The A1Π–X1Σ+ (2,0) transition in 11BH and 10BH observed by (1+2)-photon resonance-enhanced multiphoton ionization spectroscopy

25 May 2001 Chemical Physics Letters 340 (2001) 45±54 www.elsevier.nl/locate/cplett The A 1P±X 1R‡ (2,0) transition in 11BH and 10BH observed by (1 ‡ 2)-photon resonance-enhanced multiphoton ionization spectroscopy Jason Clark, Michael Konopka, Li-Min Zhang 1, Edward R. Grant * Department of Chemistry, Purdue University, West Lafayette, IN 47906, USA Received 29 September 2000; in ®nal form 5 March 2001 Abstract We report the mass-selected resonance-enhanced multiphoton ionization (REMPI) spectrum of photolytically produced diatomic boron hydride over the spectral range from 368 to 372 nm. Features recorded for time-of-¯ightresolved cation masses 12, 11 and 10 amu are assigned to the one-photon transition, A 1 P v0 ˆ 2†±X 1 R‡ v00 ˆ 0†, in 11 BH and 10 BH. Cation production at these wavelengths requires three photons. This signal must therefore re¯ect resonant one-photon absorption followed by two-photon ionization in a (1 ‡ 2)-photon process. This work represents the ®rst observation of the well-characterized A 1 P±X 1 R‡ system in ionization spectroscopy and the ®rst measurement of line positions in the A 1 P v ˆ 2 state for 10 BH. Ó 2001 Elsevier Science B.V. All rights reserved. 1. Introduction With only six electrons, BH is one of the simplest molecules in nature. It is spectroscopically bright and serves as an elementary prototype for the large class of polyatomic boron hydrides (see for example [1]). This species is of practical importance as an intermediate in the plasma deposition of boron in semiconductor, metal and ceramic materials (see for example [2]). Its A 1 P± X 1 R‡ transition system has also been suggested as a chemical laser candidate [3±5]. For these reasons, BH has been the subject of a number of experi* Corresponding author. Fax: +1-317-496-2512. E-mail address: edgrant@purdue.edu (E.R. Grant). 1 Present address: Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026. P.R. China. mental [6±14] and theoretical [15±29] investigations. Recent theoretical work on BH and other light diatomic hydrides has focussed on the extent to which non-adiabatic terms a€ect the electronic energy [30±32]. Theory predicts relatively large non-adiabatic e€ects in the rovibronic structure of BH, which should be discernible in the comparative positions of features in spectra recorded for 11 BH and 10 BH in natural isotopic abundance. High-resolution line positions are found in the Fourier transform infrared and optical emission spectra of BH recorded by Bernath and coworkers, but, with the predominance of 11 BH lines, scans establish 10 BH positions only for a subset of bands in the A 1 P±X 1 R‡ system of electronic transitions. Resonant multiphoton ionization spectroscopy o€ers a well-established means to resolve the structure of rovibrational transitions associated 0009-2614/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 ( 0 1 ) 0 0 3 4 8 - 7 46 J. Clark et al. / Chemical Physics Letters 340 (2001) 45±54 with individual molecular masses. However, to date, no ionization spectra of BH have appeared, despite the advantages of this method for detecting higher excited states and isotopically resolving spectroscopic positions. In the present Letter, we report the ®rst spectrum of BH recorded by ionization-detected absorption. We produce BH in a pulsed free-jet expansion by 193 nm photolysis of B2 H6 . Lines observed in the region from 368 to 372 nm, in spectra resolved by time-of-¯ight mass spectrometry for cation masses 12, 11 and 10 amu, are assigned to the one-photon transition, A 1 P v0 ˆ 2†±X 1 R‡ v00 ˆ 0†, in 11 BH and 10 BH. Cation production at these wavelengths requires three photons. The structure observed must therefore re¯ect resonant one-photon excitation followed by two-photon ionization in an uncommon (1 ‡ 2)photon process. These results provide clearly resolved rotational line positions, which are distinctly recorded for 11 BH and 10 BH, in a Dv ˆ 2 band system which has not previously been observed. 11 BH spectroscopic parameters established by Fernando and Bernath from an analysis of the 0; 0†, 1; 1† and 2; 2† sequence bands, extend well to describe the 2; 0† transition for 11 BH. Adjusting the constants for mass we ®nd good correspondence for 10 BH bands as well, though slightly larger residual errors raise the question of non-adiabatic contributions. (1 ‡ 2)-photon resonant ionization transitions are rare, and it is suggested that accidental double resonance with the B 1 R‡ v00 ˆ 1†±A 1 P v0 ˆ 2† lends intensity to the second, two-photon step. We conclude from these preliminary results that deliberate photoselection strategies o€er a promising means to obtain isotopically resolved structure for a great many excited states in this molecule. 2. Experimental The experiment uses a conventional pulsed supersonic molecular beam coupled with a time-of¯ight (TOF) mass spectrometer. The molecular beam is produced by expansion of B2 H6 , seeded at 5% in 3 atm. of H2 (Matheson), through a pulsed nozzle (General Valve, IOTA-1) into a chamber evacuated by two 500 l/s turbomolecular pumps. The residual pressure in the chamber is 10 6 Torr when the valve is operating at 10 Hz. The focussed output of the 193 nm photolysis laser (Lambda Physik, Compex 201) crosses the jet at the exit of the nozzle. The BH produced by photolysis of B2 H6 travels 58 cm to reach the ioncollection region of the TOF mass spectrometer. There an excimer-pumped dye laser (Lambda Physik EMG 202/FL 3002) focussed by a 30 cm lens crosses the BH beam. Operating with BPBD dye, the dye laser has a maximum output of 15 mJ per pulse with a pulse width of 10 ns. Dye laser wavelengths are calibrated by laser excited neon lines detected optogalvanically within a Fe/Ne hollow cathode lamp (Fischer Scienti®c). The vacuum-corrected neon transitions are compared to values derived from the Ashworth and Brown atlas of optogalvanic transitions [33]. Ions of di€erent masses are separated in a 1 m Wiley±McClaren time-of-¯ight mass spectrometer (Jordan) and detected by a two-stage microchannel plate detector. The ion signal is conditioned by a 10 preampli®er and then averaged by a digital oscilloscope (LeCroy 9450 300 MHz). The dye laser and data-acquisition system are controlled via an IEEE±GPIB interface by LabVIEW running on a PowerMac computer. 3. Results and discussion 3.1. Production pathways for ion fragments in the mass spectrum of B2 H6 photoproducts Fig. 1 compares mass-selected spectra recorded for masses m ˆ 12 11 BH‡ †, m ˆ 11 10 BH‡ , 11 B‡ † and m ˆ 10 10 B‡ †. Observed peak positions in these spectra are listed together with assignments in Table 1. Most lines can be assigned to the P, Q or R branches of the one-photon A 1 P±X 1 R‡ transition in 11 BH or 10 BH. Although the 2; 0† component of the A 1 P±X 1 R‡ transition has not been observed before, this assignment is a secure one. The line positions in the 11 BH‡ spectrum reported here can be tested against transition energies determined by Fernando and Bernath's very precise high-resolution Fourier-transform emis- J. Clark et al. / Chemical Physics Letters 340 (2001) 45±54 47 Fig. 1. Mass-resolved ionization-detected absorption spectra of fragments produced by the 193 nm photofragmentation of B2 H6 . Top: m ˆ 12 amu 11 BH‡ †; Center: m ˆ 11 amu 11 B‡ ; 10 BH‡ †; Bottom: m ˆ 10 amu 10 B‡ ). sion measurements of the 2; 2† band [13], taken together with infrared frequencies of the X 1 R‡ 1; 0† and 2; 1† vibrational transitions measured by Pinalto et al. [12]. Combining the uncertainties with which these transition energies are established, this procedure yields absolute A 1 P±X 1 R‡ 2; 0† positions for 11 BH to an estimated accuracy of 0:02 cm 1 . These well-established transition energies serve to accurately calibrate the laser spectrum for the 11 BH isotope. Lower mass channels in our experiment provide a simultaneous record of the 10 BH spectrum. Thus, aligning our laser wavelength scale to minimize the root-mean-square di€erence between the present 2; 0† positions for 11 BH and those determined by the combined results of the 48 J. Clark et al. / Chemical Physics Letters 340 (2001) 45±54 Table 1 Rotational line positions measured for the 0±2 band of A 1 P 11 X 1 R‡ transition of BH (cm 1 ) B 1H 10 Observed Calculated O)C R J† 0 1 2 3 4 5 6 7 8 27012.55 27029.92 27044.12 27054.81 27061.98 27065.50 27065.36 27061.38 27053.19 27012.71 27029.99 27044.00 27054.67 27061.87 27065.48 27065.33 27061.26 27053.02 Q J† 1 2 3 4 5 6 7 8 26989.06 26982.67 26972.75 26959.67 26943.24 26923.50 26900.05 26872.41 P J† 2 3 4 26941.64 26912.06 26878.92 a B 1H Observed Calculated O)C )0.16 )0.07 0.12 0.14 0.11 0.02 0.03 0.12 0.17 27025.41 27042.79 27056.94 27067.55 27074.60 27078.12 27077.80 27073.41 27025.73 27043.12 27057.19 27067.85 27075.00 27078.50 27078.19 27073.88 )0.32 )0.33 )0.25 )0.30 )0.40 )0.38 )0.39 )0.47 26989.02 26982.58 26972.88 26959.86 26943.43 26923.50 26899.94 26872.60 0.04 0.09 )0.13 )0.19 )0.19 0.00 0.11 )0.19 27001.32 26994.89 26985.13 26972.90 26955.03 27001.85 26995.32 26985.48 26972.26 26955.59 )0.53 )0.43 )0.35 0.64 )0.56 26941.85 26912.00 26879.03 )0.21 0.06 )0.11 26953.70 26923.81 26890.33 26954.30 26924.16 26890.85 )0.60 )0.35 )0.52 a O)C denotes the di€erences between observed line positions and those calculated using the constants of Table 3 in the formula m ˆ Tv0 Tv00 ‡ F 0 J 0 † F 00 J 00 †, where the prime refers to upper-state and the double prime to lower-state energies as determined by the conventional expression: F J † ˆ Bv J J ‡ 1† Dv ‰J J ‡ 1†Š2 ‡ Hv ‰J J ‡ 1†Š3 ‡ Lv ‰J J ‡ 1†Š4  J J ‡ 1†‰qv ‡ qDv J J ‡ 1†Š=2, where (+) refers to the P J † and R J † branches and ()) to the Q J † branch (see [35]). Fourier-transform measurements also calibrates the 10 BH A 1 P±X 1 R‡ 2; 0† spectrum, for which no such Fourier-transform data exists. The rootmean-square di€erence between the Fouriertransform and laser results for 11 BH, 0:2 cm 1 , serves as a reasonable measure of the uncertainty with which the current spectra determine transitions energies for A 1 P±X 1 R‡ 2; 0† lines in 11 BH and 10 BH. The spectrum observed at mass m ˆ 12 can be assigned exclusively to the A 1 P v0 ˆ 2†±X 1 R‡ v00 ˆ 0† transition in 11 BH in what must be a (1 ‡ 2)-photon resonant multiphoton ionization process. The spectrum at mass m ˆ 11 contains a similar set of features that can be assigned to the A 1 P v0 ˆ 2†±X 1 R‡ v00 ˆ 0† transition in 10 BH. This spectrum also contains other features that match precisely with the positions assigned for mass m ˆ 12 to 11 BH. This latter structure must be carried by 11 B‡ . The spectrum recorded at mass m ˆ 10 matches precisely with the subset of features in the mass m ˆ 11 scan that are assigned to the A 1 P v0 ˆ 2†±X 1 R‡ v00 ˆ 0† transition in 10 BH, and must therefore be carried by the 10 B‡ cation fragment. Thus, the spectra recorded at masses m ˆ 11 and 10 exhibit contributions from cation fragments, 11 B‡ and 10 B‡ , which appear with the resonant signatures of 11 BH and 10 BH. The question remains whether these B‡ ions are formed by ionization of neutral boron atoms following resonant photodissociation of BH, or by photofragmentation of resonantly produced BH‡ . The ionization potentials of BH and B are 9.77 and 8.296 eV, respectively [34]. The dissociation energy of BH is 3.42 eV [28]. Thus, to form B‡ at 370 nm by the resonant photodissociation of BH followed by the non-resonant three-photon 49 J. Clark et al. / Chemical Physics Letters 340 (2001) 45±54 Table 2 Estimated equilibrium molecular vibrational and rotational constants for the X 1 R‡ and A 1 P electronic states of Constants ‡ X 1R 11 Te xe xe x e Be ae ce De be D00e He He0 He00 Le L0e L00e qe q0e q00e qDe q0De q00De BH and 10 BH A 1P 10 BH )1170.39589 2364.65667 47.70980 12.025704 0.421591 0.003345 1:2344  10 3 2:2920  10 4:6500  10 7 9:88  10 8 1:14  10 9 1:53  10 9 4:50  10 12 ± ± ± ± ± ± ± ± 11 5 11 BH )1170.39589 2374.47892 48.10738 12.125918 0.426872 0.003401 1:2550  10 3 2:3400  10 4:7672  10 7 10:1  10 8 1:17  10 9 1:58  10 9 4:65  10 12 ± ± ± ± ± ± ± ± 5 10 BH 21934.7045 2342.4132 127.7618 12.199860 0.536736 )0.100776 1:4557  10 3 9:9160  10 1:2962  10 4 9:86  10 8 9:17  10 8 1:11  10 8 5:10  10 10 1:22  10 9 6:67  10 10 3:80  10 2 8:20  10 4 9:00  10 4 1:3437  10 8:0480  10 2:4620  10 6 5 5 6 BHa 21934.7045 2352.1530 128.8265 112.301526 0.543459 )0.102463 1:4801  10 3 10:124  10 1:3288  10 4 10:1  10 8 9:44  10 8 1:15  10 8 5:27  10 10 1:27  10 9 6:95  10 10 3:83  10 2 8:30  10 4 9:15  10 4 1:3662  10 8:2167  10 2:5241  10 6 5 5 6 a Constants for 11 BH are determined by polynomial ®ts to the spectroscopic parameters found for individual vibrational levels in the X 1 R‡ and A 1 P electronic states by Fourier-transform measurements (cf. Table 3) [13]. Vibrational constants for 10 BH are calculated as xe 1 q†, xe xe (1 q†2 , xe ye (1 q†3 , where xe , xe xe , xe ye , are the vibrational constants of 11 BH, and q ˆ l=li †1=2 in which l denotes reduced mass and i refers to 10 BH. Rotational constants of 10 BH are calculated as q2 Be , q4 De , q6 He , q8 Le , q2 qe and q4 qDe , respectively, where Be , De , He , Le , qe and qDe are the rotational constants established for 11 BH, see [35]. ionization of neutral B requires a total of ®ve photons. For probe frequencies that fall between A 1 P v0 ˆ 2†±X 1 R‡ v00 ˆ 0† resonances, we see little signal from the non-resonant three-photon ionization of boron atoms, despite the fact that a substantial B atom background is present from photolysis, as evidenced by large (2 ‡ 1)-photon atomic resonant ionization signals. Therefore, we judge the non-resonant three-photon ionization of photofragment boron atoms to be an unlikely source of the spectral signature recorded at the 11 ‡ B and 10 B‡ masses. Alternatively, the dissociation energy of BH‡ is only 1.95 eV [8,9]. Formation of B‡ from BH‡ following (1 ‡ 2) ionization of BH requires the absorption of just one additional 372 nm photon. It is therefore reasonable to conclude that the observed A 1 P± X 1 R‡ excitation spectrum arises from the ®rstphoton resonance condition in a overall (1 ‡ 2 ‡ 1) four-photon process. 3.2. Simulation of features in the A 1 P±X 1 R‡ (1 ‡ 2)-photon ionization-detected absorption spectrum We illustrate the comprehensiveness of the computed ®t to observed spectral positions by means of simulations. To calculate 2; 0† transition energies for 11 BH, we use the vibrationally dependent spectroscopic constants tabulated by Fernando and Bernath. Corresponding constants for the v ˆ 2 level of the A 1 P state of 10 BH are not available in the literature. To estimate these, we derive equilibrium molecular parameters by means of conventional polynomial ®ts to the 11 BH vibrationally dependent constants for v ˆ 0; 1 and 2. These equilibrium parameters can be mass scaled to obtain a companion set of equilibrium molecular parameters for 10 BH, from which to calculate vibrationally dependent spectroscopic constants for 10 BH A 1 P, v ˆ 0; 1; 2; . . . [35]. We test the 50 J. Clark et al. / Chemical Physics Letters 340 (2001) 45±54 Table 3 Vibrationally dependent spectroscopic constants for the X 1 R‡ and A 1 P states of State 11 10 a b BH BH 1 ‡a v X R 0 1 2 A 1 Pa 0 1 2 X 1 R‡b 0 1 2 A 1 Pb 0 1 2 Ref. [13]. Spectroscopic constants for Tv 0 2269.22707 4443.03454 23073.9708 25160.8602 26992.2261 0 2278.26416 4460.31356 23073.7576 25168.2576 27005.1047 10 Bv 103 Dv 11.815745 11.400848 10.992633 1.22305 1.20106 1.1800 11.906298 11.16801 10.22817 1.43853 1.5986 2.0179 11.913333 11.493263 11.079995 1.24347 1.22102 1.1995 12.004180 11.25580 10.30249 1.46267 1.6272 2.0575 11 BH and 108 Hv 9.86 10.052 10.55 5.00 )6.39 )20.0 10.11 10.308 10.82 5.10 )6.63 )20.7 10 BH 1011 Lv )4.50 )4.50 )4.50 )6.88 )18.7 )164 )4.65 )4.65 )4.65 )6.78 )19.2 )171 102 qv 105 qDv ± ± ± ± ± ± 3.7364 3.4736 3.0301 )1.6846 )1.997 )1.817 ± ± ± ± ± ± 3.8503 3.7503 3.4673 )1.7139 )2.031 )1.843 BH A 1 Pv ˆ 2 are derived from the mass-scaled equilibrium molecular constants listed in Table 2. validity of these estimates by comparing positions for A 1 P±X 1 R‡ 1; 1† and 0; 0† transitions in 10 BH, measured by Fernando and Bernath, to ones calculated from our parameters. This comparison yields a di€erence between observed and calculated positions that averages 0:057 cm 1 , which is slightly greater than that found for the comparative observed-minus-calculated positions of the basis 11 BH lines. A complete set of equilibrium molecular constants derived from the Fouriertransform data for 11 BH and mass scaled to represent 10 BH is given in Table 2. Spectroscopic constants for the ®rst three vibrational levels of the ±X 1 R‡ and A 1 P states of 11 BH and 10 BH are collected in Table 3. Di€erences between measured positions and ones calculated using these constants are included with experimental positions in Table 1. Spectra comparing experimental scans with simulated ones are shown in Figs. 2 and 3. 3.3. Non-Boltzmann rotational distributions Intensities in these simulated spectra are determined by assumed thermal populations of rotational states weighted by the appropriate HonlLondon factors for individual transitions. We have found it necessary to use a bimodal distribution to reproduce the observed structure. Nearly 90% of the intensity is carried by a distribution with a temperature of 40 K, which is typical of supersonically cooled photofragments. Evidence for this population can be found in the intense low-J PQR structure that dominates the center portions of these scans. In addition, one can clearly see weak high-J structure in the wings, particularly on the blue side at photon energies above the onset of an undulating non-resonant background. Judging by intensities, a population fraction of about 10% is required to explain these high-J features. The high rotational temperature of this outlying population suggests that BH molecules in these higher excited states are produced under low-pressure conditions, downstream from the cooling effects of the supersonic expansion. This additional contribution to the spectrum can be reasonably explained by the probe-laser photolysis of a BH precursor in the collection region of the mass spectrometer. Parent B2 H6 is transparent in the region of 370 nm, but its photolysis fragments are not. One in particular, open-shell BH2 , absorbs strongly throughout the visible and ultraviolet and dissociates to yield BH with unit quantum eciency for wavelengths shorter than 410 nm [2,36,37]. We propose that probe-laser photolysis of this higher hydride, formed by 193 nm irradiation at the exit of the pulsed jet, produces rotationally excited BH. This mechanism is consistent with our observation that the high-J BH signal also depends on the presence of the 193 nm photolysis pump. J. Clark et al. / Chemical Physics Letters 340 (2001) 45±54 51 Fig. 2. Spectra showing an experimental ionization-detected absorption scan at mass m ˆ 12 over the region from 368 to 372 nm compared with a simulation of the A 1 P±X 1 R‡ 2; 0† transition in 11 BH. The broad modulation of the baseline from 368 to 371 nm appears reproducibly in this region of the mass 11 and 12 spectrum and little elsewhere. This enhanced background production of BH may re¯ect a resonance in the absorption spectrum of BH2 , or correspond with a feature in the overall cross section for the (1 ‡ 2)-photon ionization of BH. 3.4. Photophysics of the (1 ‡ 2)-photon ionization of BH Structure associated with ®rst-photon resonant enhancement rarely appears in a three-photon ionization spectrum. Laser powers sucient to drive a second step of two-photon absorption usually suce to severely power broaden any ®rstphoton resonant transition. BH presents an obvious exception to this rule. A reasonable explanation for this unusual behavior can be seen in a speci®c feature of the electronic structure of this molecule. Fig. 4 diagrams the positions of the ®rst three electronic states of BH. Potential functions here are taken from ®ts by Luh and Stwalley to spectroscopic data [11]. Most relevant to the present discussion is the transition energy for the A 1 P±X 1 R‡ (2±0) band compared with the nearly equal gap from A 1 P 52 J. Clark et al. / Chemical Physics Letters 340 (2001) 45±54 Fig. 3. Spectra showing an experimental ionization-detected absorption scan at mass m ˆ 11 over the region from 368 to 372 nm compared with a simulation of the A 1 P±X 1 R‡ 2; 0† transition in 10 BH. v0 ˆ 2†±X 1 R‡ v ˆ 1†. This near-coincidence provides a mechanism by which the two-photon ionization of a level of A 1 P v0 ˆ 2†, ®rst-photonprepared at 370 nm, is enhanced by intermediate near-resonance with the B 1 R‡ v ˆ 1† state. To the red of this wavelength, photons resonant with the A 1 P±X 1 R‡ (1±0) band at 397 nm fall short of the B-state at the level of the second photon, and the ionization potential at that of the third. To the blue, light tuned to the energy of the A 1 P±X 1 R‡ (3-0) band at 350 nm corresponds closely with the B 1 R‡ ±A 1 P (2±3) transition. However, poor Franck±Condon factors for the ®rst step appear to diminish the importance of this facile two-photon ionization pathway. The strength of the (1 ‡ 2)-photon ionization signal in BH suggests that two-color strategies, employing ®rst-photon resonance with the strongest bands in the A 1 P±X 1 R‡ spectrum, will provide an e€ective stepwise means to reach selected higher excited states of this free radical, and, conversely, ionization assisted by higher intermediate states o€ers a general method to detect A 1 P± X 1 R‡ state absorption. 3.5. Non-adiabatic contributions to the energy of the A 1 P±X 1 R‡ system Experimental 10 BH positions are calibrated by the correspondence of accompanying 11 BH lines J. Clark et al. / Chemical Physics Letters 340 (2001) 45±54 53 Fig. 4. Potential energy diagram illustrating a mechanism by which two-photon ionization of photoprepared A 1 P BH can be assisted by intermediate near-resonance with the B 1 R‡ Rydberg state. with Fourier-transform data. Calculated 10 BH positions are obtained from ground- and excitedstate hamiltonians that have been derived to optimally ®t to 11 BH positions and then masscorrected to pertain to the lighter isotope. The residual di€erences between observed and calculated positions are slightly greater for 10 BH transitions. Given the estimated 0:1 cm 1 peakposition uncertainty in these scans, these increased di€erences between calculated line positions and those observed for 10 BH are barely signi®cant. They are nevertheless suggestive. More comprehensive measurements at higher resolution over more vibrational levels for the isotopic modi®cations, 11 BD and 10 BD, should help to establish whether these mass-scaling deviations point systematically to non-adiabatic terms in the rovibronic energy. When employed in double-resonant excitation stragegies for ionization, such as those which make use of the B 1 R‡ state, mass-resolved ionizationdetected absorption can provide well-distinguished line positions for all of the isotopic modi®cations of BH. Under such circumstances, a higher resolution source could be employed in an intensity regime for which features are una€ected by power broadening. We plan to extend this work to include such scans, which should shed de®nitive light on the magnitude of nonadiabatic contributions to the electronic structure of this benchmark molecule. Acknowledgements This work was supported by the Director, Oce of Energy Research, Oce of Basic Energy 54 J. 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