that the universe had no beginning but constantly
generates new matter as it expands, keeping the same density.
457
456
Uncertainty principle: The principle, formulated by Heisenberg, that one can never be
exactly sure of both the position and the velocity of a particle; the more accurately one
knows the one, the less accurately one can know the other.
Δx Δp ≥
ΔE Δt ≥
ħ
2
ħ
2
Avogadro's Number: 6.022 × 1023. The number of nucleons (protons and neutrons) in 1
gram of matter.
Virtual particle: In quantum mechanics, a particle that briefly dart in and out of the
vacuum but can never be directly detected, but whose existence does have measurable
effects. They violate known conservation laws but only for a short period of time, via the
uncertainty principle.
Baryon: A particle that is composed of three quarks, such as the proton or neutron.
Baryon Asymmetry Problem: The fact that the universe contains a billion times as
many baryons (ordinary matter) as antibaryons (antimatter), when they would be
expected to have been produced in equal quantities in the early universe.
Brownian Motion: The random motion of macroscopic particles that results from their
being bombarded by molecules.
Copernican Principle: The earth is not the center of the universe.
Curie Point: The temperature below which iron becomes magnetic.
Generalized Copernican Principle: There is no center of the universe, no special point
in space or time.
Hilbert Space: An abstract mathematical space used to describe quantum mechanical
states.
Occam's Razor: The principle that one should introduce no more hypotheses than are
necessary to explain the data.
Wave / particle duality: The concept in quantum mechanics that there is no distinction
between waves and particles; particles may sometimes behave like waves, and waves like
particles.
458
457
Wavelength: For a wave, the distance between two adjacent troughs or two adjacent
crests.
Weak force: The second weakest of the four fundamental forces – which is carried by
the W- and Z-bosons- that makes possible nuclear decay. It affects all matter particles,
but not force carrying particles.
Selectron: The supersymmetric partner of the electron. Not yet observed.
Weight: The force exerted on a body by a gravitational field. It is proportional to, but not
the same as, its mass.
Principle of Galilean Relativity: Velocity is relative. There is no difference between
being in motion at constant velocity and being at rest.
Parity Violation: The observation that the mirror image of a natural process is not
always fundamentally equivalent to the original process.
Quantum Electrodynamics (QED): The quantum theory of electromagnetism.
White dwarf: A stable cold star consisting of lower elements such as oxygen, lithium,
carbon, and so forth, supported by the exclusion principle repulsion between electrons.
Wormhole: A passageway between two universes or a thin tube of space-time
connecting distant regions of the universe. Wormholes might also link to parallel or baby
universes and could provide the possibility of time travel.
Neutrino-Dominated Universe: The model in which neutrinos with mass constitute the
dark matter of the universe.
Gravitational binding energy of the star:
U=−
3GM2
5R
where:
M and R denote the mass and radius of the star
G is the Gravitational constant
459
458
Core pressure of the star:
Pcore =
5GM2
4πR2
Core density of the star:
ρcore =
3M
πR3
Core Temperature of the star:
Tcore =
5μmH GM
3kB R
where:
μ denotes mean molecular weight of the matter insider the star
mH is the mass of hydrogen nucleus
kB is the Boltzmann constant
The ideal gas equation PV = NkBT does not hold good for the matter present inside a star.
Because, most stars are made up of more than one kind of particle and the gas inside the star is
ionized. There is no indication of these facts in the above equation. We need to change the ideal
gas equation, so that it holds good for the material present inside the star. It can be shown that
the required equation can be written as
PV =
1 MkB T
μ mH
where μ denotes mean molecular weight of the matter inside the star, M is the mass of the star
and mH is the mass of hydrogen nucleus.
460
459
Stellar timescales
Nuclear timescale:
tnuc =
total mass of fuel available
rate of fuel consumption
× fraction of star over which fuel is burned
tnuc =
MX
L
Q
×F
where M is the mass of the star, X is the fraction of the star (by mass) that is composed of the fuel, L is
the star's luminosity, Q is the energy released per mass of the fuel from nuclear fusion, and F is the
fraction of the star where the fuel is burned.
Einstein timescale:
tE =
Mc2
tth ≈
GM2
L
Thermal time scale
2RL
Dynamical timescale
R3
tdyn = √
GM
where c is the speed of light
461
460
Richardson-Dushman Equation:
The Richardson-Dushman equation relates the current density of a thermionic emission (js) to the
work function (W) and temperature (T) of the emitting material:
js = A T
2
𝑒
−W
kB T
where A denotes the Richardson's constant and kB is the Boltzmann constant.
In a nuclear reaction:
MA+ MB → MC+ MD
Q = (MA+ MB −MC −MD) c2
The amount of energy released or absorbed in a nuclear reaction is called the Q value, or reaction
energy.
If MA+ MB > MC+ MD→ Q > 0 ≡ exoergic reaction
If MA+ MB < MC+ MD → Q < 0 ≡ endoergic reaction
An endoergic reaction will not proceed unless the incoming particle provides the reaction energy
"Q".
Drake equation:
N = R∗ × fp × nE × fl × fi × fc × L
462
461
where:
N = the number of civilizations in our galaxy with which communication might be
possible.
R∗ = the average rate of star formation in our galaxy.
nE = the average number of planets that can potentially support life per star that has
fp = the fraction of those stars that have planets.
planets.
fl = the fraction of planets that could support life that actually develop life at some
point.
fi = the fraction of planets with life that actually go on to develop intelligent life
(civilizations).
fc = the fraction of civilizations that develop a technology that releases detectable
signs of their existence into space.
L = the length of time for which such civilizations release detectable signals into
space.
Borda–Carnot equation
∆E = ξ
1
2
ρ (v1 − v2) 2
where:
ΔE is the fluid mechanical energy loss,
ξ is an empirical loss coefficient, which is dimensionless and has a value between zero
and one, 0 ≤ ξ ≤ 1
ρ is the fluid density
v1 and v2 are the mean flow velocities before and after the expansion.
463
462
Kepler's equation
M = E – e sin E
where M is the mean anomaly, E is the eccentric anomaly, and e is the eccentricity.
Maxwell's Equations
Gauss's law for electricity
∇⦁E=
Gauss's law for magnetism
∇×E=−
(Faraday's law of induction)
Ampere's circuital law
∇ = Laplace operator
E = Electric field
ρ = charge density
B = Magnetic field
ε0 = absolute permittivity
J = current density
μ0 = absolute permeability
∂B
∂t
∇ × B = μ0 ( J + ε0
where:
ε0
∇⦁B= 0
Maxwell–Faraday equation
ρ
464
463
∂E
)
∂t
Prony equation
The Prony equation is a historically important equation in hydraulics, used to calculate the head
loss due to friction within a given run of pipe. It is an empirical equation developed by
Frenchman Gaspard de Prony in the 19th century:
hf =
L
D
(aV + bV2)
where "hf" is the head loss due to friction, calculated from: the ratio of the length to diameter of
the pipe "
friction.
L
D
", the velocity of the flow "V", and two empirical factors "a" and "b" to account for
Rankine-Hugoniot conditions
In a coordinate system that is moving with the shock, the Rankine–Hugoniot conditions can be
expressed as:
ρ1 us = ρ2 (us − u2) → Conservation of mass
p2 − p1 = ρ2 u2 (us − u2) = ρ1 u2 us → Conservation of momentum
p2 u2 = ρ1 us (
1
2
u22 + e2 − e1) → Conservation of energy
where us is the shock wave speed, ρ1 and ρ2 are the mass density of the fluid behind and inside the
shock, u2 is the particle velocity of the fluid inside the shock, p1 and p2 are the pressures in the two
regions, and e1 and e2 are the specific (with the sense of per unit mass) internal energies in the two
regions.
Sackur–Tetrode equation
465
464
The Sackur–Tetrode equation expresses the entropy S of a monatomic ideal gas in terms of its
thermodynamic state − specifically, its volume V, internal energy U, and the number of particles
N:
S
kB N
where:
kB = Boltzmann's constant
m =Mass of a gas particle
h = Planck's constant
= ln [
V
N
(
4πmU 3/2
5
) ]+
2
3h N
2
Butler–Volmer equation
j = j0 {exp [
α𝑎 zFη
RT
] − exp [ −
αc zFη
RT
]}
where:
j: electrode current density, A/m2 (defined as j = I/S)
j0: exchange current density, A/m2
E: electrode potential, V
Eeq: equilibrium potential, V
T: absolute temperature, K
z: number of electrons involved in the electrode reaction
F: Faraday constant
R: universal gas constant
αc: so-called cathodic charge transfer coefficient, dimensionless
αa: so-called anodic charge transfer coefficient, dimensionless
η: activation overpotential (defined as η = E − E eq).
466
465
Lotka–Volterra equations
dx
= αx − βxy
dy
= δxy − γy
dt
dt
where:
x is the number of prey (for example, rabbits)
y is the number of some predator (for example, foxes)
dy
dt
and
dx
represent the instantaneous growth rates of the two populations
dt
t represents time
α, β, γ, δ are positive real parameters describing the interaction of the two species
Black–Scholes equation
In mathematical finance, the Black–Scholes equation is a partial differential equation (PDE)
governing the price evolution of a European call or European put under the Black–Scholes
model. Broadly speaking, the term may refer to a similar PDE that can be derived for a variety of
options, or more generally, derivatives. For a European call or put on an underlying stock paying
no dividends, the equation is:
∂V
∂t
+
1
2
σS
2 2
∂2 V
∂S2
+ rS
∂V
∂S
– rV = 0
where V is the price of the option as a function of stock price S and time t, r is the risk-free
interest rate, and σ is the volatility of the stock.
467
466
Password length parameter
In telecommunication, a password length parameter is a basic parameter the value of which
affects password strength against brute force attack and so is a contributor to computer security.
One use of the password length parameters is in the expression P = L ×
R
, where P is the
S
probability that a password can be guessed in its lifetime, L is the maximum lifetime a password
can be used to log into a system, R is the number of guesses per unit of time, and S is the number
of unique algorithm-generated passwords.
Stellar structure
The Equation of mass conservation
dm
dr
= 4πr2ρ
where: ρ is the matter density and m is the cumulative mass inside the shell at r and G is
the gravitational constant.
The Equation of hydrostatic equilibrium
dP
dr
=−
Gm
r2
ρ
where: P is the total pressure (matter plus radiation).
The Equation of energy generation
468
467
dL
dr
= 4πr2ρq
where: L is the luminosity and q is the rate of energy generation per unit mass
The Equation of energy transport
dT
dr
=−
3κρL
64πr2 σT3
where: T is the temperature, κ is the opacity of the matter and σ is the Stefan–Boltzmann
constant
For stars:
tdyn <tth < tnuc
tdyn = timescale of collapsing star, e.g. supernova
tth = timescale of star before nuclear fusion starts, e.g. pre-main sequence lifetime
tnuc = timescale of star during nuclear fusion, i.e. main-sequence lifetime
Taft equation
log (
ks
kCH3
) = ρ* σ* + δEs
469
468
where log (
ks
kCH3
) is the ratio of the rate of the substituted reaction compared to the reference
reaction, σ* is the polar substituent constant that describes the field and inductive effects of the
substituent, Es is the steric substituent constant, ρ* is the sensitivity factor for the reaction to
polar effects, and δ is the sensitivity factor for the reaction to steric effects.
Hammett equation
log (
where:
k
k0
) = σρ
σ = substituent constant
ρ = reaction constant
k0 is the reference reaction rate of the unsubstituted reactant, and k that of a substituted
reactant.
∆s2 = −c2∆t2 + ∆x2 + ∆y2 + ∆z2
∆s2 < 0 is a timelike interval. Events separated by this interval can be causally
related.
∆s2 = 0 is a lightlike interval. Events separated by this interval can be causally
related, but only by a light speed signal.
∆s2 > 0 is a spacelike interval. Events separated by this interval cannot be causally
related.
470
469
Basic terms in chemistry
Chemistry - a science that deals with the structure and properties of substances and their
reactions, it studies matter and energy
Organic chemistry – the branch of chemistry that deals with the chemistry of carbon and
living organisms
Analytical chemistry – the branch of chemistry that studies the properties of materials
and analyzes materials
Matter - the thing that forms physical objects and occupies space, it exists in four main
states as solids, liquids, gases and plasma
Solid – a substance that has a definite shape and a definite volume, it is not compressible
Liquid – a substance (state of matter) which has an indefinite shape and a definite
volume, not easily compressible
Gas – a substance with an indefinite shape and volume, easily compressible
Melting point – the temperature at which solids turn into liquid
Condensation – the phase change when gas forms a liquid
Sublimation – the phase change when a solid state changes into a gaseous state
Evaporation – the phase change when a substance changes from a liquid state into a
gaseous state
Atom – the smallest unit of matter which has all the chemical properties of a particular
element
Molecule − the smallest possible amount of a particular substance that has all the
characteristics of that substance
Neutron − a particle found in the nucleus of an atom which has the same mass as a
proton but no charge
Element – a substance that consists only of one type of atom
Compound – a chemical substance that consists of two or more elements that together
form a molecule
Mixture − a material system made up of two or more different substances which are
mixed but are not combined chemically
471
470
Solvent − A liquid in which a substance (solute) dissolves.
Acid − a chemical with a sour taste that forms a salt when mixed with a base
Base − a chemical that reacts with an acid to form a salt, it has a pH higher than 7
Atomic number – the number of protons in an atom
Mass number – the sum of the number of protons and neutrons in one atom
Bond − a force that holds together the atoms in a molecule, an attraction between atoms
or molecules
Ion − an atom or group of atoms that has a positive or negative electric charge from
losing or gaining one or more electrons
Covalent bond – a type of bond between non-metal atoms, consists of a shared pair of
electrons
Shell / orbital – region a of space around the nucleus of an atom where an electron is
likely to be found
Steric hindrance − the phenomenon of physical blockage of a particular site within a
molecule by the presence of local atoms or groups of atoms.
Structural isomerism − isomers which differ in the order of bonding of the constituent
atoms.
Reactant – an original substance that changes when it is combined with another
substance in a chemical reaction
Product – resulting substance of a chemical reaction
Mole − A formula mass expressed in grams
Nucleophile − a substance which donates a pair of electrons in the reaction considered.
Chemical equation – a shorthand representation of a chemical reaction with formulas of
reactants to the left of an arrow and the formulas of the products to the right of an arrow
Catalyst – a substance that speeds up the rate of a chemical reaction
Enzyme − A biological catalyst.
Combination (synthesis) reaction – chemical change in which two or more substances
react to form a single (one) new substance
Period − A horizontal row in the periodic table.
472
471
Beaker − a wide glass with a lip for pouring that is used for holding and measuring
liquids
Test tube − a glass container that is shaped like a tube which is closed at one end and
that is used especially in science experiments
Funnel − a device shaped like a hollow cone with a tube extending from the point which
is used for pouring something (such as a liquid) into a narrow opening
Flask − a glass bottle used in scientific laboratories that is used to carry liquids
Thermometer − an instrument used for measuring temperature
Condenser − a device used for changing a gas into a liquid
Forceps / tweezers − a tool that is used for grasping or holding little things
Spatula − a tool that has a long handle which is bent upward and a wide, thin blade used
for lifting and turning chemicals
Bunsen burner − a piece of equipment that produces a hot flame and that is used in
scientific experiments
Dropper − a glass or plastic tube that is used to measure out liquids by drops
Tongs − a tool used for lifting or holding objects that is made of two long pieces
connected in the middle
Tautomerism − a form of structural isomerism where the two structures are
interconvertible by means of the migration of a proton.
Crucible − a pot in which metals or other substances are heated to a very high
temperature or melted
Clamp − a device that holds or presses parts tightly together
Petri dish − a small, shallow dish that has a loose cover and that is is used in scientific
experiments especially for growing bacteria
Analytical balance − a device that measures weight and shows how heavy things are.
Fume hood − a piece of laboratory equipment designed to limit exposure to dangerous
fumes
Markownikow's rule − in the ionic addition of hydrogen halides to a carbon-carbon
double bond the halogen attaches itself to the carbon atom bearing the least number of
hydrogen atoms.
473
472
Greek Alphabet and SI Prefixes
A
α
alpha
N
ν
nu
B
β
beta
Ξ
ξ
xi
Γ
γ
gamma
O
o
omicron
∆
δ
delta
Π
π
pi
E
ϵ, ε
epsilon
P
ρ
rho
Z
ζ
zeta
Σ
σ, ς
sigma
H
η
eta
T
τ
tau
Θ
θ, ϑ
theta
Y
υ
upsilon
I
ι
iota
Φ
φ, ϕ
phi
K
κ
kappa
X
χ
chi
Λ
λ
lambda
Ψ
ψ
psi
M
µ
mu
Ω
ω
omega
Double Factorial n!! =
n × (n − 2) × … × 5 × 3 × 1
for n > 0 odd
n × (n − 2) × … × 6 × 4 × 2
for n > 0 even
1
for n = −1, 0
Convergence Tests
D'Alembert's ratio test
In a series, ∑∞
𝑛=1 𝑎𝑛 , let the ratio R =
lim (
𝑛→∞
If R < 1 the series is convergent
𝑎𝑛+1
𝑎𝑛
474
473
)
If R > 1 the series is divergent
If R = 1 the test fails.
The Integral Test
∞
A sum to infinity of an converges if ∫1 𝑎𝑛 𝑑𝑛 is finite. This can only be applied to series where
an is positive and decreasing as n gets larger.
Maxwell's thermodynamic relations
∂T
( )
∂V S
=−(
∂T
( )
∂P S
∂V
( )
∂T P
∂S
( )
∂V T
475
474
=
∂P
∂V
( )
∂S P
=−(
=
)
∂S V
∂S
)
∂P T
∂P
( )
∂T V
Cramer's Rule
Two simultaneous equations in unknowns x and y,
a1x + b1y = c1 and a2 x + b2 y = c2,
have the solutions
and
c
b1
| 1
|
c2 b2
x= a b
1
| 1
|
a 2 b2
a1 c1
| a
c |
y = a 2 b2
1
| 1
|
a 2 b2
=
c1 b2 −c2 b1
=
a1 c2 −a2c1
a1 b2 −a2 b1
a1 b2 −a2 b1
When a surface intercepts electromagnetic radiation, a force and a pressure are exerted on the
surface. If the radiation is totally absorbed by the surface, the force is
F=
IA
c
(total absorption),
in which I is the intensity of the radiation, c is the speed of light, and A is the area of the surface
perpendicular to the path of the radiation. If the radiation is totally reflected back along its
original path, the force is
F=
2IA
c
(total reflection back along path).
The radiation pressure pr is the force per unit area:
and
I
pr = (total absorption)
c
pr =
2I
c
(total reflection back along path).
475
476
I=
E2
cμ0
Because E = c × B and c is such a very large number: the energy associated with the electric field
is much greater than that associated with the magnetic field.
The rate per unit area at which energy is transported via an electromagnetic wave is given by the
Poynting vector:
⃗⃗⃗⃗ × B
⃗⃗⃗⃗
E
S⃗⃗⃗ =
μ0
Masses are usually measured in atomic mass units, where
1 u = 1.660 538 86 ×10−27 kg
and energies are usually measured in electron-volts or multiples of it, where
1 eV = 1.602 176 462 × 10−19 J.
Angular wave number =
2π
Wavelength
The probability that a given particle of mass m and energy E will tunnel through a barrier of
height Ub and thickness L is given by the transmission coefficient T:
T ≈ e−2bL
8π2 m(Ub −E)
where b = √
h2
(h: Planck's constant)
476
477
Because it is a matter wave, an electron confined to an infinite potential well can exist in only
certain discrete states. If the well is one-dimensional with length L, the energies associated with
these quantum states are
En =
h 2 n2
8mL2
for n = 1, 2, 3. . .
where m is the electron mass and n is a quantum number.
Moseley's law
υ = A × (Z − b) 2
where:
υ is the frequency of the observed X-ray emission line
Z is the atomic number
A and b are constants that depend on the type of line (that is, K, L, etc. in X-ray notation)
Number of conduction electrons in sample = number of atoms in sample × number of valence electrons per atom.
1 becquerel = 1 Bq = 1 decay per second.
1 curie = 1 Ci = 3.7 × 1010 Bq
477
478
Physical Data Often Used
Average Earth–Moon distance
8
3.84 × 10 m
Average Earth–Sun distance
1.496 × 10
11
m
Average Radius of the Earth
6.37 × 10 m
Density of air (20°C and 1 atm)
1.20 kg/m
Density of water (20°C and 1 atm)
1.00 × 10 kg/m
Free-fall acceleration
9.80 m/s
6
3
3
3
2
Mass of the Earth
5.98 × 10
24
kg
Mass of the Moon
7.36 × 10
22
kg
Mass of the Sun
1.99 × 10
30
kg
5
Standard atmospheric pressure
1.013 × 10 Pa
Distance from the Earth to the most remote known quasar: 1.4 × 1026 m
Distance from the Earth to the most remote normal galaxies: 9 × 10 25 m
Distance from the Earth to the nearest large galaxy (Andromeda): 2 × 1022 m
Distance from the Sun to the nearest star (Proxima Centauri): 4 × 1016 m
One light-year: 9.46 × 1015 m
Mean orbit radius of the Earth about the Sun: 1.50 × 1011 m
Mean distance from the Earth to the Moon: 3.84 × 108 m
Distance from the equator to the North Pole: 1.00 × 107 m
Typical altitude (above the surface) of a satellite orbiting the Earth: 2 × 105 m
Length of a housefly: 5 × 10−3 m
Size of smallest dust particles: ~10−4 m
478
479
Size of cells of most living organisms: ~10−5 m
Diameter of a hydrogen atom: ~10−10 m
Diameter of an atomic nucleus: ~10−14 m
Diameter of a proton: ~10−15 m
Age of the Universe: 5 × 1017 s
Age of the Earth: 1.3 × 1017 s
One year: 3.2 × 107s
One day: 8.6 × 104 s
Time interval between normal heartbeats: 8 × 10−1 s
Period of audible sound waves: ~10−3 s
Period of typical radio waves: ~10−6 s
Period of vibration of an atom in a solid: ~10−13 s
Period of visible light waves: ~10−15 s
Duration of a nuclear collision: ~10−22 s
Time interval for light to cross a proton: ~10−24 s
1000 kg = 1 t (metric ton)
1 slug = 14.59 kg
Compressibility Factor (Z) =
PV
nRT
where P is the pressure, n is the number of moles of gas, T is the absolute temperature, and R is
the gas constant.
479
480
Garland or mala product:
A product of numbers remains the same when read from left to right or vice.
139 × 139 = 15151
152207 × 73 = 11111111
14287143 × 7 = 100010001
12345679 × 9 = 111111111
142857143 × 7 = 1000000001
11011011 × 91 = 1002002001
27994681 × 441 = 12345654321
333333666667 × 33 = 11000011000011
Kaprekar Numbers:
8426
Ascending order: 2468
Descending order: 8642
Difference: 6174
4671
Ascending order: 1467
Descending order: 7641
Difference: 6174
480
481
1, 9, 45, 55, 703, 2223 … are known as Kaprekar numbers.
Stoke's Law of Viscosity:
F = 6πηrv
F= Drag Force
η = Viscosity Coefficient
r = Radius of the Particle
v = Relative velocity of the Particle
Reynolds Number:
Re =
r×ρ×v
μ
Re = Reynolds Number
r = The diameter or length (basically length of the shape of the object)
ρ = The density of the fluid
v = The velocity of the object
μ = Viscosity of the fluid;
Eotvos Ramsay-Shield relation:
[
M
ρ
]
2
3
γ = k (Tc − T − 6)
481
482
M=Molecular Weight
ρ = density
γ = Surface Tension
k = Eotvos-Ramsay Coefficient
Tc = Critical Temperature
T = System Temperature
Young-Laplace Equation:
Pin = Pout +
2γ
Pin = Pressure Inside the Curved Surface
Pout = Pressure Outside the Curved Surface
γ = Surface Tension
r = Radius of Curvature of the Curved Surface
r
Dieterici Equation of State:
P = Pressure
V = Volume
a , b = Dieterici Constants
n = Number of Moles
R = Universal Gas Constant
T = Temperature
Pe
an
RTV
(V − nb) = nRT
482
483
Energy of Polyatomic Gas (Non-Linear):
E = 3 (n −1) RT
E = Average energy per mole
n = Number of atoms in a non-linear Molecule
R= Gas Constant
T= Temperature
Energy of Polyatomic Gas (Linear):
E=
5
2
RT + (3n − 5) RT
E = Average energy per mole
n = Number of atoms in a linear Molecule
R= Gas Constant
T= Temperature
Collision Frequency of a single gas:
ZAA =
π n σ cave
√2
ZAA=Collision frequency
n = Molecules per unit Volume
σ = Diameter of the gas molecules
cave = Average Velocity of the gas molecules
483
484
Root Mean Square, Average, Median Velocity of Gas:
3RT
crms = √
M
8RT
cave = √
πM
2RT
cm = √
M
crms, cave , cm = Root Mean Square, Average Velocity and Most Probable Velocity of gas
molecules
M= Molecular Weight
T =Temperature
R= Universal Gas Constant
Clausius Clapeyron Equation:
ln (
P2
P1
)=
ΔHm
R
P1 and P2 = Initial and Final Pressure
ΔHm = Molar Enthalpy of vaporization
T1 and T2 = Initial and Final Temperature
R= Gas Constant
[
484
485
1
T1
−
1
T2
]
Relative Population of rotational energy states:
Nj
N0
= exp (−
B h c J (J+1)
kB T
NJ = Number of molecule in J state
N0 = Number of molecule in the ground state (J= 0)
kB =Boltzmann Constant
T = Temperature
B = Rotational Constant
h = Plank Constant
c = Velocity of light
J = Rotational Quantum Number
Double Bond Equivalent (DBE) = C + 1 −
C= Number of Carbon atoms present
H = Number of Hydrogen atoms present
X= Number of Halogen atoms present (Cl, Br, I or F)
N= Number of Nitrogen atoms present
Langmuir Isotherm:
θ=
KP
1+KP
485
486
)
H
2
−
X
2
+
N
2
K = Equilibrium Constant of Adsorption
P = Partial Pressure or Concentration of the absorbate
θ = The fraction of adsorbent surface covered by adsorbate
Slater's Rule:
Zeff = Z − σ
Zeff = Effective nuclear charge
Z = Atomic Number
σ = number of shielding electrons
Interplanar Spacing of Cubic Lattice:
dhkl =
dhkl = Lattice Spacing
a = Lattice Constant
h , k , l = Miller Indices
a
√h2 + k2 + 𝑙 2
Interplanar Spacing of Tetragonal Lattice:
1
d2
d= Interplanar Spacing
h , k, l = Miller Indices
a, c = Lattice Constants
=
h2 + k2
a2
486
487
+
𝑙2
c2
The Dead Sea is much denser and heavier than freshwater because of its
salt content, which would make it impossible for us to sink.
Pi is an irrational number, which means that it is a real number that cannot be
expressed by a simple fraction.
If we travel faster than the speed of light, we will age less.
Gravitational potential energy increases as height increases.
Adding a resistor in series increases the total resistance of a circuit.
Adding a resistor in parallel decreases the total resistance of a circuit.
The insulator does not permit the free flow of electrons
Light slows down, bends toward the normal and has a shorter
wavelength when it enters a medium with a higher index of refraction
A prism produces a rainbow from white light by the
phenomenon of dispersion
487
Spectrum of Electromagnetic Radiation
Region
Wavelength
Wavelength
Frequency
Energy
(Angstroms)
(centimeters)
(Hz)
(eV)
Radio
> 109
> 10
< 3 × 109
< 10−5
Microwave
109 −106
10 − 0.01
3 × 109 − 3 × 1012
10−5 − 0.01
Infrared
106 − 7000
0.01 − 7 × 10−5
3 × 1012 − 4.3 × 1014
Visible
7000 − 4000
7 × 10−5 − 4 × 10−5
4.3 × 1014 − 7.5 × 1014
2−3
Ultraviolet
4000 − 10
4 × 10−5 − 10−7
7.5 × 1014 − 3 × 1017
3 − 103
X−Rays
10 − 0.1
10−7 − 10−9
3 × 1017 − 3 × 1019
103 − 105
Gamma Rays
< 0.1
< 10−9
> 3 × 1019
> 105
0.01 − 2
Doppler Effect
When a wave source moves toward us, we will perceive waves with a shorter wavelength and
higher frequency than the waves emitted by the source.
When a wave source moves away from us, we will perceive waves with a longer wavelength and
lower frequency.
At the critical angle a wave will be refracted to 90 degrees. At angles larger than the critical
angle, light is reflected not refracted.
488
Natural abundance of some elements
Isotope
% Natural Abundance
Atomic Mass
1H
99.985
1.007825
2H
0.015
2.0140
12C
98.89
12 (formerly by definition)
13C
1.11
13.00335
14N
99.64
14.00307
15N
0.36
15.00011
16O
99.76
15.99491
17O
0.04
16.99913
18O
0.2
17.99916
28Si
92.23
27.97693
29Si
4.67
28.97649
30Si
3.10
29.97376
32S
95.0
31.97207
33S
0.76
32.97146
34S
4.22
33.96786
489
35Cl
75.77
34.96885
37Cl
24.23
36.96590
79Br
50.69
78.9183
81Br
49.31
80.9163
There are 2 basic types of elementary particles: Hadrons and Leptons
There are 2 types of Hadrons: Baryons and Mesons
Made up of 3 quarks
Made up of a quark and antiquark
As the frequency of an electromagnetic radiation increases, its energy
increases and its wavelength decreases and its velocity remains constant as
long as it doesn't enter a medium with a different refractive index
Ionized gases conduct electric current using positive ions,
negative ions and electrons.
490
Thermal DeBroglie wavelength of an electron:
λD = √
h2
2πme kB T
where: h is the Planck's constant, me is the mass of the electron, kB is the Boltzmann's constant,
and T is the temperature.
Debye screening wave vector =
1
Debye length
The Debye length of semiconductors:
εkB T
LD = √ 2
q Ndop
where:
ε is the dielectric constant,
kB is the Boltzmann's constant,
T is the absolute temperature in Kelvins,
q is the elementary charge, and
Ndop is the net density of dopants (either donors or acceptors).
491
488
The Bjerrum length is given by:
λB =
e2
4πε0 εr kB T
where: e is the elementary charge, εr is the relative dielectric constant of the medium and ε0 is the
vacuum permittivity.
Drift velocity = electrical mobility of the particle × magnitude of the applied electric field
Fusion energy gain factor =
Pfusion
Pheating
Pfusion = power produced in a nuclear fusion reactor
Pheating = power of external heating required to keep fusion going
The Hall parameter, β, in a plasma is the ratio between the electron gyrofrequency, Ωe, and the
electron-heavy particle collision frequency, ν:
β=
Ωe
ν
=
eB
νme
where:
e is the elementary charge (approximately 1.6×10−19 C)
B is the magnetic field (in teslas)
492
489
me is the electron mass (approximately 9.1×10−31 kg)
Magnetic Reynolds number:
Rm =
UL
η
where:
U is a typical velocity scale of the flow
L is a typical length scale of the flow
η is the magnetic diffusivity
Péclet number =
advective transport rate
diffusive transport rate
Nusselt number =
hL
k
where h is the convective heat transfer coefficient of the flow, L is the
characteristic length, k is the thermal conductivity of the fluid.
Magnetic Prandtl number =
493
490
momentum diffusivity
magnetic diffusivity
The magnetic pressure PB is given in SI units (P in Pa, B in T, μ0 in H/m) by:
PB =
B2
2μ0
where: B is the strength of magnetic field and μ0 is the permeability of free space.
Static resistance =
small change in current
Static conductance =
Differential conductance =
1
Static resistance
small change in current
small change in voltage
The acceleration gradient for a linear plasma wave is:
me ne
494
491
current
small change in voltage
Differential resistance =
E=c√
voltage
ε0
In this equation, E is the electric field, c is the speed of light in vacuum, me is the mass of the
electron, ne is the plasma electron density (in particles per metre cubed), and ε0 is the permittivity
of free space.
Bond distance d in Rydberg matter is given by:
d = 2.9 n2a0
where n is the principal quantum number and a0 is the Bohr radius.
The ram pressure is a function of wind speed and density. The formula is
P = mp n v2
where mp is the proton mass, pressure P is in nPa (nanopascals), n is the density in particles/cm 3
and v is the speed in km/s of the solar wind.
For a gas composed of a single atomic species, the Saha equation is written:
ni+1 ne
ni
=
2 gi+1
exp
λ3 gi
[−
εi+1 − εi
kB T
]
where: ni + 1 and ni are the number of atoms in the (i + 1) th and ith ionization states, respectively;
g i + 1 and gi describe how energy is partitioned among the (i + 1)
495
492
th
and ith ionization states; εi + 1
and εi are the energies of the ionization states; ne is the number of electrons; and T is the
temperature. λ =
√
h2
2πme kB T
is the thermal de Broglie wavelength of an electron. The other
quantities in the equation are physical constants: me is the mass of the electron, kB is the
Boltzmann's constant, and h is Planck's constant.
Bowen ratio =
sensible heating
latent heating
Bejan number =
entropy generation contributed by heat transfer
entropy generation contributed by heat transfer+ entropy generation contributed by fluid friction
Antoine equation
log10 p = A −
B
C+T
where: p is the vapor pressure, T is temperature and A, B and C are component-specific
constants.
Kopp–Neumann law:
496
493
The Kopp–Neumann law, named for Kopp and Franz Ernst Neumann, is a common approach
for determining the specific heat C (in J·kg−1·K−1) of compounds using the following equation:
C = ∑𝑁
𝑖 =1(𝐶𝑖 ∙ 𝑓𝑖 )
where: N is the total number of compound constituents, and Ci and fi denote the specific
heat and mass fraction of the ith constituent. This law works surprisingly well at roomtemperature conditions, but poorly at elevated temperatures.
Stefan number =
sensible heat
latent heat
Duhem–Margules equation:
(
dlnPA
dlnPB
)
=(
)
dlnxA T, P
dlnxB T, P
where PA and PB are the partial vapor pressures of the two constituents and x A and xB are the
mole fractions of the liquid.
Airway Conductance =
Airway Resistance =
1
Airway Resistance
Atmospheric Pressure−Alveolar Pressure
Volumetric Airflow
497
494
Cardiac index =
Cardiac output
Body surface area
=
Stroke volume × Heart rate
Body surface area
Stroke volume = End-systolic volume − End-diastolic volume
Mean arterial pressure = (cardiac output × systemic vascular resistance) + central venous pressure
In practice, the contribution of central venous pressure (which is small) is generally ignored and so:
Mean arterial pressure = cardiac output × systemic vascular resistance
Pulse pressure = systolic pressure − diastolic pressure
Ejection fraction (%) =
stroke volume
end diastolic volume
498
495
× 100
Body mass index =
body mass
(body height)2
Low-density lipoprotein:
LDL = C – HDL − kT
where: HDL is High Density Lipoprotein, C is total cholesterol, T denote the triglycerides, and k
is 0.20 if the quantities are measured in mg/dl and 0.45 if in mmol/l.
Widmark formula:
Blood Alcohol Content =
Alcohol consumed in grams
Body weight in grams × r
× 100
In this formula, "r" is the gender constant: r = 0.55 for females and 0.68 for males.
Creatinine Clearance:
CrCl (male) =
(140 − age) (weight in kg)
72 × serum creatinine
For women, this result is multiplied by the factor 0.85.
499
496
The Doppler frequency shift for active radar is as follows, where FD is Doppler frequency, FT
is transmit frequency, vR is radial velocity, and c is the speed of light:
FD = 2 × FT ×
vR
c
For Passive radar:
FD = FT ×
vR
c
Output voltage of the transducer:
Vout =
P × K × Vsa
Vsi
where:
P is the actual measured pressure.
K is the nominal transducer scale factor.
Vsa is the actual transducer supply voltage.
Vsi is the ideal transducer supply voltage.
Critical damping coefficient =
500
497
actual damping
critical damping
True Positive
True Positive Rate =
True Positive +False Negative
False Positive Rate =
False Positive
True Negative +False Positive
The specific intensity Iν of radiation is defined by:
Iν =
dP
(cosθ dσ) dν dΩ
where dP is the power received by a detector with projected area (cosθ dσ) in the solid angle dΩ
and in the frequency range ν to ν + dν.
Iλ is the brightness per unit wavelength:
Iλ =
dP
(cosθ dσ) dλ dΩ
These two quantities are related by:
Iλ
Iν
=
dν
dλ
=
c
λ2
The spectral energy density of radiation is:
uν =
1
c
∫ Iν dΩ
The mean photon energy of blackbody radiation is:
E = 2.7 kBT
501
498
The flux density of isotropic radiation is:
Sν = π Iν
The Nyquist approximation for the spectral power generated by a warm resistor in the limit
hν ≪ kBT is
Pν = kBT
At any frequency, the exact Nyquist formula is
Pν =
exp(
hν
hν
)−1
kB T
The CMB temperature at redshift z is
T = T0 (1 + z)
T0 is the temperature of the CMB as observed in the present day (2.725 K)
The total power emitted by an accelerated charge is given by Larmor's formula:
P=
q2 a 2
6πε0 c3
which is valid only if v << c
where a is the proper acceleration, q is the charge, and c is the speed of light.
If an antenna delivers Po watts to the load connected to its output terminals (e.g. the receiver)
when irradiated by a uniform field of power density S watts per square meter, the antenna's
aperture Ae in square meters is given by: Ae =
Po
S
502
499
PN
B
where:
= kBT
PN is the noise power
B is the total bandwidth over which that noise power is measured
kB is the Boltzmann constant (1.381×10−23 J/K)
T is the noise temperature
The minimum mean density of a pulsar with period P is:
ρ>
3π
GP2
G is the Newtonian constant of gravitation
The spin-down luminosity of a pulsar is:
−
dErot
dt
I is the moment of inertia
Erot is the rotational kinetic energy
=
−4π2 I
The characteristic age of a pulsar is defined by:
τ=
P
2×
503
500
dP
dt
P3
×
dP
dt
Bremermann's limit:
c2
h
≈ 1.36 × 1050 bits per second per kilogram
is a limit on the maximum rate of computation that can be achieved in a self-contained system in
the material universe.
Bekenstein bound:
S≤
2πkB RE
ℏc
where S is the entropy, kB is Boltzmann's constant, R is the radius of a sphere that can enclose
the given system, E is the total mass–energy including any rest masses, ℏ is the reduced Planck
constant, and c is the speed of light.
In informational terms, with S = kB × I × ln 2, the bound is given by
I≤
2πRE
ℏc ln2
where I is the information expressed in number of bits contained in the quantum states in the
sphere. The ln 2 factor comes from defining the information as the logarithm to the base 2 of the
number of quantum states. Using mass–energy equivalence (E=Mc2), the informational limit
may be reformulated as
I≤
2πcRM
ℏ ln2
504
501
Band ratio (TM)
Mineral
5/7
clay, carbonate, silica, mica group
3/1
heamtite goethite and jarosite
5/4
bare rock and soil
Geology:
Drainage density =
Asymmetry factor =
Bifurcation ratio =
total length of channel in a drainage basin
total area
area of the basin to the right of the trunk stream
total area of the drainage basin
× 100
The number of streams of one order
The number of streams of the next higher order in a drainage network
Discharge = width of the channel × depth of the channel × velocity of flow
the length of the stream channel
Channel sinuosity = the straight line distance between the end points of the selected channel reach
Ripple index =
ripple wavelength
ripple height
Symmetry index =
505
502
stoss length
lee length
Tonnage = Volume of ore-block × Specific gravity
Metal content = tonnage × grade (or assay value)
Mineral matter = 1.1 × Ash content
Weight loss due to Volatile Matter = Total Weight loss – moisture
% Volatile Matter =
Fixed carbon = 100 – (% moisture + % Ash content + % volatile matter)
% moisture =
% Ash content =
Dry mineral matter free volatile matter = 100 − Dry mineral matter free Fixed carbon
% Fixed carbon on dry ash free basis = 100 – (% moisture + % Ash content)
Analysis on dry ash free basis =
Darcy's law:
Weight loss due to volatile matter
Weight of sample
× 100
Weight loss due to moisture
× 100
Weight of sample
Weight of residue
× 100
Weight of sample
% Volatile Matter
100−(% moisture + % Ash content)
permeability
× 100
Instantaneous flow rate = − dynamic viscosity of the fluid × pressure drop
Plasticity index = Liquid limit – Plastic limit
Consistency index =
Bulk density of soil =
Liquid limit – water content
Liquid limit – Plastic limit
dry weight of soil
volume of soil
506
503
dry weight of soil
Particle density of soil =
Mass wetness =
Void ratio =
Porosity =
Degree of saturation =
Uniformity coefficient =
Coefficient of curvature:
Cc =
volume of solid
mass of water
mass of soil
volume of voids
volume of solids
void volume
total volume
volume of water in a soil
volume of voids
× 100
The size opening that will just pass 60% of the sand (d60 value)
The size opening that will just pass 10% of the sand sample (d10 value)
(Size of particle corresponding to 30% finer)2
Size of the particle corresponding to 60% finer × Size of the particle corresponding to 10% finer
the density of a substance
Relative density =
Total core recovery =
Sum of length of core pieces
Solid core recovery =
Sum of length of solid , cylindrical, core pieces > core diameter
Rock quality designation =
the density of a given reference material
Total length of core run
× 100
Total length of core run
Sum of length of core pieces >100mm
Total length of core run
Rock quality designation Rock mass quality
< 25%
Very poor
25-50%
Poor
51-75%
Fair
76-90%
Good
91-100%
Excellent
507
504
× 100
× 100
Rock quality designation (RQD) = 115 − 3.5 Jn
Rock tunneling index =
where:
RQD
Jn
×
Jr
Ja
×
Jw
SRF
Jn = Joint set number (1−20)
Jr = Joint roughness (1−20)
Ja = Joint alteration number
Jw = Joint water flow (1−20)
SRF = stress reduction factor
Geological strength index = 9log[
Slake durability index =
where:
C−D
A−D
RQD
Jn
× 100
×
Jr
Ja
] + 44
D = dry drum mass
A = drum mass with rock before run
C = drum mass with rock after run
elastic modulus of a particular material in a cross−section
Modular ratio =
Point load index (Is) → The force needed to fracture a sample of rock between conical
points: Is =
P
D2
elastic modulus of the base or the reference material
, where P is force and D is the distance between the points, both at failure.
Is is related to uniaxial compressive strength (approximately equal to Is × 24)
Wyllie time-average equation:
1
wave velocity in rock
=
porosity in rock
velocity of the fluid in the pores
508
505
+
(1− porosity in rock)
velocity of the rock matrix
sinC =
1
n
where:
C is the critical angle.
n is the refractive index of the medium.
Substance medium
Refractive index
Critical angle
Water
1.33
48.75°
Crown glass
1.52
41.14°
Dense flint glass
1.62
37.31°
Diamond
2.42
24.41°
Science
Technology
Explores new knowledge methodically through
The application of scientific knowledge for various
observation and experimentation.
purposes.
The wave nature of light was demonstrated convincingly for the first time in 1801 by Thomas
Young by a wonderfully simple experiment. He let a ray of sunlight into a dark room, placed a
dark screen in front of it, pierced with two small pinholes, and beyond this, at some distance, a
white screen. He then saw two darkish lines at both sides of a bright line, which gave him
sufficient encouragement to repeat the experiment, this time with spirit flame as light source,
with a little salt in it to produce the bright yellow sodium light. This time he saw a number of
dark lines, regularly spaced; the first clear proof that light added to light can produce darkness.
This phenomenon is called interference. Thomas Young had expected it because he believed in
the wave theory of light.
− Dennis Gabor
509
506
Physical quantities with same dimensional formula:
Physical Quantity
Dimensional Formula
Momentum and impulse
[M1L1T-1]
Angular momentum and Planck's constant
[M1L2T-1]
Work, Energy, Moment of a force, Torque and couple
[M1L2T-2]
Frequency, Angular Frequency, Angular velocity and Velocity gradient
[M0L0T-1]
Pressure, Stress, Elastic constant and Energy density
[M1L-1T-2]
Force constant (spring), Surface Tension and surface energy
[M1L0T-2]
Radius of gyration, light year and wavelength
[M0L1T0]
The Spectral Lines for Atomic Hydrogen:
Series
n1
n2
Spectral Region
Lyman
1
2, 3 …
Ultraviolet
Balmer
2
3, 4 …
Visible
Paschen
3
4, 5 …
Infrared
Brackett
4
5, 6 …
Infrared
Pfund
5
6, 7 …
Infrared
Formal charge
(F.C.) on an atom
in a Lewis structure
=
Total number of
valence electrons in
the free atom
Total number of
−
non bonding
(lone pair)
electrons
510
507
Total number of
−
1
2
bonding (shared)
electrons
Bonding molecular orbital
Anti Bonding molecular orbital
Molecular orbitals formed by the additive
Molecular orbitals formed by the subtractive
effect of the atomic orbitals
effect of atomic orbitals
Probability of finding the electrons is more
Probability of finding the electrons is less
ΔG0 = ΔH0−TΔS0
ΔH0
ΔS0
ΔG0
–
+
–
Reaction spontaneous at all temperatures
–
–
– (at low Temperature)
Reaction spontaneous at low temperature
–
–
+ (at high Temperature)
Reaction non-spontaneous at high temperature
+
+
+ (at low Temperature)
Reaction Non-spontaneous at low temperature
+
+
– (at high Temperature)
Reaction spontaneous at high temperature
+
–
+ (at all Temperature)
Reaction non-spontaneous at all temperatures
Description
Temperature Corrected Density = (Density of Fuel Oil @ 15⁰C) × [1− {(T−15) × 0.00064}]
where: T = temperature of oil in bunker tanks in degree Celsius
Metric Tonnes = (Actual Sounder Volume) × (Temperature Corrected Density)
Specific Fuel Oil Consumption (SFOC):
SFOC (g/KWh) =
Mass of fuel consumed per hour
Power developed in KW
Engine distance in nautical mile = (Pitch × revolutions per day)
511
508
List of physical quantities:
Base quantity
Description
SI base unit
Length
The one-dimensional extent of an object
metre
Mass
A measure of resistance to acceleration
kilogram
Time
The duration of an event
second
Electric Current
Rate of flow of electrical charge per unit time
ampere
Temperature
Average kinetic energy per degree of freedom of
Kelvin
a system
Amount of substance
The quantity proportional to the number of
mole
particles in a sample, with the Avogadro
constant as the proportionality constant
Luminous intensity
Wavelength-weighted power of emitted light
candela
per unit solid angle
Derived quantity
Description
SI derived unit
Young's modulus
Ratio of stress to strain
pascal (Pa = N/m2)
Work
Transferred energy
joule (J)
Weight
Gravitational force on an object
newton (N = kg⋅m/s2)
512
Derived quantity
Wavevector
Wavenumber
Wavelength
Volumetric flow rate
Volume
Velocity
Description
Repetency or spatial frequency vector: the
number of cycles per unit distance
Repetency or spatial frequency: the number
of cycles per unit distance
Perpendicular distance between repeating
units of a wave
Rate of change of volume with respect to
SI derived unit
m−1
m−1
m
time
m3⋅s−1
Three dimensional extent of an object
m3
Moved distance per unit time: the first time
derivative of position
m/s
Product of a force and the perpendicular
Torque
distance of the force from the point about
newton-metre (N⋅m)
which it is exerted
Thermal resistivity
Thermal resistance
Thermal conductivity
Thermal conductance
Measure for the ease with which a material
resists conduction of heat
Measure for the ease with which an object
resists conduction of heat
Measure for the ease with which a material
conducts heat
Measure for the ease with which an object
conducts heat
513
K⋅m/W
K/W
W/(m⋅K)
W/K
Derived quantity
Temperature gradient
Surface tension
Description
steepest rate of temperature change at a
particular location
Energy change per unit change in surface
area
SI derived unit
K/m
N/m or J/m2
Stress
Force per unit oriented surface area
Pa
Strain
Extension per unit length
unitless
Spin
Quantum-mechanically defined angular
momentum of a particle
kg⋅m2⋅s−1
Specific volume
Volume per unit mass (reciprocal of density)
m3⋅kg−1
Specific heat capacity
Heat capacity per unit mass
J/(K⋅kg)
Specific energy
Energy density per unit mass
J⋅kg−1
Solid angle
Reluctance
Refractive index
Reaction rate
Radiant intensity
Radiance
Ratio of area on a sphere to its radius
squared
resistance to the flow of magnetic flux
Factor by which the phase velocity of light is
reduced in a medium
Rate of a chemical reaction for unit time
Power of emitted electromagnetic radiation
per unit solid angle
Power of emitted electromagnetic radiation
514
steradian (sr)
H−1
unitless
mol/(m3⋅s)
W/sr
W/(m2⋅sr)
Derived quantity
Description
SI derived unit
per unit solid angle per emitting source area
Pressure
Force per unit area
pascal (Pa = N/m2)
Power
Rate of transfer of energy per unit time
watt (W)
Pop
Plane angle
Rate of change of crackle per unit time: the
sixth time derivative of position
Ratio of circular arc length to radius
m/s6
radian (rad)
Measure for how the polarization of a
Permittivity
material is affected by the application of an
F/m
external electric field
Measure for how the magnetization of
Permeability
material is affected by the application of an
H/m
external magnetic field
Optical power
Momentum
Moment of inertia
Molar heat capacity
Measure of the effective curvature of a lens
or curved mirror; inverse of focal length
Product of an object's mass and velocity
Inertia of an object with respect to angular
acceleration
Heat capacity of a material per unit amount
of substance
dioptre (dpt = m−1)
kg⋅m/s
kg⋅m2
J/(K⋅mol)
Molar entropy
Entropy per unit amount of substance
J/(K⋅mol)
Molar energy
Amount of energy present in a system per
J/mol
515
Derived quantity
Description
SI derived unit
unit amount of substance
Molar concentration
Mean lifetime
Mass fraction
Magnetization
Magnetic flux density
Magnetic flux
Magnetic field strength
Mach number (or mach)
Luminous
flux (or luminous power)
Linear density
Jounce (or snap)
Jerk
Amount of substance per unit volume
Average time for a particle of a substance to
decay
Mass of a substance as a fraction of the total
mass
Amount of magnetic moment per unit
volume
Measure for the strength of the magnetic
field
Measure of magnetism, taking account of the
strength and the extent of a magnetic field
Strength of a magnetic field
Ratio of flow velocity to the local speed of
sound
mol⋅m−3
s
kg/kg
A/m
tesla (T = Wb/m2)
weber (Wb)
A/m
unitless
Perceived power of a light source
lumen (lm = cd⋅sr)
Mass per unit length
kg⋅m−1
Change of jerk per unit time: the fourth time
derivative of position
Change of acceleration per unit time: the
516
m/s4
m/s3
Derived quantity
Description
SI derived unit
third time derivative of position
Irradiance
Intensity
Inductance
Impulse
Impedance
Electromagnetic radiation power per unit
surface area
Power per unit cross sectional area
Magnetic flux generated per unit current
through a circuit
Transferred momentum
Resistance to an alternating current of a
given frequency, including effect on phase
W/m2
W/m2
henry (H)
newton-second (N⋅s = kg⋅m/s)
ohm (Ω)
Illuminance
Luminous flux per unit surface area
lux (lx = cd⋅sr/m2)
Heat flux density
Heat flow per unit time per unit surface area
W/m2
Heat capacity
Energy per unit temperature change
J/K
Heat
Thermal energy
joule (J)
Half-life
Frequency
Force
Entropy
Time for a quantity to decay to half its initial
value
Number of (periodic) occurrences per unit
time
Transfer of momentum per unit time
Logarithmic measure of the number of
available states of a system
517
s
hertz (Hz = s−1)
newton (N = kg⋅m⋅s−2)
J/K
Derived quantity
Description
SI derived unit
Energy density
Energy per unit volume
J⋅m−3
Energy
Energy
J
Electrical resistivity
Electrical resistance
Electrical conductivity
Electrical conductance
Bulk property equivalent of electrical
resistance
Electric potential per unit electric current
Measure of a material's ability to conduct an
electric current
Measure for how easily current flows
through a material
ohm-metre (Ω⋅m)
ohm (Ω = V/A)
S/m
siemens (S = Ω−1)
Energy required to move a unit charge
Electric potential
through an electric field from a reference
volt (V = J/C)
point
Electric field strength
Strength of the electric field
V/m
Electric displacement field
Strength of the electric displacement
C/m2
Electric charge density
Electric charge per unit volume
C/m3
Electric charge
The force per unit electric field strength
coulomb (C = A⋅s)
Dynamic viscosity
Dose equivalent
Measure for the resistance of an
incompressible fluid to stress
Received radiation adjusted for the effect on
biological tissue
518
Pa⋅s
sievert (Sv = m2/s2)
Derived quantity
Description
SI derived unit
Current density
Electric current per unit cross-section area
A/m2
Crackle
Chemical potential
Change of jounce per unit time: the fifth time
derivative of position
Energy per unit change in amount of
substance
m/s5
J/mol
Inertial force that appears to act on all
Centrifugal force
objects when viewed in a rotating frame of
N⋅rad = kg⋅m⋅rad⋅s−2
reference
Catalytic activity
Change in reaction rate due to presence of
concentration
a catalyst per unit volume of the system
Capacitance
Stored charge per unit electric potential
farad (F = C/V)
Area density
Mass per unit area
kg⋅m−2
Area
Extent of a surface
m2
kat⋅m−3
The angle incremented in a plane by a
Angular velocity
segment connecting an object and a
rad/s
reference point per unit time
Angular momentum
Angular acceleration
Acceleration
Measure of the extent and direction of an
object rotates about a reference point
Change in angular velocity per unit time
Rate of change of velocity per unit time: the
second time derivative of position
519
kg⋅m2/s
rad/s2
m/s2
Derived quantity
Description
SI derived unit
Absorbed dose rate
Absorbed dose received per unit of time
Gy/s
Measure of sustained displacement: the first
Absement
Ionizing radiation energy absorbed by
(Radioactive) Dose
biological tissue per unit mass
(Radioactive) Activity
(Mass) Density (or volume
density)
m⋅s
integral with respect to time of displacement
gray (Gy = m2/s2)
Number of particles decaying per unit time
becquerel (Bq = Hz)
Mass per unit volume
kg/m3
The Earth spins at 1,000 mph but it travels through space at an incredible 67,000 mph.
Every year over one million earthquakes shake the Earth.
The dinosaurs (a diverse group of reptiles of the clade Dinosauria) became
extinct before the Rockies or the Alps were formed.
The first synthetic human chromosome was constructed by US scientists in 1997.
There are 60,000 miles of blood vessels in the human body.
520
If the Sun were the size of a beach ball then Jupiter would be the size of a
golf ball and the Earth would be as small as a pea.
List of Nobel laureates in Physics
1901
Wilhelm Röntgen
"in recognition of the extraordinary services he has
rendered by the discovery of the
remarkable rays subsequently named after him"
1902
Hendrik Lorentz
"in recognition of the extraordinary service they
rendered by their researches into the influence
Pieter Zeeman
1903
of magnetism upon radiation phenomena"
Antoine Henri Becquerel
"for his discovery of spontaneous radioactivity"
Pierre Curie
"for their joint researches on
the radiation phenomena discovered by
1904
Marie Skłodowska-Curie
Professor Henri Becquerel"
Lord Rayleigh
"for his investigations of the densities of the most
important gases and for his discovery of argon in
connection with these studies"
1905
Philipp Eduard Anton von
"for his work on cathode rays"
Lenard
1906
Joseph John Thomson
"for his theoretical and experimental investigations
on the conduction of electricity by gases"
1907
Albert Abraham Michelson
"for his optical precision instruments and
the spectroscopic and metrological investigations
521
carried out with their aid"
1908
Gabriel Lippmann
"for his method of reproducing colours
photographically based on the phenomenon
of interference"
1909
Guglielmo Marconi
"for their contributions to the development of
wireless telegraphy"
Karl Ferdinand Braun
1910
1911
Johannes Diderik van der
"for his work on the equation of state for gases and
Waals
liquids"
Wilhelm Wien
"for his discoveries regarding the laws governing the
radiation of heat"
1912
Nils Gustaf Dalén
"for his invention of automatic valves designed to be
used in combination with gas accumulators
in lighthouses and buoys"
1913
Heike Kamerlingh-Onnes
"for his investigations on the properties of matter at
low temperatures which led, inter alia, to the
production of liquid helium"
1914
Max von Laue
"For his discovery of the diffraction of X-rays by
crystals", an important step in the development of Xray spectroscopy.
1915
William Henry Bragg
"'For their services in the analysis of crystal
structure by means of X-rays', an important step in
William Lawrence Bragg
the development of X-ray crystallography"
522
Not awarded due to World War I
1916
1917
Charles Glover Barkla
"'For his discovery of the characteristic Röntgen
radiation of the elements', another important step in the
development of X-ray spectroscopy"
1918
Max Planck
"for the services he rendered to the advancement of
physics by his discovery of energy quanta"
1919
Johannes Stark
"for his discovery of the Doppler effect in canal rays and
the splitting of spectral lines in electric fields"
1920
Charles Édouard
"for the service he has rendered to precision
Guillaume
measurements in physics by his discovery of anomalies
in nickel-steel alloys"
1921
Albert Einstein
"for his services to theoretical physics, and especially for
his discovery of the law of the photoelectric effect"
1922
Niels Bohr
"for his services in the investigation of the structure
of atoms and of the radiation emanating from them"
1923
1924
Robert Andrews
"for his work on the elementary charge of electricity and
Millikan
on the photoelectric effect"
Manne Siegbahn
"for his discoveries and research in the field of X-ray
spectroscopy"
1925
James Franck
"for their discovery of the laws governing the impact of
523
an electron upon an atom"
Gustav Hertz
1926
Jean Baptiste Perrin
"for his work on the discontinuous structure of matter,
and especially for his discovery of sedimentation
equilibrium"
1927
1928
1929
Arthur Holly Compton
"for his discovery of the effect named after him"
Charles Thomson Rees
"for his method of making the paths of electrically
Wilson
charged particles visible by condensation of vapour"
Owen Willans
"for his work on the thermionic phenomenon and
Richardson
especially for the discovery of the law named after him"
Louis Victor Pierre
"for his discovery of the wave nature of electrons"
Raymond, 7th Duc de
Broglie
1930
Chandrasekhara
"for his work on the scattering of light and for the
Venkata Raman
discovery of the effect named after him"
1931
1932
Not awarded
Werner Heisenberg
"for the creation of quantum mechanics, the application
of which has, inter alia, led to the discovery of
the allotropic forms of hydrogen"
1933
Erwin Schrödinger
"for the discovery of new productive forms of atomic
theory"
Paul Dirac
524
Not awarded
1934
1935
James Chadwick
"for the discovery of the neutron"
1936
Victor Francis Hess
"for his discovery of cosmic radiation"
Carl David Anderson
"for his discovery of the positron"
Clinton Joseph
"for their experimental discovery of the diffraction of
Davisson
electrons by crystals"
1937
George Paget Thomson
1938
Enrico Fermi
"for his demonstrations of the existence of new
radioactive elements produced by neutron irradiation,
and for his related discovery of nuclear reactions
brought about by slow neutrons"
1939
Ernest Lawrence
"for the invention and development of the cyclotron and
for results obtained with it, especially with regard to
artificial radioactive elements"
1940
Not awarded due to World War II
1941
1942
1943
Otto Stern
"for his contribution to the development of the molecular
ray method and his discovery of the magnetic moment of
525
the proton"
1944
Isidor Isaac Rabi
"for his resonance method for recording the magnetic
properties of atomic nuclei"
1945
Wolfgang Pauli
"for the discovery of the Exclusion Principle, also called
the Pauli principle"
1946
Percy Williams
"for the invention of an apparatus to produce extremely
Bridgman
high pressures, and for the discoveries he made there
within the field of high pressure physics"
1947
Edward Victor
"for his investigations of the physics of the upper
Appleton
atmosphere especially for the discovery of the socalled Appleton layer"
1948
Patrick Maynard Stuart
"for his development of the Wilson cloud
Blackett
chamber method, and his discoveries therewith in the
fields of nuclear physics and cosmic radiation"
1949
Hideki Yukawa
"for his prediction of the existence of mesons on the
basis of theoretical work on nuclear forces"
1950
Cecil Frank Powell
"for his development of the photographic method of
studying nuclear processes and his discoveries
regarding mesons made with this method"
1951
John Douglas
"for their pioneer work on the transmutation of atomic
Cockcroft
nuclei by artificially accelerated atomic particles"
Ernest Thomas Sinton
526
Walton
1952
Felix Bloch
"for their development of new methods for nuclear
magnetic precision measurements and discoveries in
connection therewith"
Edward Mills Purcell
1953
Frits Zernike
"for his demonstration of the phase contrast method,
especially for his invention of the phase contrast
microscope"
1954
Max Born
"for his fundamental research in quantum mechanics,
especially for his statistical interpretation of
the wavefunction"
Walther Bothe
"for the coincidence method and his discoveries made
therewith"
1955
Willis Eugene Lamb
"for his discoveries concerning the fine structure of the
hydrogen spectrum"
Polykarp Kusch
"for his precision determination of the magnetic
moment of the electron"
1956
John Bardeen
"for their researches on semiconductors and their
discovery of the transistor effect"
Walter Houser Brattain
William Bradford
Shockley
527
1957
Tsung-Dao Lee
"for their penetrating investigation of the so-called parity
laws which has led to important discoveries regarding
the elementary particles"
Chen-Ning Yang
1958
Pavel Alekseyevich
"for the discovery and the interpretation of
Cherenkov
the Cherenkov effect"
Ilya Frank
Igor Yevgenyevich
Tamm
1959
Emilio Gino Segrè
"for their discovery of the antiproton"
Owen Chamberlain
1960
Donald Arthur Glaser
"for the invention of the bubble chamber"
1961
Robert Hofstadter
"for his pioneering studies of electron scattering in
atomic nuclei and for his thereby achieved discoveries
concerning the structure of the nucleons"
Rudolf Ludwig
"for his researches concerning the resonance absorption
Mössbauer
of gamma radiation and his discovery in this connection
of the effect which bears his name"
1962
Lev Davidovich Landau
"for his pioneering theories for condensed matter,
especially liquid helium"
1963
Eugene Paul Wigner
"for his contributions to the theory of the atomic
528
nucleus and the elementary particles, particularly
through the discovery and application of
fundamental symmetry principles"
Maria Goeppert-Mayer
"for their discoveries concerning nuclear shell structure"
J. Hans D. Jensen
1964
Nicolay Gennadiyevich
"for fundamental work in the field of quantum
Basov
electronics, which has led to the construction
of oscillators and amplifiers based on the maser–
laser principle"
Alexander Prokhorov
Charles Hard Townes
1965
Richard Phillips
"for their fundamental work in quantum
Feynman
electrodynamics (QED), with deep-ploughing
consequences for the physics of elementary particles"
Julian Schwinger
Shin'ichirō Tomonaga
1966
Alfred Kastler
"for the discovery and development of optical methods
for studying Hertzian resonances in atoms"
1967
Hans Albrecht Bethe
"for his contributions to the theory of nuclear reactions,
especially his discoveries concerning the energy
production in stars"
1968
Luis Walter Alvarez
"for his decisive contributions to elementary particle
physics, in particular the discovery of a large number
529
of resonance states, made possible through his
development of the technique of using hydrogen bubble
chamber and data analysis"
1969
Murray Gell-Mann
"for his contributions and discoveries concerning the
classification of elementary particles and their
interactions"
1970
Hannes Olof Gösta
"for fundamental work and discoveries in magneto-
Alfvén
hydrodynamics with fruitful applications in different
parts of plasma physics"
Louis Néel
"for fundamental work and discoveries
concerning antiferromagnetism and ferrimagnetism whic
h have led to important applications in solid state
physics"
1971
Dennis Gabor
"for his invention and development of the holographic
method"
1972
John Bardeen
"for their jointly developed theory of superconductivity,
usually called the BCS-theory"
Leon Neil Cooper
John Robert Schrieffer
1973
Leo Esaki
"for their experimental discoveries regarding tunneling
phenomena in semiconductors and superconductors,
respectively"
Ivar Giaever
Brian David Josephson
"for his theoretical predictions of the properties of
530
a supercurrent through a tunnel barrier, in particular
those phenomena which are generally known as
the Josephson effect"
1974
Martin Ryle
"for their pioneering research in radio astrophysics: Ryle
for his observations and inventions, in particular of
Antony Hewish
the aperture synthesis technique, and Hewish for his
decisive role in the discovery of pulsars"
1975
Aage Bohr
"for the discovery of the connection between collective
motion and particle motion in atomic nuclei and the
Ben Roy Mottelson
development of the theory of the structure of the atomic
nucleus based on this connection"
Leo James Rainwater
1976
Samuel Chao Chung
"for their pioneering work in the discovery of a heavy
Ting
elementary particle of a new kind"
Burton Richter
1977
Philip Warren
"for their fundamental theoretical investigations of the
Anderson
electronic structure of magnetic and disordered
systems"
Nevill Francis Mott
John Hasbrouck Van
Vleck
1978
Pyotr Leonidovich
"for his basic inventions and discoveries in the area
Kapitsa
of low-temperature physics"
531
Arno Allan Penzias
"for their discovery of cosmic microwave background
radiation"
Robert Woodrow
Wilson
1979
Sheldon Lee Glashow
"for their contributions to the theory of the unified weak
and electromagnetic interaction between elementary
Abdus Salam
particles, including, inter alia, the prediction of the weak
neutral current"
Steven Weinberg
1980
James Watson Cronin
"for the discovery of violations of fundamental symmetry
principles in the decay of neutral K-mesons"
Val Logsdon Fitch
1981
Nicolaas Bloembergen
"for their contribution to the development of laser
spectroscopy"
Arthur Leonard
Schawlow
1982
Kai Manne Börje
"for his contribution to the development of high-
Siegbahn
resolution electron spectroscopy"
Kenneth G. Wilson
"for his theory for critical phenomena in connection
with phase transitions"
1983
Subrahmanyan
"for his theoretical studies of the physical processes of
Chandrasekhar
importance to the structure and evolution of the stars"
532
William Alfred Fowler
"for his theoretical and experimental studies of
the nuclear reactions of importance in the formation of
the chemical elements in the universe"
1984
Carlo Rubbia
"for their decisive contributions to the large project,
which led to the discovery of the field particles W and Z,
Simon van der Meer
communicators of weak interaction"
1985
Klaus von Klitzing
"for the discovery of the quantized Hall effect"
1986
Ernst Ruska
"for his fundamental work in electron optics, and for the
design of the first electron microscope"
Gerd Binnig
"for their design of the scanning tunneling microscope"
Heinrich Rohrer
1987
Johannes Georg
"for their important break-through in the discovery
Bednorz
of superconductivity in ceramic materials"
Karl Alexander Müller
1988
Leon Max Lederman
"for the neutrino beam method and the demonstration
of the doublet structure of the leptons through the
Melvin Schwartz
discovery of the muon neutrino"
Jack Steinberger
1989
Norman Foster Ramsey
"for the invention of the separated oscillatory
fields method and its use in the hydrogen maser and
533
other atomic clocks"
Hans Georg Dehmelt
"for the development of the ion trap technique"
Wolfgang Paul
1990
Jerome I. Friedman
"for their pioneering investigations concerning deep
inelastic scattering of electrons on protons and bound
Henry Way Kendall
neutrons, which have been of essential importance for
the development of the quark model in particle physics"
Richard E. Taylor
1991
Pierre-Gilles de Gennes
"for discovering that methods developed for studying
order phenomena in simple systems can be generalized
to more complex forms of matter, in particular to liquid
crystals and polymers"
1992
Georges Charpak
"for his invention and development of particle detectors,
in particular the multiwire proportional chamber"
1993
Russell Alan Hulse
"for the discovery of a new type of pulsar, a discovery
that has opened up new possibilities for the study
of gravitation"
Joseph Hooton Taylor
Jr.
1994
Bertram Brockhouse
"for the development of neutron spectroscopy" and "for
pioneering contributions to the development of neutron
scattering techniques for studies of condensed matter"
Clifford Glenwood
"for the development of the neutron
diffraction technique" and "for pioneering contributions
534
Shull
to the development of neutron scattering techniques for
studies of condensed matter"
1995
Martin Lewis Perl
"for the discovery of the tau lepton" and "for pioneering
experimental contributions to lepton physics"
Frederick Reines
"for the detection of the neutrino" and "for pioneering
experimental contributions to lepton physics"
1996
David Morris Lee
"for their discovery of superfluidity in helium-3"
Douglas D. Osheroff
Robert Coleman
Richardson
1997
Steven Chu
"for development of methods to cool and trap atoms with
laser light."
Claude CohenTannoudji
William Daniel Phillips
1998
Robert B. Laughlin
"for their discovery of a new form of quantum fluid with
fractionally charged excitations"
Horst Ludwig Störmer
Daniel Chee Tsui
1999
Gerard 't Hooft
"for elucidating the quantum structure of electroweak
535
interactions in physics"
Martinus J. G. Veltman
2000
Zhores Ivanovich
"for developing semiconductor heterostructures used in
Alferov
high-speed- and optoelectronics"
Herbert Kroemer
2001
Jack St. Clair Kilby
"for his part in the invention of the integrated circuit"
Eric Allin Cornell
"for the achievement of Bose–Einstein condensation in
dilute gases of alkali atoms, and for early fundamental
Carl Edwin Wieman
studies of the properties of the condensates"
Wolfgang Ketterle
2002
Raymond Davis Jr.
"for pioneering contributions to astrophysics, in
particular for the detection of cosmic neutrinos"
Masatoshi Koshiba
Riccardo Giacconi
"for pioneering contributions to astrophysics, which
have led to the discovery of cosmic X-ray sources"
2003
Alexei Alexeyevich
"for pioneering contributions to the theory
Abrikosov
of superconductors and superfluids"
Vitaly Lazarevich
Ginzburg
Anthony James
536
Leggett
2004
David J. Gross
"for the discovery of asymptotic freedom in the theory of
the strong interaction"
Hugh David Politzer
Frank Wilczek
2005
Roy J. Glauber
"for his contribution to the quantum theory of optical
coherence"
John L. Hall
"for their contributions to the development of laserbased precision spectroscopy, including the optical
frequency comb technique"
Theodor W. Hänsch
2006
John C. Mather
"for their discovery of the blackbody
form and anisotropy of the cosmic microwave
background radiation"
George F. Smoot
2007
Albert Fert
"for the discovery of giant magnetoresistance"
Peter Grünberg
2008
Makoto Kobayashi
"for the discovery of the origin of the broken
symmetry which predicts the existence of at least three
families of quarks in nature"
Toshihide Maskawa
Yoichiro Nambu
"for the discovery of the mechanism of spontaneous
broken symmetry in subatomic physics"
537
2009
Charles K. Kao
"for groundbreaking achievements concerning the
transmission of light in fibers for optical
communication"
Willard S. Boyle
"for the invention of an imaging semiconductor circuit –
the CCD sensor"
George E. Smith
2010
Andre Geim
"for groundbreaking experiments regarding the twodimensional material graphene"
Konstantin Novoselov
2011
Saul Perlmutter
"for the discovery of the accelerating expansion of the
Universe through observations of distant supernovae"
Brian P. Schmidt
Adam G. Riess
2012
Serge Haroche
"for ground-breaking experimental methods that enable
measuring and manipulation of
individual quantum systems."
David J. Wineland
2013
François Englert
"for the theoretical discovery of a mechanism that
contributes to our understanding of the origin of mass
Peter Higgs
of subatomic particles, and which recently was
confirmed through the discovery of the predicted
fundamental particle, by
the ATLAS and CMS experiments at CERN's Large
Hadron Collider"
538
2014
Isamu Akasaki
"for the invention of efficient blue light-emitting
diodes which has enabled bright and energy-saving
white light sources"
Hiroshi Amano
Shuji Nakamura
2015
Takaaki Kajita
"for the discovery of neutrino oscillations, which shows
that neutrinos have mass"
Arthur B. McDonald
2016
David J. Thouless
"for theoretical discoveries of topological phase
transitions and topological phases of matter"
F. Duncan M. Haldane
John M. Kosterlitz
2017
Rainer Weiss
"for decisive contributions to the LIGO detector and the
observation of gravitational waves"
Kip Thorne
Barry Barish
2018
Arthur Ashkin
"for groundbreaking inventions in the field of laser
physics", in particular "for the optical tweezers and their
application to biological systems"
Gérard Mourou
"for groundbreaking inventions in the field of laser
physics", in particular "for their method of generating
Donna Strickland
high-intensity, ultra-short optical pulses"
539
2019
James Peebles
"for theoretical discoveries in physical cosmology"
Michel Mayor
"for the discovery of an exoplanet orbiting a solar-type
star"
Didier Queloz
2020
Roger Penrose
"for the discovery that black hole formation is a robust
prediction of the general theory of relativity"
Reinhard Genzel
"for the discovery of a supermassive compact object at
the centre of our galaxy"
Andrea Ghez
Each rubber molecule is made of 65,000 individual atoms.
Around a million, billion neutrinos from the Sun will pass through our body every day.
Quasars are the most distant objects in the Universe which emit more
energy than 100 giant galaxies.
540
List of Nobel laureates in Chemistry
Jacobus Henricus van 't
"[for his] discovery of the laws of chemical
Hoff
dynamics and osmotic pressure in solutions"
1902
Hermann Emil Fischer
"[for] his work on sugar and purine syntheses"
1903
Svante August Arrhenius
"[for] his electrolytic theory of dissociation"
1904
Sir William Ramsay
"[for his] discovery of the inert gaseous elements in
1901
air, and his determination of their place in the
periodic system"
1905
Adolf von Baeyer
"[for] the advancement of organic chemistry and
the chemical industry, through his work
on organic dyes and hydroaromatic compounds"
1906
Henri Moissan
"[for his] investigation and isolation of the
element fluorine, and for [the] electric
furnace called after him"
1907
Eduard Buchner
"for his biochemical researches and his discovery
of cell-free fermentation"
1908
Ernest Rutherford
"for his investigations into the disintegration of the
elements, and the chemistry of radioactive
substances"
1909
Wilhelm Ostwald
"[for] his work on catalysis and for his
investigations into the fundamental principles
541
governing chemical equilibria and rates of
reaction"
1910
Otto Wallach
"[for] his services to organic chemistry and the
chemical industry by his pioneer work in the field
of alicyclic compounds"
1911
Maria Skłodowska-Curie
"[for] the discovery of the
elements radium and polonium, by the isolation of
radium and the study of the nature and
compounds of this remarkable element"
1912
Victor Grignard
"for the discovery of the [...] Grignard reagent"
Paul Sabatier
"for his method of hydrogenating organic
compounds in the presence of finely disintegrated
metals"
1913
Alfred Werner
"[for] his work on the linkage of atoms in
molecules [...] especially in inorganic chemistry"
1914
1915
Theodore William
"[for] his accurate determinations of the atomic
Richards
weight of a large number of chemical elements"
Richard Martin
"for his researches on plant pigments,
Willstätter
especially chlorophyll"
1916
Not awarded
1917
542
1918
Fritz Haber
"for the synthesis of ammonia from its elements"
Not awarded
1919
1920
Walther Hermann Nernst
"[for] his work in thermochemistry"
1921
Frederick Soddy
"for his contributions to our knowledge of the
chemistry of radioactive substances, and his
investigations into the origin and nature
of isotopes"
1922
Francis William Aston
"for his discovery, by means of his mass
spectrograph, of isotopes, in a large number of
non-radioactive elements, and for his enunciation
of the whole-number rule"
1923
Fritz Pregl
"for his invention of the method of microanalysis of organic substances"
Not awarded
1924
1925
Richard Adolf Zsigmondy
"for his demonstration of the heterogeneous
nature of colloid solutions and for the methods he
used"
1926
The (Theodor) Svedberg
"for his work on disperse systems"
1927
Heinrich Otto Wieland
"for his investigations of the constitution of
the bile acids and related substances"
543
1928
1929
Adolf Otto Reinhold
"[for] his research into the constitution of
Windaus
the sterols and their connection with the vitamins"
Arthur Harden
"for their investigations on the fermentation of
sugar and fermentative enzymes"
Hans Karl August Simon
von Euler-Chelpin
1930
Hans Fischer
"for his researches into the constitution
of haemin and chlorophyll and especially for his
synthesis of haemin"
1931
Carl Bosch
"[for] their contributions to the invention and
development of chemical high pressure methods"
Friedrich Bergius
1932
Irving Langmuir
"for his discoveries and investigations in surface
chemistry"
Not awarded
1933
1934
Harold Clayton Urey
"for his discovery of heavy hydrogen"
1935
Frédéric Joliot
"[for] their synthesis of new radioactive elements"
Irène Joliot-Curie
1936
Peter Debye
"[for his work on] molecular structure through his
investigations on dipole moments and
544
the diffraction of X-rays and electrons in gases"
1937
Walter Norman Haworth
"for his investigations on carbohydrates
and vitamin C"
Paul Karrer
"for his investigations on carotenoids, flavins and
vitamins A and B2"
1938
Richard Kuhn
"for his work on carotenoids and vitamins"
1939
Adolf Friedrich Johann
"for his work on sex hormones"
Butenandt
Leopold Ruzicka
"for his work on polymethylenes and
higher terpenes"
1940
Not awarded
1941
1942
1943
George de Hevesy
"for his work on the use of isotopes as tracers in
the study of chemical processes"
1944
Otto Hahn
"for his discovery of the fission of heavy nuclei"
1945
Artturi Ilmari Virtanen
"for his research and inventions in agricultural
and nutrition chemistry, especially for his fodder
545
preservation method"
1946
James Batcheller
"for his discovery that enzymes can be
Sumner
crystallized"
John Howard Northrop
"for their preparation of enzymes and virus
proteins in a pure form"
Wendell Meredith
Stanley
1947
Sir Robert Robinson
"for his investigations on plant products of
biological importance, especially the alkaloids"
1948
Arne Wilhelm Kaurin
"for his research on electrophoresis and
Tiselius
adsorption analysis, especially for his discoveries
concerning the complex nature of the serum
proteins"
1949
William Francis Giauque
"for his contributions in the field of chemical
thermodynamics, particularly concerning the
behaviour of substances at extremely low
temperatures"
1950
Otto Paul Hermann Diels
"for their discovery and development of the diene
synthesis"
Kurt Alder
1951
Edwin Mattison
"for their discoveries in the chemistry
McMillan
of transuranium elements"
546
Glenn Theodore Seaborg
1952
Archer John Porter
"for their invention of partition chromatography"
Martin
Richard Laurence
Millington Synge
1953
Hermann Staudinger
"for his discoveries in the field of macromolecular
chemistry"
1954
Linus Pauling
"for his research into the nature of the chemical
bond and its application to the elucidation of the
structure of complex substances"
1955
Vincent du Vigneaud
"for his work on biochemically important sulphur
compounds, especially for the first synthesis of a
polypeptide hormone"
1956
Sir Cyril Norman
"for their researches into the mechanism of
Hinshelwood
chemical reactions"
Nikolay Nikolaevich
Semenov
1957
Lord (Alexander R.) Todd
"for his work on nucleotides and nucleotide coenzymes"
1958
Frederick Sanger
"for his work on the structure of proteins,
547
especially that of insulin"
1959
Jaroslav Heyrovský
"for his discovery and development of
the polarographic methods of analysis"
1960
Willard Frank Libby
"for his method to use carbon-14 for age
determination in archaeology, geology, geophysics,
and other branches of science"
1961
Melvin Calvin
"for his research on the carbon dioxide
assimilation in plants"
1962
Max Ferdinand Perutz
"for their studies of the structures of globular
proteins"
John Cowdery Kendrew
1963
Karl Ziegler
"for their discoveries in the field of the chemistry
and technology of high polymers"
Giulio Natta
1964
1965
Dorothy Crowfoot
"for her determinations by X-ray techniques of the
Hodgkin
structures of important biochemical substances"
Robert Burns Woodward
"for his outstanding achievements in the art of
organic synthesis"
1966
Robert S. Mulliken
"for his fundamental work concerning chemical
bonds and the electronic structure of molecules by
the molecular orbital method"
548
1967
Manfred Eigen
"for their studies of extremely fast chemical
reactions, effected by disturbing the equilibrium
Ronald George Wreyford
by means of very short pulses of energy"
Norrish
George Porter
1968
Lars Onsager
"for the discovery of the reciprocal
relations bearing his name, which are
fundamental for the thermodynamics of
irreversible processes"
1969
Derek H. R. Barton
"for their contributions to the development of the
concept of conformation and its application in
1970
Odd Hassel
chemistry"
Luis F. Leloir
"for his discovery of sugar nucleotides and their
role in the biosynthesis of carbohydrates"
1971
Gerhard Herzberg
"for his contributions to the knowledge of
electronic structure and geometry of molecules,
particularly free radicals"
1972
Christian B. Anfinsen
"for his work on ribonuclease, especially
concerning the connection between the amino acid
sequence and the biologically active conformation"
Stanford Moore
"for their contribution to the understanding of the
549
connection between chemical structure and
William H. Stein
catalytic activity of the active centre of
the ribonuclease molecule"
1973
Ernst Otto Fischer
"for their pioneering work, performed
independently, on the chemistry of
Geoffrey Wilkinson
the organometallic, so called sandwich
compounds"
1974
Paul J. Flory
"for his fundamental work, both theoretical and
experimental, in the physical chemistry
of macromolecules"
1975
John Warcup Cornforth
"for his work on the stereochemistry of enzymecatalyzed reactions"
Vladimir Prelog
"for his research into the stereochemistry of
organic molecules and reactions"
1976
William N. Lipscomb
"for his studies on the structure
of boranes illuminating problems of chemical
bonding"
1977
Ilya Prigogine
"for his contributions to non-equilibrium
thermodynamics, particularly the theory
of dissipative structures"
1978
Peter D. Mitchell
"for his contribution to the understanding of
biological energy transfer through the formulation
of the chemiosmotic theory"
550
1979
Herbert C. Brown
"for their development of the use of boron- and
phosphorus-containing compounds, respectively,
1980
Georg Wittig
into important reagents in organic synthesis"
Paul Berg
"for his fundamental studies of the biochemistry of
nucleic acids, with particular regard
to recombinant-DNA"
Walter Gilbert
"for their contributions concerning
the determination of base sequences in nucleic
1981
Frederick Sanger
acids"
Kenichi Fukui
"for their theories, developed independently,
concerning the course of chemical reactions"
Roald Hoffmann
1982
Aaron Klug
"for his development of crystallographic electron
microscopy and his structural elucidation of
biologically important nucleic acid-protein
complexes"
1983
Henry Taube
"for his work on the mechanisms of electron
transfer reactions, especially in metal complexes"
1984
Robert Bruce Merrifield
"for his development of methodology for chemical
synthesis on a solid matrix"
1985
Herbert A. Hauptman
"for their outstanding achievements in
551
developing direct methods for the determination of
Jerome Karle
1986
Dudley R. Herschbach
crystal structures"
"for their contributions concerning the dynamics
of chemical elementary processes"
Yuan T. Lee
John C. Polanyi
1987
Donald J. Cram
"for their development and use of molecules
with structure-specific interactions of high
selectivity"
Jean-Marie Lehn
Charles J. Pedersen
1988
Johann Deisenhofer
"for their determination of the three-dimensional
structure of a photosynthetic reaction centre"
Robert Huber
Hartmut Michel
1989
Sidney Altman
"for their discovery of catalytic properties of RNA"
Thomas Cech
1990
Elias James Corey
"for his development of the theory and
methodology of organic synthesis"
1991
Richard R. Ernst
"for his contributions to the development of the
552
methodology of high resolution nuclear magnetic
resonance (NMR) spectroscopy"
1992
Rudolph A. Marcus
"for his contributions to the theory of electron
transfer reactions in chemical systems"
1993
Kary B. Mullis
"for contributions to the developments of methods
within DNA-based chemistry [...] for his invention
of the polymerase chain reaction (PCR) method"
Michael Smith
"for contributions to the developments of methods
within DNA-based chemistry [...] for his
fundamental contributions to the establishment of
oligonucleotide-based, site-directed
mutagenesis and its development for protein
studies"
1994
George A. Olah
"for his contribution to carbocation chemistry"
1995
Paul J. Crutzen
"for their work in atmospheric chemistry,
particularly concerning the formation
and decomposition of ozone"
Mario J. Molina
F. Sherwood Rowland
1996
Robert F. Curl Jr.
"for their discovery of fullerenes"
Sir Harold W. Kroto
Richard E. Smalley
553
1997
Paul D. Boyer
"for their elucidation of the enzymatic
mechanism underlying the synthesis of adenosine
John E. Walker
triphosphate (ATP)"
Jens C. Skou
"for the first discovery of an ion-transporting
enzyme, Na+, K+ -ATPase"
1998
Walter Kohn
"for his development of the density-functional
theory"
John A. Pople
"for his development of computational methods in
quantum chemistry"
1999
Ahmed Zewail
"for his studies of the transition states of chemical
reactions using femtosecond spectroscopy"
2000
Alan J. Heeger
"for their discovery and development of conductive
polymers"
Alan G. MacDiarmid
Hideki Shirakawa
2001
William S. Knowles
"for their work on chirally catalysed hydrogenation
reactions"
Ryōji Noyori
K. Barry Sharpless
"for his work on chirally catalysed oxidation
reactions"
554
2002
John B. Fenn
"for the development of methods for identification
and structure analyses of biological
Koichi Tanaka
macromolecules [...] for their development of soft
desorption ionisation methods for mass
spectrometric analyses of biological
macromolecules"
Kurt Wüthrich
"for the development of methods for identification
and structure analyses of biological
macromolecules [...] for his development
of nuclear magnetic resonance spectroscopy for
determining the three-dimensional structure of
biological macromolecules in solution"
2003
Peter Agre
"for discoveries concerning channels in cell
membranes [...] for the discovery of water
channels"
Roderick MacKinnon
"for discoveries concerning channels in cell
membranes [...] for structural and
mechanistic studies of ion channels"
2004
Aaron Ciechanover
"for the discovery of ubiquitin-mediated protein
degradation"
Avram Hershko
Irwin Rose
2005
Yves Chauvin
"for the development of the metathesis method in
555
organic synthesis"
Robert H. Grubbs
Richard R. Schrock
2006
Roger D. Kornberg
"for his studies of the molecular basis
of eukaryotic transcription"
2007
Gerhard Ertl
"for his studies of chemical processes on solid
surfaces"
2008
Osamu Shimomura
"for the discovery and development of the green
fluorescent protein, GFP"
Martin Chalfie
Roger Y. Tsien
2009
Venkatraman
"for studies of the structure and function of
Ramakrishnan
the ribosome"
Thomas A. Steitz
Ada E. Yonath
2010
Richard F. Heck
"for palladium-catalyzed cross couplings in
organic synthesis"
Ei-ichi Negishi
Akira Suzuki
556
2011
Dan Shechtman
"for the discovery of quasicrystals"
2012
Robert Lefkowitz
"for studies of G-protein-coupled receptors"
Brian Kobilka
2013
Martin Karplus
"for the development of multiscale models for
complex chemical systems"
Michael Levitt
Arieh Warshel
2014
Eric Betzig
"for the development of super-resolved
fluorescence microscopy"
Stefan W. Hell
William E. Moerner
2015
Tomas Lindahl
"for mechanistic studies of DNA repair"
Paul L. Modrich
Aziz Sancar
2016
Jean-Pierre Sauvage
"for the design and synthesis of molecular
machines"
Fraser Stoddart
557
Ben Feringa
2017
Jacques Dubochet
"for developing cryo-electron microscopy for the
high-resolution structure determination of
biomolecules in solution"
Joachim Frank
Richard Henderson
2018
Frances Arnold
"for the directed evolution of enzymes"
George Smith
"for the phage display of peptides and antibodies"
Sir Gregory Winter
2019
John B. Goodenough
"for the development of lithium ion batteries"
M. Stanley Whittingham
Akira Yoshino
2020
Emmanuelle Charpentier
"for the development of a method for genome
editing"
Jennifer Doudna
Light would take 0.13 seconds to travel around the Earth.
To escape the Earth's gravity a rocket need to travel at 7 miles a second.
558
No one shall expel us from the paradise which Cantor has created for us.
{Expressing the importance of Georg Cantor's set theory in the development of mathematics.}
― David Hilbert
The largest dinosaur ever discovered was Seismosaurus which was over 100
feet long and weighed up to 80 tones.
The risk of being struck by a falling meteorite for a human is one
occurrence every 9,300 years.
559
List of Nobel laureates in Physiology or Medicine
1901
Emil Adolf von Behring
"for his work on serum therapy, especially its
application against diphtheria, by which he has
opened a new road in the domain of medical science
and thereby placed in the hands of the physician a
victorious weapon against illness and deaths"
1902
Sir Ronald Ross
"for his work on malaria, by which he has shown how
it enters the organism and thereby has laid the
foundation for successful research on this disease and
methods of combating it"
1903
Niels Ryberg Finsen
"[for] his contribution to the treatment of diseases,
especially lupus vulgaris, with concentrated light
radiation, whereby he has opened a new avenue for
medical science"
1904
Ivan Petrovich Pavlov
"in recognition of his work on the physiology
of digestion, through which knowledge on vital aspects
of the subject has been transformed and enlarged"
1905
Robert Koch
"for his investigations and discoveries in relation
to tuberculosis"
1906
Camillo Golgi
"in recognition of their work on the structure of
the nervous system"
Santiago Ramón y Cajal
1907
Charles Louis Alphonse
"in recognition of his work on the role played
560
1908
Laveran
by protozoa in causing diseases"
Ilya Ilyich Mechnikov
"in recognition of their work on immunity"
Paul Ehrlich
1909
Emil Theodor Kocher
"for his work on the physiology, pathology and surgery
of the thyroid gland"
1910
Albrecht Kossel
"in recognition of the contributions to our knowledge
of cell chemistry made through his work on proteins,
including the nucleic substances"
1911
Allvar Gullstrand
"for his work on the dioptrics of the eye"
1912
Alexis Carrel
"[for] his work on vascular suture and
the transplantation of blood vessels and organs"
1913
Charles Richet
"[for] his work on anaphylaxis"
1914
Robert Bárány
"for his work on the physiology and pathology of
the vestibular apparatus"
1915
1916
Not awarded
1917
1918
561
1919
Jules Bordet
"for his discoveries relating to immunity"
1920
Schack August
"for his discovery of the capillary motor regulating
Steenberg Krogh
mechanism"
Not awarded
1921
1922
Archibald Vivian Hill
"for his discovery relating to the production of heat in
the muscle"
Otto Fritz Meyerhof
"for his discovery of the fixed relationship between the
consumption of oxygen and the metabolism of lactic
acid in the muscle"
1923
Sir Frederick Grant
"for the discovery of insulin"
Banting
John James Rickard
Macleod
1924
Willem Einthoven
"for the discovery of the mechanism of
the electrocardiogram"
Not awarded
1925
1926
Johannes Andreas Grib
"for his discovery of the Spiroptera carcinoma"
Fibiger
1927
Julius Wagner-Jauregg
"for his discovery of the therapeutic value
of malaria inoculation in the treatment of dementia
paralytica"
562
1928
Charles Jules Henri
"for his work on typhus"
Nicolle
1929
Christiaan Eijkman
"for his discovery of the antineuritic vitamin"
Sir Frederick Gowland
"for his discovery of the growth-stimulating vitamins"
Hopkins
1930
Karl Landsteiner
"for his discovery of human blood groups"
1931
Otto Heinrich Warburg
"for his discovery of the nature and mode of action of
the respiratory enzyme"
1932
Sir Charles Scott
"for their discoveries regarding the functions
Sherrington
of neurons"
Edgar Douglas Adrian
1933
Thomas Hunt Morgan
"for his discoveries concerning the role played by
the chromosome in heredity"
1934
George Hoyt Whipple
"for their discoveries concerning liver therapy in cases
of anaemia"
George Richards Minot
William Parry Murphy
1935
Hans Spemann
"for his discovery of the organizer effect in embryonic
development"
563
1936
Sir Henry Hallett Dale
"for their discoveries relating to chemical transmission
of nerve impulses"
Otto Loewi
1937
Albert Szent-Györgyi von
"for his discoveries in connection with the biological
Nagyrapolt
combustion processes, with special reference
to vitamin C and the catalysis of fumaric acid"
1938
Corneille Jean François
"for the discovery of the role played by
Heymans
the sinus and aortic mechanisms in the regulation
of respiration"
1939
Gerhard Domagk
"for the discovery of the antibacterial effects
of prontosil"
1940
Not awarded
1941
1942
1943
1944
Carl Peter Henrik Dam
"for his discovery of vitamin K"
Edward Adelbert Doisy
"for his discovery of the chemical nature of vitamin K"
Joseph Erlanger
"for their discoveries relating to the highly
differentiated functions of single nerve fibres"
Herbert Spencer Gasser
1945
Sir Alexander Fleming
"for the discovery of penicillin and its curative effect in
564
various infectious diseases"
Sir Ernst Boris Chain
Howard Walter Florey
1946
Hermann Joseph Muller
"for the discovery of the production of mutations by
means of X-ray irradiation"
1947
Carl Ferdinand Cori
"for their discovery of the course of the catalytic
conversion of glycogen"
Gerty Theresa Cori, née
Radnitz
1948
Bernardo Alberto
"for his discovery of the part played by the hormone of
Houssay
the anterior pituitary lobe in the metabolism of sugar"
Paul Hermann Müller
"for his discovery of the high efficiency of DDT as a
contact poison against several arthropods"
1949
Walter Rudolf Hess
"for his discovery of the functional organization of
the interbrain as a coordinator of the activities of the
internal organs"
1950
António Caetano Egas
"for his discovery of the therapeutic value of leucotomy
Moniz
(lobotomy) in certain psychoses"
Philip Showalter Hench
"for their discoveries relating to the hormones of
the adrenal cortex, their structure and biological
effects"
Edward Calvin Kendall
Tadeusz Reichstein
565
1951
Max Theiler
"for his discoveries concerning yellow fever and how to
combat it"
1952
1953
Selman Abraham
"for his discovery of streptomycin, the
Waksman
first antibiotic effective against tuberculosis"
Sir Hans Adolf Krebs
"for his discovery of the citric acid cycle"
Fritz Albert Lipmann
"for his discovery of co-enzyme A and its importance
for intermediary metabolism"
1954
John Franklin Enders
"for their discovery of the ability
of poliomyelitis viruses to grow in cultures of various
types of tissue"
Frederick Chapman
Robbins
Thomas Huckle Weller
1955
1956
Axel Hugo Theodor
"for his discoveries concerning the nature and mode of
Theorell
action of oxidation enzymes"
André Frédéric
"for their discoveries concerning heart
Cournand
catheterization and pathological changes in
the circulatory system"
Werner Forssmann
Dickinson W. Richards
1957
Daniel Bovet
"for his discoveries relating to synthetic compounds
that inhibit the action of certain body substances, and
566
especially their action on the vascular system and the
skeletal muscles"
1958
George Wells Beadle
"for their discovery that genes act by regulating
definite chemical events"
Edward Lawrie Tatum
Joshua Lederberg
"for his discoveries concerning genetic
recombination and the organization of the genetic
material of bacteria"
1959
Arthur Kornberg
"for their discovery of the mechanisms in the biological
synthesis of ribonucleic acid and deoxyribonucleic
acid"
Severo Ochoa
1960
Sir Frank Macfarlane
"for discovery of acquired immunological tolerance"
Burnet
Sir Peter Brian Medawar
1961
Georg von Békésy
"for his discoveries of the physical mechanism of
stimulation within the cochlea"
1962
Francis Harry Compton
"for their discoveries concerning the molecular
Crick
structure of nucleic acids and its significance for
information transfer in living material"
James Dewey Watson
Maurice Hugh Frederick
Wilkins
567
1963
Sir John Carew Eccles
"for their discoveries concerning the ionic mechanisms
involved in excitation and inhibition in the peripheral
Sir Alan Lloyd Hodgkin
and central portions of the nerve cell membrane"
Sir Andrew Fielding
Huxley
1964
Konrad Bloch
"for their discoveries concerning the mechanism and
regulation of the cholesterol and fatty
acid metabolism"
Feodor Lynen
1965
François Jacob
"for their discoveries concerning genetic control of
enzyme and virus synthesis"
André Lwoff
Jacques Monod
1966
Peyton Rous
"for his discovery of tumour-inducing viruses"
Charles Brenton Huggins
"for his discoveries concerning hormonal
treatment of prostatic cancer"
1967
Ragnar Granit
"for their discoveries concerning the primary
physiological and chemical visual processes in the eye"
Haldan Keffer Hartline
George Wald
1968
Robert W. Holley
"for their interpretation of the genetic code and its
568
function in protein synthesis"
Har Gobind Khorana
Marshall W. Nirenberg
1969
Max Delbrück
"for their discoveries concerning the replication
mechanism and the genetic structure of viruses"
Alfred D. Hershey
Salvador E. Luria
1970
Julius Axelrod
"for their discoveries concerning the
humoral transmittors in the nerve terminals and the
Ulf von Euler
mechanism for their storage, release and inactivation"
Sir Bernard Katz
1971
Earl W. Sutherland, Jr.
"for his discoveries concerning the mechanisms of the
action of hormones"
1972
Gerald M. Edelman
"for their discoveries concerning the chemical
structure of antibodies"
Rodney R. Porter
1973
Karl von Frisch
"for their discoveries concerning organization and
elicitation of individual and social behavior patterns"
Konrad Lorenz
Nikolaas Tinbergen
569
1974
Albert Claude
"for their discoveries concerning the structural and
functional organization of the cell"
Christian de Duve
George E. Palade
1975
David Baltimore
"for their discoveries concerning the interaction
between tumour viruses and the genetic material of
the cell"
Renato Dulbecco
Howard Martin Temin
1976
Baruch S. Blumberg
"for their discoveries concerning new mechanisms for
the origin and dissemination of infectious diseases"
D. Carleton Gajdusek
1977
Roger Guillemin
"for their discoveries concerning the peptide
hormone production of the brain"
Andrew V. Schally
Rosalyn Yalow
"for the development of radioimmunoassays of peptide
hormones"
1978
Werner Arber
"for the discovery of restriction enzymes and their
application to problems of molecular genetics"
Daniel Nathans
Hamilton O. Smith
570
1979
Allan M. Cormack
"for the development of computer assisted
tomography"
Sir Godfrey N.
Hounsfield
1980
Baruj Benacerraf
"for their discoveries concerning genetically
determined structures on the cell surface that
Jean Dausset
regulate immunological reactions"
George D. Snell
1981
Roger W. Sperry
"for his discoveries concerning the functional
specialization of the cerebral hemispheres"
David H. Hubel
"for their discoveries concerning information
processing in the visual system"
Torsten N. Wiesel
1982
Sune K. Bergström
"for their discoveries concerning prostaglandins and
related biologically active substances"
Bengt I. Samuelsson
Sir John R. Vane
1983
Barbara McClintock
"for her discovery of mobile genetic elements"
1984
Niels K. Jerne
"for theories concerning the specificity in development
and control of the immune system and the discovery of
Georges J.F. Köhler
the principle for production of monoclonal antibodies"
571
César Milstein
1985
Michael S. Brown
"for their discoveries concerning the regulation
of cholesterol metabolism"
Joseph L. Goldstein
1986
Stanley Cohen
"for their discoveries of growth factors"
Rita Levi-Montalcini
1987
Susumu Tonegawa
"for his discovery of the genetic principle for
generation of antibody diversity"
1988
Sir James W. Black
"for their discoveries of important principles for drug
treatment"
Gertrude B. Elion
George H. Hitchings
1989
J. Michael Bishop
"for their discovery of the cellular origin
of retroviral oncogenes"
Harold E. Varmus
1990
Joseph E. Murray
"for their discoveries concerning organ and cell
transplantation in the treatment of human disease"
E. Donnall Thomas
1991
Erwin Neher
"for their discoveries concerning the function of
572
single ion channels in cells"
Bert Sakmann
1992
Edmond H. Fischer
"for their discoveries concerning
reversible protein phosphorylation as a biological
regulatory mechanism"
Edwin G. Krebs
1993
Sir Richard J. Roberts
"for their discoveries of split genes"
Phillip A. Sharp
1994
Alfred G. Gilman
"for their discovery of G-proteins and the role of these
proteins in signal transduction in cells"
Martin Rodbell
1995
Edward B. Lewis
"for their discoveries concerning the genetic control of
early embryonic development"
Christiane NüssleinVolhard
Eric F. Wieschaus
1996
Peter C. Doherty
"for their discoveries concerning the specificity of
the cell mediated immune defence"
Rolf M. Zinkernagel
1997
Stanley B. Prusiner
"for his discovery of Prions - a new biological principle
of infection"
1998
Robert F. Furchgott
"for their discoveries concerning nitric oxide as a
573
signaling molecule in the cardiovascular system"
Louis J. Ignarro
Ferid Murad
1999
Günter Blobel
"for the discovery that proteins have intrinsic signals
that govern their transport and localization in the cell"
2000
Arvid Carlsson
"for their discoveries concerning signal transduction in
the nervous system"
Paul Greengard
Eric R. Kandel
2001
Leland H. Hartwell
"for their discoveries of key regulators of the cell cycle"
Sir Tim Hunt
Sir Paul M. Nurse
2002
Sydney Brenner
"for their discoveries concerning 'genetic regulation of
organ development and programmed cell death'"
H. Robert Horvitz
Sir John E. Sulston
2003
Paul Lauterbur
"for their discoveries concerning magnetic resonance
imaging"
Sir Peter Mansfield
574
2004
Richard Axel
"for their discoveries of odorant receptors and the
organization of the olfactory system"
Linda B. Buck
2005
Barry J. Marshall
"for their discovery of the bacterium Helicobacter
pylori and its role in gastritis and peptic ulcer disease"
J. Robin Warren
2006
Andrew Z. Fire
"for their discovery of RNA interference - gene silencing
by double-stranded RNA"
Craig C. Mello
2007
Mario R. Capecchi
"for their discoveries of principles for introducing
specific gene modifications in mice by the use
of embryonic stem cells."
Sir Martin J. Evans
Oliver Smithies
2008
Harald zur Hausen
"for his discovery of human papilloma viruses
causing cervical cancer"
Françoise Barré-Sinoussi
"for their discovery of human immunodeficiency virus"
Luc Montagnier
2009
Elizabeth H. Blackburn
"for the discovery of how chromosomes are protected
by telomeres and the enzyme telomerase"
Carol W. Greider
575
Jack W. Szostak
2010
Sir Robert G. Edwards
"for the development of in vitro fertilization"
2011
Bruce A. Beutler
"for their discoveries concerning the activation
of innate immunity"
Jules A. Hoffmann
Ralph M. Steinman
"for his discovery of the dendritic cell and its role
in adaptive immunity"
2012
Sir John B. Gurdon
"for the discovery that mature cells can
be reprogrammed to become pluripotent"
Shinya Yamanaka
2013
James E. Rothman
"for their discoveries of machinery
regulating vesicle traffic, a major transport system in
our cells"
Randy W. Schekman
Thomas C. Südhof
2014
John O'Keefe
"for their discoveries of cells that constitute a
positioning system in the brain"
May-Britt Moser
Edvard I. Moser
2015
William C. Campbell
"for their discoveries concerning a novel
576
Satoshi Ōmura
Tu Youyou
therapy against infections caused by roundworm
parasites"
"for her discoveries concerning a novel
therapy against malaria"
2016
Yoshinori Ohsumi
"for his discoveries of mechanisms for autophagy"
2017
Jeffrey C. Hall
"for their discoveries of molecular mechanisms
controlling the circadian rhythm"
Michael Rosbash
Michael W. Young
2018
James P. Allison
"for their discovery of cancer therapy by inhibition of
negative immune regulation"
Tasuku Honjo
2019
William Kaelin Jr.
"for their discoveries of how cells sense and adapt to
oxygen availability"
Peter J. Ratcliffe
Gregg L. Semenza
2020
Harvey J. Alter
"for the discovery of Hepatitis C virus"
Michael Houghton
Charles M. Rice
577
In Mathematics the art of proposing a
question must be held of higher value
than solving it.
― Georg Cantor
A mathematical proof should
resemble a simple and clear-cut
constellation, not a scattered
cluster in the Milky Way.
― G.H. Hardy
578
"{Replying to G. H. Hardy's suggestion that the number of a taxi (1729) was 'dull', showing
off his spontaneous mathematical genius}
No, it is a very interesting number; it is the smallest number expressible as a sum of two cubes in
two different ways, the two ways being 13 + 123 and 93 + 103."
— Srinivasa Ramanujan
Source of Information:
https://www.wikipedia.org
579
Related papers
“Mujeres, vestido y justicia. El caso de un “dress code” con pena de cárcel (1724)”
Investigaciones Históricas: Historia Moderna y Contemporánea, 2024
Call for paper: Special Issue "Training Special Education Teachers and Staff to Use Evidence-Based Practices"
Education Sciences , 2024
Ode to Autumn -A Close Reading
International Journal of Creative Research Thoughts, 2024
Maimonides in Popular Culture
Maimonides in Popular Culture,” The Golden Path: Maimonides Across Eight Centuries, ed. David Sclar (London: Liverpool University Press, 2023), Yeshiva University Museum exhibition catalog, 2023., 2023
Planning for recreation and tourism in forests: Results from the consultation stage of the EU's Tourfor project
Tourism Geographies, 2002
Estatuária do desejo: a escrita erótica e o jogo da imitação em "Lucíola"
Opiniães – Revista dos Alunos de Literatura Brasileira, 2015
O Uso Do Mangá Como Ferramenta De Apoio À Formação Social e Intelectual
Revista Científica Cognitionis, 2022
Edible triangle: A model of early intervention in feeding difficulties for the under threes
Journal of child and adolescent behavior, 2017
Barriers to Political Analysis in Aid Bureaucracies: From Principle to Practice in DFID and the World Bank
World Development, 2015
The role of metal cation in electron-induced dissociation of tryptophan
European Physical Journal D, 2010
3D Triangulations for Industrial Applications
2012 25th SIBGRAPI Conference on Graphics, Patterns and Images, 2012
Related topics
- Find new research papers in:
- Physics
- Chemistry
- Biology
- Health Sciences
- Ecology
- Earth Sciences
- Cognitive Science
- Mathematics
- Computer Science