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January 1

Coal, at a train yard.

In the late 1960s era, my father brought home some coal to augment wood being burned in our fireplace. We lived in NC (southern US) in a rural town, with many freight trains passing through. My memory is that he purchased at the local train depot. But I could be wrong. Still, I'm trying to figure out where normal people, who needed coal, would access this commodity, in the southern US.

My husband's grandparents (born 1899/1900) lived in NYC, heated with a coal-fired furnace, for decades. As did the parents of my husband's friends, when he grew up in mid-state NY. Radiators were a marvel to me, when I first saw them, 1979.

Why was the coal available at the train yard? Was it used to fuel locomotives, or was there some on hand, as it was being shipped through/to our area? Dad is long gone, so I can't ask him. Thanks. Tribe of Tiger ^{Let's Purrfect!} 03:53, 1 January 2023 (UTC)

In the UK (and I assume it would have been the same in the US) coal was the fuel for steam locomotives, and practically every railway station had its own coal depot from where coal was distributed to the populace, usually by truck in 1cwt sacks, for a regular weekly or fortnightly delivery. Between towns coal was distributed by train in long lines of open waggons. Shantavira|^{feed me} 09:28, 1 January 2023 (UTC)

Yes, our local coal merchant in the 1960s was based at our local London Underground station, presumably a hangover from before its electrification in the 1940s. Delivering wholesale coal by rail had to be a lot cheaper than by road. Alansplodge (talk) 14:25, 1 January 2023 (UTC)

Most of what is now the London Underground was electrified in 1905. Coal-fired steam trains continued to be used until the 1960s though on Britain's main-line railways and some outer, above-ground parts of the Underground: perhaps Alan's local station was on one of those parts, maybe on the Metropolitan Line. Most of the main-line railway system converted to diesel trains, although of course some lines went directly to electric and some were electrified later. --174.89.144.126 (talk) 23:39, 1 January 2023 (UTC)

See Leytonstone tube station: The station was first served by the Central line on 5 May 1947 when it became the temporary terminus of the line, passengers changing on to steam shuttle onwards to Epping. This ceased on 14 December 1947. But we digress. Alansplodge (talk) 10:59, 2 January 2023 (UTC)

Yes, that's one of the outer, above-ground bits I was talking about. But it wasn't a London Underground station at all until 1947. --174.89.144.126 (talk) 09:55, 3 January 2023 (UTC)

I don't know any specifics for the US, but I suppose this was pretty similar all over the western world. Steam trains ran on coal, mostly. There were a few areas where wood or oil burners were popular for a while. But that's not why people got coal from the railway yard. When people used coal for domestic heating, every town had a coal merchant, who got deliveries by rail (or boat, for places with river or canal access), so those merchants were located at rail yards. People either got their coal from there or those merchants ran deliveries by road vehicle, also to surrounding places without rail/boat access. This coal wasn't necessarily the same coal as that burned in the locomotives; see coal rank. This caused some difficulties in my home country (Netherlands) during World War One. There were a few coal mines in the country, and the coal they delivered was fine for domestic heating, but the volatile content was too high for use in locomotives, so the railways had to rely on coal imported from Germany, a country not particularly eager to export such strategic commodities in wartime. It was one of the reasons to switch to electric trains in the 1920s, as Dutch coal was fit for power stations. PiusImpavidus (talk) 11:16, 1 January 2023 (UTC)

There is a nontrivial amount of information about coal yards available on the internet, like this rather interesting webpage, or this ad for "Chicago's Most Modern Coal Yard"; I'm sure the subject was discussed to no end in trade magazines like Coal Age and The Black Diamond. There might be enough good coverage to warrant an article. Shells-shells (talk) 11:51, 1 January 2023 (UTC)

You can try googling "coal yard near me". ←Baseball Bugs ^{What's up, Doc?} carrots→ 18:48, 1 January 2023 (UTC)

Steam radiators are very common in New York City and ubiquitous in New York City buildings of a certain age though many post Great Depression buildings use other technologies e.g. ohmic heating. Some post world war buildings still use dirty home heating oil (either diesel-like or heavier and dirtier in carbon and sometimes sulfur (acid rain), though less dirty than coal). Futures contracts for home heating oil mandate pickup at New York Harbor, so it is more popular within truck driving distance of the fuel ships, as it is often delivered by truck. Sagittarian Milky Way (talk) 19:25, 1 January 2023 (UTC)

• In the early 20th century New England, many homes were heated by coal. My maternal great-grandfather was a "coal man" who worked for a coal delivery service in Lowell, Massachusetts that brought coal to homes and business for heating. Being himself born in the late 19th century, my mom said that in his youth, he started delivering with a horse and cart, but mostly worked with a truck to deliver the coal. This image here is probably what he looked like while doing his deliveries. By the mid 20th century, many such homes had converted to other forms of heating (often municipal natural gas or heating oil, or in some cases, cord-wood, which my family used until the very late 1990s.) and I suspect the process of regular home coal delivery tapered off by the 1960s or so. There would likely have been a few families after that who still used coal heating, and would have had to arrange their own supply. --Jayron32 14:02, 3 January 2023 (UTC)

In the United States, coal pockets were very common at rail stops. A coal pocket is a place used to load/unload cars like coal cars, but can be used for anything else that is poured into open cars like grain or gravel. It was very common for coal pockets to have street-level openings where people could purchase coal. Where I live, the coal pocket is still by the tracks and still sells coal even though it is completely unrelated to rail activities now. 12.116.29.106 (talk) 19:48, 3 January 2023 (UTC)

We had coal-fired (well, phurnacite-fired) central heating installed in the 70s. The coal merchant had an office in the nearest town, with a board in the window with difference types of coal stuck on to it and labelled, but the coal-yard was at the nearby railway station (closed a decade before). I remember Mum saying you had to watch the men like hawks when they made a delivery, as they would try to get you to sign for more sacks than they had actually delivered. DuncanHill (talk) 16:12, 5 January 2023 (UTC)

Back to distribution / sourcing: coal-fired railroad engines frequently lost (dropped) coal off of their fuel carriers. Pre-WWII, it was quite common for people to walk along the rails and collect coal that had fallen from trains. Perhaps some was sold at the station. DOR (HK) (talk) 21:07, 7 January 2023 (UTC)

There are still coal-fired steam engines run for historical reasons. Maybe the OP could ask them where they get their coal. ←Baseball Bugs ^{What's up, Doc?} carrots→ 21:21, 7 January 2023 (UTC)

liger

It's impossible for two separate spevies to breed, then how did this happen?

https://en.wikipedia.org/wiki/Liger

Can it be done with any different animal pairing? Rambo XTerminator (talk) 16:31, 1 January 2023 (UTC)

See species problem. The basic definition is that if two animals can have offspring that itself is capable of having offspring, the two original animals are of the same species. However, it's impossible to apply that definition consistently. PiusImpavidus (talk) 17:21, 1 January 2023 (UTC)

It's likewise impossible to produce a Mule. ←Baseball Bugs ^{What's up, Doc?} carrots→ 18:44, 1 January 2023 (UTC)

No biologist will use this in this form as a definition. Hybrid offspring, that is, the offspring resulting of two animals of different species interbreeding, is in fact fairly common. However, such hybrid individuals are normally not able to produce offspring themselves, so then the line stop there. Mules and Hinnies are sterile. If it turns out that animals of species that are classified differently can produce a viable hybrid population that reproduces in the wild, taxonomists will probably revise the species assignment. However, another cause of speciation can be that the two species inhabit geographically separate habitats, forming a natural barrier to interbreeding. Lions are found in Africa, tigers in Asia. A recent issue is the mating of brown bears and polar bears. Until recently, their habitats were separate and any grizzly–polar bear hybrids were the result of rare chance encounters, but climate change is driving the polar bears into brown bear territory.  --Lambiam 00:22, 2 January 2023 (UTC)

Another relevant article is introgression. As molecular-genetic analyses become more routine, it has become increasingly apparent that occasional hybridisation between species is commoner, even in animals, than hitherto realised. Some gene flow between species is not usually considered sufficient reason to revise the taxonomy and consider them the same species, but the decision becomes a matter of opinion about what is most appropriate and convenient. Jmchutchinson (talk) 09:09, 2 January 2023 (UTC)

This article also highlights the narluga, a hybrid of a female narwhal and a male beluga whale, which is apparently fertile. The article says that hybrids "are not evolutionary dead-ends, and in some cases, may serve as evolutionary accelerators". Alansplodge (talk) 11:18, 2 January 2023 (UTC)

• Human-defined categories are basically buckets with firmly-defined walls and clear criteria. They are things we as humans create to make it easier for us to understand the world. The world itself is under no obligation to conform to the categories we have created for our own convenience. A "species" is one of those categories we created; it's fairly useful in that many living things we run into are conveniently categorized as a certain species, and any given definition of "species" (of which there are many) works reasonably well for most cases. That being said, there are a non-trial number of living things that do not easily allow themselves to be defined to easily, and basically break any reasonable categorization scheme we come up with. As noted above, this is the species problem, a rather famous example is the classification of potatoes into our usual understanding of what a "species" is. As noted in This paper, "the Biological Species Concept... cannot be applied to them" Simply put, the genetics and biology of wild potatoes (and we're not even talking about cultivated potatoes here, which adds even more complexity) break the concept of species. The common term for this is Species complex, but even that fails to really capture the mess that potatoes present to taxonomy. There are other messy problems, such as Ring species as well. --Jayron32 02:32, 3 January 2023 (UTC)

January 2

Relativistic Quantum Mechanics exists, so why many say the reconciliation between QM and SR is impossible?

Many phylosophers of science write that it's not possible to reconcile QM and Special Relativity. A major problem is that the experimental violation of Bell's inequalities implies that any theory which makes the same prediction of classical QM has to be non-local, whereas in SR everything is local. So my question is: since one can modify the Schroedinger equation to make it Lorentz-invariant, why doesn't this solve all the issues? We have a more general theory, which is local and makes predicions at least as accurately as non-relativistic QM, don't we?

Thanks! 2.42.134.212 (talk) 15:51, 2 January 2023 (UTC)

Relativistic quantum mechanics is indeed well-studied. The major unsolved problem is reconciling quantum mechanics and general relativity, i.e., finding a consistent theory of quantum gravity. Could you perhaps provide a source of philosophers of science challenging the reconciliation of QM and SR? ^Complex/_Rational 17:15, 2 January 2023 (UTC)

Tim Maudlin, a leading expert in the phylosophy of QM, says so in his 2-volume book on the phylosophy of physics, and also around min. 31:40 in this video interview: https://www.youtube.com/watch?v=OduDEz77h9U. Maudlin does not say explicitly "special relativity", but he argues that the main problem is the nonexistence of the concept of simultaneity in relativity, which applies to SR.

— Preceding unsigned comment added by 2.42.134.212 (talk) 19:43, 2 January 2023 (UTC)

You probably shouldn't be getting your information from someone claiming to be a "philosopher of quantum mechanics" or writing books on the "philosophy of physics." These aren't philosophical topics. You are better off using actual physicists or physical chemists to discuss this topic, rather than someone who "who studies the metaphysical foundations of physics and logic." I'm literally running a quantum mechanical calculation right now that uses a modified Hamiltonian explicitly account for relativistic effects in core electrons of large atoms while finding solutions to the Schrodinger equation. That Tim Maudlin doesn't think that is possible is, well, his problem and not a problem of the actual scientific fields of knowledge. Indeed, our understanding of quantum mechanics as a model to explain observable is dependent upon relativity. It explains why, for example, gold atoms have smaller atomic radii than we would expect from the amount of shielding from the large number of core electrons. Relativistic effects cause a contraction of the radii. That lead-acid batteries work better than tin-acid batteries is another example. --OuroborosCobra (talk) 22:04, 2 January 2023 (UTC)

Maudlin graduated in physics and Trevis Norsen is a physicist. However, is your answer simply that they are telling nonsense? 2.42.134.212 (talk) 22:10, 2 January 2023 (UTC)

Well my unerstanding is that GR is basically non-linear dealing with bent space-time whereas QM currently only deals nicely with a flat space-time, and that is is a major reason the Holographic principle is so exciting - it indicates there may be a way of making GR linear - but there's still lots of efforts to make QM deal with bent space-time. So nothing to do with what either of thos philosophers said which I find surprising - are you sure you followed what they were saying right? NadVolum (talk) 22:40, 2 January 2023 (UTC)

I had a look at the bit pointed out at 3:40 in the video with Tim Maudlin and I'm pretty certain he is just wrong. Entanglement is definitely weird but there's nothing there conflicting with relativity. I'm not sure where he gets the idea that simultaneity is required i QUantum Mechanics - it's not needed for anything to do with entanglement. NadVolum (talk) 23:00, 2 January 2023 (UTC)

Relativistic quantum mechanics does not "solve the issue", which is the spooky action at a distance. Bell's inequalities continue to hold under Lorentz invariance, so there is some coordination between events (observations of entangled particles) whose separation in spacetime is not a timelike interval. They are not causally related in any theory admitting only local reality. It is hard to assign a meaning to Maudlin's statement that relativity was "designed" [his words] for local theories. Relativity did away with the concept of absolute simultaneity of Newtonian physics. But although Newtonian universal time allows the concept of simultaneity, it offered no role for nonlocal instantaneous coordination. So it seems more reasonable to say that relativity was not conceived to deal with nonlocal spacelike coordination. Neither was QM; the spookiness was an unexpected consequence of the theory. So I am tempted to say that if someone says it is hard to reconcile special relativity with quantum theory, it is not because of any specific aspect of special relativity but because it is hard to reconcile macroscopic preconceptions of how the world ought to behave with quantum theory. If this an issue that needs to be solved while holding on to these preconceptions, special relativity is not the solution. Neither does it stand in the way.  --Lambiam 01:50, 3 January 2023 (UTC)

Thanks, Lambian, this seems a good answer to me. In my understanding, the main difference between QFT and NRQM is in the degrees of freedom that the wavefunction is a function of. For the rest, the mathematical structure is the same and so I cann see why the problems with the spooky action at a distance don't go away. My only doubt is in which sense there is a "relativistic" QM... So I formulate a more direct question: is relativistic QM able to predict the outcomes of the experiments made by Aspect? (My guess: yes). If so, the violation of Bell's inequalities shows that it's a nonlocal theory...but then how can it be "relativistic"? 2.42.134.212 (talk) 07:45, 3 January 2023 (UTC)

RQM is relativistic in the sense of invariance under the Lorentz transformations. Since NRQM is a a special case of RQM, the violation is equally predicted by RQM. Consider that Aspect's experimental set-up did not get anywhere close to lightspeed w.r.t. the observer. :)  --Lambiam 11:04, 3 January 2023 (UTC)

Invariance under LT implies that the same two events can be simultaneous in a reference frame and non simultaneous in another. Now if two objects A,B are entangled, NRQM prescribes that the state of A can become determined when the state of B is measured, and here "when" means "in the same exact moment". How to make sense of this in relativistic QM? 2.42.134.212 (talk) 19:37, 3 January 2023 (UTC)

There is no requirement for anything to be simultaneous. If one person does a measurement on one particle then they know what the result would be if the same measurement is performed on a second particle entangled with it.It does not matter if one is causally before or after the other or somewhere there cannot be a causal link. There is no way of detecting an effect from the entanglement until one gets to a time and place where both experiments have been done. The same exact moment only refers to th person doing an experiment, it does not affect the person with the second particle. Our common experience way of dealing with it is to think one experiment does something to the other and therefore that one must be first but that is not so. NadVolum (talk) 23:31, 3 January 2023 (UTC)

Because Einstein objected to the "spooky action at a distance" of QM (or, more concisely in German, its requiring spukhafte Fernwirkung), and Einstein was the father of the theory of relativity, there is a misunderstanding that his objection was informed by an implied incompatibility between QM and his cherished theory.^[1] But, clearly, the instantaneous action at a distance in the classical Newtonian setting of absolute time is no less spooky.  --Lambiam 09:04, 4 January 2023 (UTC)

Dead hand grip

The painting

It appears that Viktor Vasnetsov's painting After the Battle of Igor Svyatoslavich with the Cumans contains an odd part, where a dead warrior on the upper right still grasps a bow firmly with a raised hand (even if resting on something else). Can a dead body actually hold an object like this or is it more like an error on Vasnetsov's part? 212.180.235.46 (talk) 19:29, 2 January 2023 (UTC)

Perhaps the warrior is wounded rather than dead. Cullen328 (talk) 19:33, 2 January 2023 (UTC)

Rigor mortis can set in very quickly indeed if a person has been engaged in hard work - like fighting in a battle. I like the way he's omitted any blood! More likely his glove is such that he would have to deliberately open his hand to let go of the bow. Or it could just be artistic license like the lack of blood! NadVolum (talk) 23:14, 2 January 2023 (UTC)

Whether or not a dead body can do so in reality, the idea that it can is widespread, so it is perhaps allowable artistic licence in such a work. {The poster formerly known as 87.81.230.195} 51.194.245.235 (talk) 02:36, 3 January 2023 (UTC)

From my cold, dead hands... Alansplodge (talk) 09:58, 3 January 2023 (UTC)

It looks look like the hand is just resting on the bow as opposed to grasping it. The bow itself leans on a dead body and on the ground. Ruslik_Zero 10:19, 4 January 2023 (UTC)

Or it might be a case of cadaveric spasm... —Wasell^(T) 🌻🇺🇦 16:55, 5 January 2023 (UTC)

January 5

square spasms in the right leg

Wikipedia does not give medical advice --Jayron32 12:17, 6 January 2023 (UTC)
The following discussion has been closed. Please do not modify it.
Is it due to a transfer virus or another source of lack of proteins? And if yes, to what frequencies? Enrico Spazzini 36 (talk) 19:51, 5 January 2023 (UTC) Wikipedia does not give medical advice Wikipedia is an encyclopedia anyone can edit. As a result, medical information on Wikipedia is not guaranteed to be true, correct, precise, or up-to-date! Wikipedia is not a substitute for a doctor or medical professional. None of the volunteers who write articles, maintain the systems or assist users can take responsibility for medical advice, and the same applies for the Wikimedia Foundation. If you need medical assistance, please call your national emergency telephone number, or contact a medical professional (for instance, a qualified doctor/physician, nurse, pharmacist/chemist, and so on) for advice. Nothing on Wikipedia.org or included as part of any project of Wikimedia Foundation Inc., should be construed as an attempt to offer or render a medical opinion or otherwise engage in the practice of medicine. Please see the article Wikipedia:Medical disclaimer for more information. Martin of Sheffield (talk) 20:18, 5 January 2023 (UTC) I'm wondering what a "square" spasm would be. ←Baseball Bugs What's up, Doc? carrots→ 21:17, 5 January 2023 (UTC) I'm even wondering if a doctor would be able to understand anything in this jumbled mess. But anyway... 80.214.28.89 (talk) 22:19, 5 January 2023 (UTC) Don't feed the trolls.  --Lambiam 23:24, 5 January 2023 (UTC) Not even to ask, "Kenneth, what are the frequencies?"? —Tamfang (talk) 01:59, 6 January 2023 (UTC)

January 6

Seedless fruits questions.

Is there disadvantages to eating seedless fruits, because they were breded differently? Seedless watermelon, tangerines, and grapes. As a health benefits question. I'm also confused as to how seedless fruit are made. Wikipedia has an article on seedless fruit, which says things like developed without fertilization (or fertilization without ovules), or and without pollination. How does fruit even reproduce without pollination? How does fruit fertilize without ovules? Thanks. 67.165.185.178 (talk) 13:31, 6 January 2023 (UTC).

Many fruits grown for food crops are propagated by grafting and not by sexual reproduction. This allows for consistent fruit from year-to-year, as sexual reproduction can cause genetic mixing that will change the characteristics of fruit. --Jayron32 14:13, 6 January 2023 (UTC)

I find that seedless watermelons and grapes always taste unripe (bleh). Doubtless this is because the pathways for the development of seeds and for ripening are intertwined. Abductive (reasoning) 19:30, 6 January 2023 (UTC)

De gustibus non est disputandum --Jayron32 19:36, 6 January 2023 (UTC)

What happens to bacteria in your intestines during fasting.

Of course I see so much health videos on Youtube lately on saying no to carbs, and no to sugars, and so avoid eating bread/rice. And some of the videos say, we eat for the health of the bacteria in our intestines. And a lot of videos talk about fasting and intermitting fasting. But what no 1 seems to cover is, when we fast, what happens to our bacteria, do they not get starved? Do they die off, and get excreted out? Such that, do your intestines get filled with new bacteria again, the next time you eat? 67.165.185.178 (talk) 13:35, 6 January 2023 (UTC).

If you Google "gut flora during fasting", you get a number of good, scholarly works, such as [This Nature article and This NIH article, among others. --Jayron32 14:11, 6 January 2023 (UTC)

Chemistry: dissolving formula.

I been seeing comments on science forums of people saying 1000 g of water (1 L) can dissolve 2000 g of sugar, and 30-40 g of salt. But they didn't say how they came up with them. What formula are they using? I never remembered a dissolving formula in college, heh. 67.165.185.178 (talk) 13:38, 6 January 2023 (UTC).

IP editor. Accurate solubility values are found by measurement rather than calculation and are very temperature dependent. Pubchem has some values available and their source at this URL (for sucrose, other sugars will vary). Mike Turnbull (talk) 13:58, 6 January 2023 (UTC)

That sounded to me like Bacon's monks debating the number of teeth a horse has. Still it could well be an interesting project to find one. NadVolum (talk) 13:59, 6 January 2023 (UTC)

Lots of calculation packages can give approximate values as estimates. See Chemicalize for example. Mike Turnbull (talk) 14:06, 6 January 2023 (UTC)

Has no theory been developed to approach this from first principles? Isn't it possible to calculate the energy associated with various solute concentrations and find the minimum?  --Lambiam 20:58, 6 January 2023 (UTC)

There's the article Solubility equilibrium and I guess people have put a fair amount of thought into it which doesn't get near Wikipedia. NadVolum (talk) 21:37, 6 January 2023 (UTC)

January 7

Hand warmer heat

I'm trying to find out how much energy is produced by an iron-oxidation style of chemical hand warmer, and not having much luck with wikipedia or web search. Any help? The reaction itself is described here but I don't know how to calculate the heat released by the reaction. Let's say the typical unit is about 100g which includes both the "fuel" (iron powder) and the oxidizer. Any help would be appreciated. Thanks. 2601:648:8200:990:0:0:0:B9C2 (talk) 07:37, 7 January 2023 (UTC)

According to various sources, 4Fe(s) + 3O₂(g) → 2Fe₂O₃(s) releases 1652kJ/mol heat, and one mole of iron weighs 55.845 g, so for every 55.845 g of Fe we get 1/4 × 1652 kJ = 413 kJ. To proceed, we need to know how much of the content by weight is iron. The reaction as described uses pure O₂ as the oxidizer. We may assume the oxygen is not included in the unit but supplied by the ambient air, but according to the info in Hand warmer § Air activated (iron), such units contain, next to iron, also cellulose, activated carbon, vermiculite and salt.  --Lambiam 09:05, 7 January 2023 (UTC)

I remember seeing a packet a few days ago, and reading the ingredients. I don't fully remember it though, I do remember seeing cellulose and vermiculite, but I also saw "a polymer" and not activated carbon, which does not appear to be a polymer. 67.165.185.178 (talk) 13:40, 7 January 2023 (UTC).

Thanks. I guess I'll assume the packet is 55.845% iron, so if the energy of a 100g packet is released over 8 hours, that's a little over 14 watts. 2601:648:8200:990:0:0:0:B9C2 (talk) 20:23, 7 January 2023 (UTC)

Are the following calculations related to the distance between gold and alpha in Rutherford's gold foil experiment properly referenced?

When an object traveling speed v reverses direction, speed v will become zero at the time the direction reverses. The object’s KE also becomes zero. In Wikipedia’s article on the Geiger-Marsden experiments the alpha particle’s mass $=6.645e^{-27}$ kg, and initial velocity $=1.53e^{7}$ m/s. Therefore, the alpha particle’s initial KE is:

$KE={\frac {1}{2}}mv^{2}={\frac {1}{2}}6.645e^{-27}*(5.53e^{7})^{2}=1.016e^{-11}Joule$

The electric potential energy due to distance (r) between charges is:

$U_{E}(r)=K_{E}{\frac {qQ}{r}}{}$

An alpha particle’s velocity becomes zero, then the electric potential energy between the alpha and the gold can equal the alpha’s initial KE:

${\frac {K_{E}qQ}{r}}=KE$

The distance between charges (r) when electric potential energy equals kinetic energy is:

$r={\frac {K_{E}qQ}{KE}}$

In the Geiger-Marsden experiments the Coulomb constant = $8.998e^{9}N.m^{2}/C^{2},q=1.266e^{-17},Q=3.204e^{-19}$. Therefore, the distance between the alpha and the gold when alpha velocity is zero is:

$r={\frac {kqQ}{KE_{\alpha }}}={\frac {8.99e^{9}*1.266e^{-17}*3.204e^{-19}}{1.016e^{-11}}}=3.59e^{-15}$

The radius of gold’s atomic nucleus is $7e^{-15}$ meters. Therefore, when alpha velocity becomes zero, the alpha particle will be within the gold nucleus. Vze2wgsm1 (talk) 13:12, 7 January 2023 (UTC)

In your computation of KE you used 5.53e⁷ (sic!) instead of 1.53e7 (also written as $1.53\cdot 10^{7}$ but never the way you wrote it). The correct result is $r_{\mathrm {min} }=4.69\cdot 10^{-14}\,\mathrm {m}$, which keeps the alpha particle outside the gold nucleus. --Wrongfilter (talk) 20:33, 7 January 2023 (UTC)

If the question truthfully is a search for proper references, I seem to recall an entire chapter in Modern Physics - Chapter 4, in fact - that introduces the conceptual ideas, explores them in great depth, and then works the math. It's got diagrams, it's got numbers, it's got explanations, it dispels the common "gotchas" and experimental subtleties, ... why, it's almost as though this is so standard that someone chose to write it down in one place, where thousands of educated people look at and study from it during a typical class in elementary physics.

Not only was this in the book - my edition even had a special multimedia enhancement, "More of Chapter 4": Rutherford’s Prediction and Geiger’s and Marsden’s Results, which has been mirrored at this University of California at San Diego's physics website.

If the query is a weakly-veiled request for someone to spend the time and effort to vet your personal effort to work-out-your-own-math, I think we can safely refer you to our standard reference on working-out-your-own-math. It's just not something we do, frankly.

Nimur (talk) 22:49, 7 January 2023 (UTC)

Is the length unit in this thermal lance graph correct?

Is this a fair correction?

The graph on https://pubs.acs.org/doi/full/10.1021/acs.iecr.1c00532 shows the length unit as cm. I know almost nothing about thermal lances but comparing it with the graphic and looking at how quickly the temperature drops, I think metres is more reasonable. Is this correct? Thanks, cmɢʟee⎆τaʟκ 14:38, 7 January 2023 (UTC)

Idon't know either but looking at a picture of a thermal lance I don't think meters would be correct as they don't look like glow all that much any distance from the tip. They burn down fairly rapidly and the oxygen would cool as it expands near the end. NadVolum (talk) 16:46, 7 January 2023 (UTC)

The abstract alone at [2] does not justify changing the graph scales (by 100x) or adding a 300 kelvin asymptote unless you can find verification in the full article or other WP:RS. Philvoids (talk) 19:52, 7 January 2023 (UTC)

In the publication, Figure 6, the asymptote is drawn as a fat straight line, just as fat as the graphed curve. Due to its fatness, given the y-scale, it covers the range from 258.4K to 337.4K. Its middle value, 297.9K, is close enough to 300K.  --Lambiam 21:47, 7 January 2023 (UTC)

Thermal lances can be several metres long, but the temperature drops quickly as a function of the distance from the tip, flattening out well within a distance of 1 cm, at least in the theoretical model on which the authors of the publication linked to base their graph. In the abstract they write their mathematical model is "validated", which I assume means it conforms to experimental data.  --Lambiam 20:57, 7 January 2023 (UTC)