Rotational Raman Spectrum of CO2

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I am indebted to the Award Committee of the Sigma Xi Society for a grant, which aided me in the preparation of this paper. 1 E. D. Williams and L. N. Adams, J. Wash. Acad. Sci., 13, 419, 1923. H. Jeffreys, The Earth, 2nd Edition, Chap. 12. 3 Celia H. Paine, Stellar Atmosphere, Harvard Univ. Press, 1925. ' R. A. Millikan and C. Cameron, Phys. Rev., 32, 533, 1928. 5 H. Jeffreys, The Earth, Chap. 8. 6 J. H. Jeans, Astronomy and Cosmogonoy, 2nd Edition, Chap. 5. 7 A. M. Berkenheim, Zest. f. Phys. Chem., 141A, 35, 1929. 8 L. Pauling, Zeit. f. Krystailographie, 67, 379, 1928. 2

ROTATIONAL RAMAN SPECTRUM OF CO2 BY W. V. HOUSTON AND C. M. LEWIs NORMAN BRIDGE LABORATORY OF PHYSICS, CALIFORNIA INSTITUTE OF TECHNOLOGY

Communicated February 18, 1931

The Raman effect provides a convenient means of studying the rotation spectrum of many molecules, and avoids many of the difficulties inherent in work in the infra-red. The principal obstacle to rapid work is the low intensity of the scattered light. This may necessitate an inconveniently long exposure time, if a high dispersion spectrograph is used. However, by extending the methods first used by Rasetti,1 we have been able to get good photographs of the oxygen rotation band in two hours. The gas is contained in a quartz tube about 20 in. long and 1 in. inside diameter. The walls are 1/16 in. thick and have withstood a pressure of 400 lbs. per sq. in. Although the increased pressure improves the intensity, it also broadens the lines to such an extent that the CO2 rotation band cannot be resolved at pressures much above 75 lbs. per sq. in. The exciting source is a water-cooled mercury arc in the form of a very narrow U. Its effective length is about 35 in. and it operates with 10 amp. The arc and the tube are enclosed in a chromium-plated cylindrical reflector which serves to conserve the light as well as to support the apparatus. A small dish of mercury is placed inside the Hilger E1 spectrograph. This reduces the intensity of the scattered X2536 exciting line to such an extent that it is nearly the same as its ordinarily weak companion, X2534. Since the structure of the CO2 band is almost at the limit of resolution of the spectrograph, it is necessary to control the temperature very carefully during the 10 or 12 hours of the exposure. For this purpose the spectrograph is enclosed in a box made of celotex, and the temperature of the room outside is maintained constant within half a degree by a thermostat.

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PHYSICS: HOUSTON AND LEWIS

PROe. N. A. S.

Figure 1 is a tracing made from a microphotometer curve of one of the CO2 plates. The rotation band appears to be composed of equidistant lines, with no evidence of the irregularities in spacing and intensity which would be produced by the presence of more than one moment of inertia.

The measured values of the wave-length changes are given in table 1. Since the position of the over-exposed exciting line is rather hard to deTABLE 1 n

J

1 2 3 4 5 6 7 8 9* 10 11 12

0

13 14 15 16 17 18

2 4 6 8 10

12 14 16 18 20 22 24 26 28 30 32 34

OBS. .

.

.

.

.

.

11.58 14.76 18.25 21.59 24.52 27.58 30.66 33.92 37.08 40.21 43.42 46.45 49.84 52.46 55.54

SHIFT IN CM -1 CALC.

2.36 5.51 8.66 11.81 14.96 18.11 21.26 24.41 27.56 30.71 33.86 37.01 40.16 43.31 46.46 49.61 52.76 55.91

OBS. *

. .

..

. . ..

.

8.93 -11.67 -14.91 -18.02 -21.46 -24.67 -

....

.

-30.73 -33.29 -36.97 -40.23 -43.36 -46.52 -49.50 -53.46 .....

termine, the shifts are measured from a point half-way between the positively and negatively shifted lines. This differed by 0.36 cm.-' from the estimated position of the mercury line.

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The calculated wave numbers are from the equation v = (3.150/8) (4J + 6). (1) This formula, together with the values used for J, shows that the rotational quantum number, J, changes by two units in a transition, that only even rotational states are present, and that the moment of inertia is 70.2 X 10-40 g. cm.2 Since the positions of the lines are probably not more than 0.5 cm.-' in error, this value for the moment of inertia is probably correct within one or two per cent. The large difference between this value and the ordinarily accepted one due to Barker2 may indicate that the rotation of the molecule is very considerably disturbed by its vibration. If this were true one might also expect that the moment of inertia would increase appreciably for values of J as high as 30. However, the measurements are not precise enough to make sure as to this point. The uniqueness of the above interpretation of equation (1) is guaranteed by the fact that the position and the ordinal number n of the line nearest the intensity maximum can be determined. (The * in table 1 indicates this line.) Let a be the number of units by which J changes in a transition, and let a be the number of units between one existing value of J and the next. Then (2) EJ= BhcJ(J + 1) and (3) Av = 2a6B where AV is the wave number difference between two adjacent lines in the Raman spectrum. Also, from the relative population of the rotational states, J* = (n* - 1)6 + a = (kT/2Bhc)'/2 - 1/2 (4) where n* is the ordinal number of the strongest line, and a is the lowest value of J. Furthermore, (5) V* = a { (2BkT/hc)"12 + aB} and vl = aB (2a + a + 1), (6) where vi is the shift of the first line. From the last four equations the quantities a, 6, and a can be shown to lie nearest the integers 2, 2, and 0. With these values equation 3 gives B equal to (3.150/8). 1 F. Rasetti, Phys. Rev., 34, 367, 1929. 2 E. F. Barker, Astrophys. J., 55, 391, 1922.