A Method for the Estimation of the Average Life of Excited Mercury Atoms

Average life of excited mercury atoms.—(1) In mixtures with hydrogen, computed from rate of dissociation of hydrogen, found by Franck and Cario. A theory is developed which gives the relation between the rate of dissociation of ${\mathrm{H}}_2$ molecules by collision with excited Hg atoms and the pressure of ${\mathrm{H}}_2$, when the rate of production of excited Hg atoms is kept constant. It is shown to be in accord with Franck and Cario's experimental results, leading to a value for ${\sigma }^2\tau$ of 7.22 ${10}^{-22\mathrm{}}$, where $\sigma$ is the distance between centers of ${\mathrm{H}}_2$ molecules and excited Hg atoms at a collision and $\tau$ is the average duration of the excited state. Assuming $\sigma$ to be of the order of magnitude of atomic diameters, $\tau$ is found to be about ${10}^{-7\mathrm{}}$ sec. The equation derived here and a different one of Cario's are compared and the former found to be in better agreement with experiment. (2) In mixtures with air, computed from diminution of the fluorescence by adding air, found by R. W. Wood. The same theory is applied to the fluorescence experiments of Wood, assuming a constant rate of production of excited atoms, but the agreement is not good. The theory is extended to cover the possibility of successive impacts of the excited Hg atom, and the form of the relation is found to be the same in this case. It is found that the theory does accord qualitatively with the experimental data of higher pressures, indicating an increased rate of production of excited Hg atoms for the same illumination, and a smaller value of $\tau$ with air than with ${\mathrm{H}}_2$.