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Rotational specific heat and half quantum numbers

Tolman, Richard C. (1923) Rotational specific heat and half quantum numbers. Physical Review, 22 (5). pp. 470-478. ISSN 0031-899X. doi:10.1103/PhysRev.22.470.

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Application of half quantum numbers to the theory of the rotational specific heat of hydrogen.—It is shown from a consideration of infra-red rotation-oscillation spectra, that the lowest possible azimuthal quantum number for a non-oscillating rotating molecule of the rigid "dumb-bell" model can have only the values zero, one, or one-half. An elementary theory of quantization in space for the new case of half quantum numbers is then developed which shows that the a priori probabilities for successive levels of rotational energy stand in the ratios of 1, 2, 3,.... The specific heat curve for diatomic hydrogen to 300°K is then calculated on the basis of the energy levels and of a priori probabilities corresponding to half quantum numbers, and is compared with the experimental points and with the curves calculated by Reiche using zero and one as the lowest possible azimuthal quantum number. At low temperatures the new curve agrees with the experimental data as well as any curve of Reiche's. At the higher temperatures, none of the curves agree with all the experimental points. The moment of inertia for the hydrogen molecule corresponding to the new curve is J=1.387×10^-41 gm cm2, about two-thirds the values assumed by Reiche, 2.095 to 2.293×10^-41, and agrees better with the conclusion of Sommerfeld from the separation of lines in the many lined spectrum of hydrogen, that the moment of inertia of an excited hydrogen molecule is 1.9×10^-41 gm cm2, which should be greater than that of the unexcited molecules involved in specific heats. Hence the possibility of half quantum numbers seems worthy of consideration.

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Additional Information:©1923 The American Physical Society. Received 16 May 1923. In conclusion the writer wishes to express his appreciation to Professors Charles G. Darwin and Paul S. Epstein for very helpful suggestions and criticisms.
Issue or Number:5
Record Number:CaltechAUTHORS:TOLpr23b
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2410
Deposited By: Tony Diaz
Deposited On:03 Apr 2006
Last Modified:08 Nov 2021 19:47

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