Duration of Molecules in Upper Quantum States

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: $A_{21}=\left(\frac{8\pi {\nu }^2}{c^2{N}_1}\right)\left(\frac{p_1}{p_2}\right)\int 0^{\infty }\alpha d\nu$ where $A_{21}$ is the chance per unit time that a molecule will jump spontaneously from quantum state 2 to quantum state 1, $\nu$ is the frequency of the light emitted in such a jump, $p_1$ and $p_2$ are the a priori probabilities of quantum states 1 and 2, and $\alpha$ is the absorption coefficient of the substance measured under conditions such that $N_1$ is the number of molecules per unit volume in the lower quantum state 1. The integral $\int \alpha d\nu$ 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 $\tau$ of molecules which decay from state 2 to state 1 is the reciprocal of $A_{21}$. Values of $A_{21}$ and $\tau$ are calculated from existing data for the mercury line $\lambda 2537$, for a number of lines belonging to the alkali doublets, for the iodine line $\lambda 5461$, 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.