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Duration of molecules in upper quantum states

Tolman, Richard C. (1924) Duration of molecules in upper quantum states. Physical Review, 23 (6). pp. 693-709. ISSN 0031-899X. http://resolver.caltech.edu/CaltechAUTHORS:TOLpr24

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Abstract

Values of rate of decay and mean life of atoms and molecules in upper quantum states calculated from data on the intensity of absorption lines.—By combining Füchtbauer's method of determining from the intensity of absorption lines the probability that a molecule will absorb a quantum of energy, with Einstein's views as to the mechanism of light absorption and emission, the following equation is derived for calculating the rate at which molecules jump from upper to lower quantum states: A21=8πν2/c2N1p1/p2∫0∞αdν where A21 is the chance per unit time that a molecule will jump spontaneously from quantum state 2 to quantum state 1, ν is the frequency of the light emitted in such a jump, p1 and p2 are the a priori probabilities of quantum states 1 and 2, and α is the absorption coefficient of the substance measured under conditions such that N1 is the number of molecules per unit volume in the lower quantum state 1. The integral ∫αdν is to be taken over the total effective width of the absorption line corresponding to the passage of molecules from quantum state 1 to quantum state 2. The mean life τ of molecules which decay from state 2 to state 1 is the reciprocal of A21. Values of A21 and τ are calculated from existing data for the mercury line λ2537, for a number of lines belonging to the alkali doublets, for the iodine line λ5461, and for a very considerable number of lines belonging to the rotation-oscillation spectra of the hydrogen halides. The values obtained agree with the meager data made available by other experimental methods. From these results the following conclusions are drawn. The mean life of molecules and atoms in upper quantum states may vary for different states at least over the range 1 to 10-8 seconds. The rate of decay is not a simple function of the frequency of the emitted light. The rate corresponding to the emission of a line of high frequency may be greater or less than that for a line of lower frequency. The data now available for the alkali doublets 1s-mp1 and 1s-mp2 indicate a higher rate of decay the smaller the change in total quantum number for the line under consideration. The rate of decay from a given mp1 state is m times as great as from the corresponding mp2 state (already stated in another form by Füchtbauer and Hofmann). In the case of the rotation-oscillation spectra of the hydrogen halides the rate of decay is greater for quantum states with one unit of oscillation and many of rotation, than for those with one unit of oscillation and only a few of rotation; and in the case of different molecules but the same quantum numbers the rate of decay is greater for the molecule with the greater frequency of oscillation. Finally the possibility and method of calculating absolute values of A21 from the Bohr correspondence principle is indicated.


Item Type:Article
Additional Information:©1924 The American Physical Society. Received 10 January 1924. The writer wishes to express his thanks to Mr. James B. Friauf for assisting in the computations involved in the article.
Record Number:CaltechAUTHORS:TOLpr24
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:TOLpr24
Alternative URL:http://dx.doi.org/10.1103/PhysRev.23.693
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2411
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:03 Apr 2006
Last Modified:26 Dec 2012 08:48

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