On the Molecular Spectrum of Hydrogen emitted by an Arc Discharge.

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1 On the Molecular Spectrum of Hydrogen emitted by an Arc Discharge. By Hirosi HASUNUMA. (Read July 19, 1937.) Introduction and Summary. In 1923 Kiuti(1) found that the molecular spectrum of hydrogen emitted by an electric arc runned in hydrogen atmosphere was very much different in relative intensities of lines from the ordinary many-lined spectrum obtained with Geissler discharge. He selected out certain lines in the yellow region which were specially enhanced in the arc spectrum as forming a band series. The series was considered by him as to constitute a compound band system together with Fulcher bands, the only band series known at that time. In the light of the theory of band spectra fully developed since then and from the very complete band analysis of hydrogen made by Richardson and others(2), this explanation is not right. The series which Kiuti obtained is nothing but a series of alternate lines of the R-branch belonging to 3d3IIb-2p3II, 0-0 band in Richardson's analysis. After Kiuti, Sandeman and Allen(3) also investigated the arc spectrum of hydrogen by somewhat different conditions of excitation, and besides verifying Kiuti's series, gave several other series which they attributed to triatomic hydrogen. That the hydrogen spectrum emitted by an arc makes an appearance much different from the ordinary one is seen, e.g., in the reproduction Fig. 1. It contains not only lines observed in the ordinary spectrum, with different relative intensities, but also a number of new lines. The reexamination of the arc spectrum seemed to be very desirable, and the author worked with much the same conditions of are as Kiuti, and the results of analysis will be communicated in the following. Branches of various bands of hydrogen as observed hitherto are extended to the 6th or 7th member, maximum intensity occuring near the band origin. It is naturally expected that in the spectrum of arc (1) M. Kiuti, Proc. Phys. Math. Soc. Japan, 5, 9 (1923). (2) O. W. Richardson, Molecular Hydrogen and its Spectrum (Yale University Press, 1934). (3) I. Sandeman, Proc. Roy. Soc. London A. 108, 607 (1925); 110, 326 (1927). H. S. Allen and I. Sandeman, Proc. Roy. Soc. London A. 114, 293 (1927).

2 126 Hirosi HASUNUMA. [Vol. 20 still higher members can be excited. In fact it was found in the present experiment that in the bands belonging to the electronic transitions 3d3, 3IIb, 3IIa, 3 b, 3 a-2p3ii and 3p3II-2s3 ( -band), with vibrational transitions 0-0 and 1-1 for all, branches could be traced up to the 12th or even to the 21st member, being verified by intensity relations and to some extent by the combination principle, and maximum intensity being displaced to the 7th or 8th member. For some bands the arrangement of various rotational lines were not very regular, or they stopped at a certain member rather abruptly. These may be explained by perturbations among upper terms. Almost all of intense lines emitted by the arc were identified to members of known band series. Experimental procedure. The light source used was an electric arc lighted in hydrogen gas of nearly atmospheric pressure between a cathode of 0.25 mm thick tungsten wire and an anode of tungsten block. It was started by direct contact of the electrods, and maintained with a current of about 2.6 A which was supplied from 330 volt accumulators through sufficient series resistance. The arc consisted of a narrow filament of intense pink light running from the whitely heated cathode to a spot on the surface of anode also heated to nearly white. The filament was focused on the slit of a spectrograph by a condensing lens, which must be frequently adjusted during the exposure as the anode spot travelled along the anode surface. The spectrograph was of a Littrow type and consisted of a plane grating, 6 x 8 cm2 ruled surface, and an objective of 160 cm focus. The third order spectrum, which had dispersions 3.1 A/mm in the red and 3.3 A/mm in the green, was employed. For comparison with the arc spectrum, ordinary Geissler spectrum was produced by a discharge tube having a illuminating portion 50 cm long and 6 mm thick and equipped with water-cooling arrangement to permit a large current (300 ma). Both spectra were photographed in juxtaposition, and wave-lengths of new lines were determined in reference to known ones in the Geissler spectrum, the wave-lengths of the latter being taken from the measurement of Gale, Monk and Lee(1). The Geissler spectrum contained more lines than were measured by G.M.L., many of them coinciding with new lines from the arc. The spectrum of the are thus obtained consisted of intense and broad Balmer lines, molecular lines and continuous radiation super- (1) H. G. Gale, F. S. Monk and K. O. Lee, Astrop. J. 67, 89 (1928). The author used the abbreviation G.M.L. for their name in the following.

3 On the Molecular Spectrum of Hydrogen emitted. 127 Fig. 1.

4 128 Hirosi HASUNUMA. [Vol. 20 imposing. Owing to this continuous background detection of faint lines were difficult. Strong molecular lines rather gathered in the yellow and orange region and there appeared no conspicuous linegroups in the blue and violet region. ave-numbers. Wave-numbers W of lines emitted by the arc and their eye-estimated intensities (A) are listed in Table 1, togather with the intensities given by G.M.L. (G). The classifications of them are given in the last column. Bars - in the intensity G column denote that the lines have been recorded neither by G.M.L. nor by Merton and Barratt(1). M.B. denote the lines which have not been given by G.M.L., but given by Merton and Barratt. The letters a, b and h attached to the figures in the column G are what G.M.L. used, while b in the column A means that the line was very broad. For lines belonging to the -band or to 3d3, 3IIb, 3IIa, 3 b, 3 a-2p3ii are given full designations such as b0-0 Q3, meaning Q3 of the band 3d3 b-2p3ii, 0-0. For the rest of lines only their initial electronic states are indicated. These classifications contain those already made by Richardson and others,(2) and those which were made in the present work (italic). Accuracy in the wave-numbers of new lines is limited by broadness of arc lines, the errors amounting to 0.1 cm-1 in general and larger errors may be expected for blended lines. The breadths of arc lines were about 0.3 or 0.4 cm-1, an amount which can be explained by the Doppler broadening. Any shifts of known lines have not been observed. It must be noted that all the lines but one that have been recorded by Merton and Barratt and not by G.M.L. appeared in the arc spectrum with intensities greatly increased. The 0-0 band of 3d3-2p3II and 3d3IIb-2p3II. The distinctive appearance of the spectrum of arc is due to the presence of two series of strong lines, one extending from yellow to red with intervals about 75) cm-1 and the other being Kiuti's series. It is found that the former is the R-branch of the 3d3-2p3II, 0-0 baud of Richardson prolonged to higher members, while the latter, supplemented with a less intense parhydrogen line in each interval, constitutes the R-branch of the 3d3IIb-2p3II, 0-0 band. The search for higher members for these series was easy as they were regularly spaced and there were no other con- (1) T. R. Merton and S. Barratt, Phil. Trans. Roy. Soc. A 220, 369 (1922). (2) Richardson's book (loc. cit.); Richardson and Rymer, Proc. Roy. Soc. London A 147, 24, 251, 272 (1934).

5 1938] On the Molecular Spectrum of Hydrogen emitted. 129 TABLE 1.

6 130 Hirosi HASUNUMA. [Vol. 20 TABLE 1. (Continued)

7 1938] On the Molecular Spectrum of Hydrogen emitted. 131 TABLE 1. (Continued)

8 132 Hirosi HASUNUMA. [Vol. 20 TABLE 1. (Continued)

9 1938] On the Molecular Spectrum of Hydrogen emitted. 133 TABLE 1. (Continued)

10 134 Hirosi HASUNUMA. [Vol. 20 TABLE 1. (Continued)

11 19381 On, the Molecular Spectrum of Hydrogen emitted. 135 TABLE 1. (Continue )

12 136 Hirosi HASUNUMA. [Vol 20 spicuous lines. The extensions thus made being assumed to be correct, the extension of the Q- and P-branches of the same bands was then tried. This was at first made also by regularity of spacings, and then was verified by combination relations. The latter consisted of taking rotational differences of the final states from each band. The results of extension are given in Table 2 a and b, in which lower members of each series already investigated by Richardson are given in italic, and the final rotational differences in Table 4. The final rotational differences obtained from different bands are fairly constant. The intensities of members varied in a regular way within each series, with alternation for every other member, excepting lines which are blends. The maximum of intensity occurred at higher members (the 7th or 8th member) in the arc spectrum than in the case of G.M.L. The Geissler spectrum used by the author for comparison corresponded to a little higher temperature and gave more lines for each series than that of G.M.L., and served much in classification. In the 3d3-2p3II band, while the R-branch were very strong and traced as far as K=19, probably extending farther over the limit of TABLE 2. The 3d triplet complex-2p3ii 0-0 bands. a) The 3d3-2p3II band. * Blended lines

13 1938] On the Molecular Spectrum of Hydrogen emitted, 137 TABLE 2. (Continued) (1) Richardson's value: R (0a; -). (2) Richardson's value : R (1 ; --), Q (2h ; 3*).

14 138 Hir si HASUNUMA. [Vol. 20 TABLE 2 (Continued) (1) Richardson's value : P (6); It is difficult to separate from a line definitly, but the centre of the arc line seems to be displaced toward shorter wave length side of the corresponding Geissler line , (2) Richardson's value : R (0 ; ); Q (0 ; 1). the present observation, the Q-branch was weak and the P-branch could not be extended at all. Thus the hither members of the R-branch could not be verified by combination relations. In the band 3d3IIb-2p3II, the Q-branch was very weak or absent in lower members and became

15 1938] On the Molecular Spe trum of Hydrogen emitted. 139 stronger in higher ones. The distribution of intensity among different branches of a band and also that within a branch may be explained by the effect of uncoupling occuring in the upper states, and it is very interesting that these distributions, including also the cases of other bands, are entirely in parallel with those in the corresponding bands in helium which were studied by Fujioka and Kronig(1) experimentally and theoretically. Uncoupling occurs to a greater degree in hydrogen than in helium, and the present 3d bands may be compared rather with the case of 4d complex, instead of 3d complex in He. The R-branch of the 3d3IIb-2p3II band were developed to a line as high as K=21. The energy level of the upper state of the R(21) line, i.e. 3d3IIb v=0, K=22(2), is about cm-1 above K=1 level of the 3d3IIb, v=0. The K=22 level is hence to lie 2070 cm-1 below the ionization limit(3) of H2, and farther it is higher than the highest known v=4 level. The lower level, 2p3IIa, v=0, K=21 is about m-1 above 2p3IIa, v=0, K=1. c (1) R. de L. Kronig and Y. Fujioka, Zeits. Phy. 63, 168 (1930)_ Y. Fujioka, Zeits. Phy. 63, 175 (1930). (2) The rotational differences of the upper and the lower states could he known only up to the 18th rotational level exactly ; this value, cm-1 was obtained by extrapolation from there. (3) The value of the energy level 2p3II, v=0, K=1 relative to the ionization limit is determined in the following ways. (i) Richardson obtained a Rydberg-Ritz type formula v=a-r/(n /n2) for 0-0, Q(1) lines of the bands np3ii-2s3, n=3,4,.. 8 The running term, extrapolated to n=2, gives the values 29503cm-1 for the depth of 2p3II, v=0, K=I below ionized molecule having one rotational quantum. (O. W. Richardson, Proc. Roy. Soc. London A, 113, 368 (1926)) (i') Richardson also applied the Rydberg-Ritz formula to v0's of the same bands p3ii-2s3 (n=3,4,5). From it the value cm-1 is obtained for ve of 2p3II n by extrapolation. As Richardson used hand formula of the old quantum theory, it suffices to subtract the rotational energy for K=1, 68.2cm-1, in order to get the term value of 2p3II, v=0, K=1 relative to the ionized molecule without rotation nor vibration. The latter is given as 29378cm-1. (Richardson's book p. 184). (ii) Rydberg formula may be applied to the series nd3, 3IIb, 3IIa, 3 b-2p8ii (n=3,4). The fixed terms are determined to he 29681, 29740, 29664, and 29425cm-1 corresponding to the four series. The mean value 29635cm-1 may be considered as the term value of 2p3II without rotation, but this value may be inaccurate because the above series contain only few members and further because the upper states are strongly uncoupled and irregular. (Richardson's book p. 243). (iii) The fixed term of the Rydberg-Ritz formula mentioned in (i') gives the term value ve of 2s3, v=0, K=0 as cm-1. Then that of 2s3, v=0, K=3 is cm-1, as the rotational difference F(3)-F(0) is cm-1. Now according to Kiuti and IIasu-

16 140 Hirosi HASUNUMA. [Vol. 20 The 0-0 bands of 3d3IIa-2p3II, 3d3 b-2p3ii and 3d3 a-2p3ii. The extention of these bands was done at the same time as the above bands, in such a way that the same final rotational differences could be obtained for all, and the results are given in Tab. 2 ; e, d and e. The band 3d3 a-2p3ii stopped abruptly at the lines whose upper term is 3d3 a, v=0, K=9, the energy of the last term being lower than expected by regularity. The stopping may not mean complete absence of still higher members, but that the anomaly in spacing made further extension difficult. This perturbation may be due to interaction of the levels 3d3 a, v=0 with the levels 3d3, v=1, as will be mentioned later. The 1-1 bands of 3d3, 3IIb, 3II, 3 b, 3 1-2p3II. The extension of these bands was carried out in a similar manner as in the case of the 0-0 bands. The result and the rotational differences of the final v=l states are tabulated in Tabs. 3 and 5 respectively. Contrary to the case of the 0-0 band, the 3d3-2p3II, 1-1 band showed strong perturbation, and the extension of its, branches ceased at the lines whose common upper term is 3d3, v=1, K=8. The last term had a higher energy than is expected. The other 1-1 bands showed less strong perturbations like those of the 2d3IIa, 3 b-2p3ii 0-0 bands. The author tried to extend the 2-2 band and others of the same systems. They were very weak and definite results could not be obtained. Perturbation. As mentioned above, sonic bands showed anomalies obviously due to perturbations' of the upper states. Especially those of 3d3 a-2p3ii, 0-0 and 3d3-2p3II, 1-1 were very distinguished. Now, on examining the height of various upper levels it is found that just the term sequences 3d3 a, v=0 and 3d3, v=1 are to cross each other at a point between K=9 and K=10 (Fig. 2). Thus it is expected that perturbation occurs near this point very strongly, as the observation really revealed it. and a terms do not perturb each other properly, but in the present case, owing to strong uncoupling effect, higher terms of the 3d3, v=1 or the 3d3 a, v=0 possess also numa (Proe. phy. Math. Soc. Japan 19, 821 (1937)). The term 2p3II, v=0, K=4 is 8cm-1 above 2s3, v=0, K=3, i.e., 28929cm-1. From the rotational difference of 2p3II, v=0 F( 4)-F(1)=538.5cm 1, the term values of 2p3II, v=0, K=1 becomes 29468cm-1. This may be the most reliable one as the calculation do not include any extrapolation. In the text the values 29408cm-1 for 2p8II, v=0, K=1 and hence, 12340cm-1 for 3d3IIb, v=0, K=1 were taken.

17 1938] On the Molecular Spectrum of Hydrogen, emitted. 141 TABLE 3. The 3d triplet complex-2p3ii 1-1 bands. (1) Richardson's value: R (0; -).

18 142 Hirosi HASUNUMA. [Vol. 20 TABLE 3 (Continued)

19 1938] On the Molecular Spectrum of Hydrogen emitted. 143 Fig. 2. The relative position of term systems 3d3IIa and 3 a v=0 and 3d3 v=1. (The dotted lines are extrapolated ones.) the properties of 3IIa and 3 a or 3 and 3IIa respectively. The perturbation will be of the same nature as that which Dieke(1) treated in the case of 3p triplet complex. Similar interactions may occur among other upper states of v=0 and v=1 respectively. The 3d3 b, v=0 and 3d3IIb, v=1, being m-1 apart at K=2, approach within cm-1 at K=14, while c the 3d'IIU and 3d345 v=0 which interact in uncoupling have interval cm-1 at K=14. 3d3IIa v=0 and 3d3 v=1 approach within 235 cm-1 at K=15 (extrapolated), while the interval between 3d3 and 3IIa v=0 is cm-1 at K=15. These approaches between different terms may cause anomalies in intervals of band series, which seemed to be verified experimentally to some extent. Recently the 3d1, 1IIa and 1IIb which are analogous to the present upper states were investigated by Dieke and Lewis(2). They found a deviation from uncoupling formula in the states 3d1 and 1IIa while the 1IIb is normal, and attributed the deviation to the perturbation by 3s1. Similar perturbation by 3s3 may be expected(3) in the present 3d3, 3IIa and 3 a, as the 3s3 which was analysed by Richardson and Rymer(4) falls in the same region with 3d complex. The 3s3 series runs nearly parallel with 3d3IIa on the lower energy side of it, and thus it may displace 3d3IIa to the higher energy, and the 3d3 to the lower. The interaction between 3s3 and 3d3IIa is to become large at higher members as the distance of them seems to decrease at higher members, although the 3s3-2p3II band were too weak to be extended. The rotational structure of the upper and the lower states. The rotational structure of the final 2p3II states can be obtained from Tabs. 4 and 5. The final rotational differences consist of two independent sets ; the one (1) G. H. Dieke, Phys. Rev. 48, 610 (1935). (2) G. H. Dieke and M. N. Lewis, Phys. Rev. 52, 100 (1937). (3) The higher members of IIa and a may have property by uncoupling. (4) O. W. Richardson and T. B. Rymer, Proc. Roy. Soc. London A, 147, 24 (1934).

20 144 Hirosi HASUNUMA. [Vol. 20 of them relates to antisymmetrical and the other to symmetrical terms. As symmetrical and antisymmetrical terms do not intercombine, the absolute intervals of the A-type doubling of 2p3II states can not be known. If the doublet interval at K=1 of v=0, which is probably very small, be put zero, the values of successive rotational terms can be calculated. In Fig. 3 the intervals of the A-type doubling for the successive members are given. TABLE 4. Final rotational differences of the 3d triplet complex-2p3ii 0-0 bands.

21 1938] On the Molecular Spectrum of Hydrogen emitted. 145 TABLE 5. Final rotational differences of the 3d triplet complex-2p3ii 1-1 bands. Fig. 3. The A-type doubling of 2p3Ii v= 0 and I states. 3p3IIa -3p3IIb. The usual rotational term formula containing terms up to K2(K+1)2 is insufficient to express the rotational structure thus obtained. By introducing the 3rd order term K3(K+1,3 the rotational terms up to about K=13 can be well expressed, but for higher levels the 4th order term K4(K+1)4 are needed.

22 146 Hirosi HASUNUMA. [Vol. 20 TABLE 6. The Rotational Difference of Sd3, 3IIb, 3IIa, 3 b, and 3 a. The coefficients of higher order terms suffer considerable alteration by slight modifications of final rotational differences, which are possible owing to presence of blended lines etc., and so the numerical values of them will not be given. From the knowledge of the final rotational structure, those of the initial states can be obtained, and the differences of successive rotational terms are given in Tab. 6, The quantum-number R in the first column means K-* where * has the values +2, +1, 0, -1 and -2 for 3, 3IIb, 3IIa, 3 b and 3 a respectively. We can see from the table that for the higher terms the coupling is of Hund's d-type, A-uncoupling being nearly perfect. The author, however, has given up detailed theoretical calculation, and applied the formula, which was used by Kronig and Fujioka(1) in dealing with the uncoupling in Helium bands, to the present term series 3d3IIb and 3 b v=0 which suffer comparatively small perturbations. If W1(K) and W2(K) be the term values of 3IIb and 3 b respectively then after Kronig and Fujioka (1) R. de L. Kronig and Y. Fujioka ; Y. Fujioka loc. cit.

23 1938] On the Molecular Spectrum of Hydrogen emitted. 147 where W0 Hence and B12 are constants. must be independent of K. From the observation, the A's for successive K have been obtained as given in Tab. 7. They are not constant, but change regularly with increasing K.(1) The -bands. With respect to the -bands, Q-branches of 0-0 and 1-1 could be also considerably extended, and to the 0-0 P-branch two lines were added (Tab. ). These extensions were made mainly 8 depending on apparent regularity of spacing of lines and on the behaviour of each lines in the arc and the comparison Geissler spectra. The irregularity and vanishing of the TABLE 8 The (3d3II-2s3 ) bands. (1) One of the causes of the inconstancy may be that the formula of Kronig and Fujioka takes only the 1st order term, proportional to K(K+1)-2 in the matrix element 12 of uncoupling into account; in the hydrogen molecule, however, the effect of higher order terns may be considerable as is the case with the rotational formula This may mean that B12 is no more constant.

24 148 Hirosi HASUNUMA. [Vol. 20 Fig. 4. The A-type doubling of 3p3II v=0. R- and P-branches of 1-1 band has been explained by Dieke(1) by the perturbation of 3p3, v=4 levels on 3p3II6, Fig. 5. The relative position of term systems 3p3IIb v=0 and 3p3 v=3. (The dotted lines are extrapolated ones.) v=1 levels. The R- and P- branches of the 0-0 band seem to undergo also effect of perturbation and could not be extended except that P8 and 9 were added. This perturbation may be due to interaction between 3p3, v=3 state and 3p3IIt, 0, as their relative v= positions are such as shown in Fig. 5. The A-type doubling derived from the observation is represented by Fig. 4. The downward deviation of it for higher members and the vanishing of lines beyond K=9 are what can be expected from the same perturbation. In conclusion the author expresses his sincere thanks to Professor M. Kiuti for kind guidance throughout this work. Department of Physics, Faculty of Science, Tokyo Imperial University. (Received November 15, 1937.) (1) G. H. Dieke, loc. cit.

by Wood,I Fuchtbauer2 and others; and for mercury, cadmium, lead, The apparatus used in the present work with zinc was similar to that

by Wood,I Fuchtbauer2 and others; and for mercury, cadmium, lead, The apparatus used in the present work with zinc was similar to that 738 PHYSICS: J. G. WINANS PRoc. N. A. S. approaches the normal effect more and more closely as k, increases, so that this also would probably resemble a normal triplet. The patterns which we should expect