Absorption and Collision Broadening of the Mercury Resonance Line

Radiation emitted by a mercury resonance lamp. It is shown how an approximate expression for the frequency distribution of the radiation from a resonance lamp can be arrived at, and that it can be represented approximately by a Gauss error curve with a half-breadth depending upon the geometry of the lamp and upon the vapor density, and in general greater than that of the absorption line.Absorption coefficient and ratio of emission to absorption line breadth. Assuming that all five components of the mercury resonance line are alike both in emission and in absorption, and that any one component of the emission and of the absorption line is a Gauss error curve of half-breadth $\ensuremath{\Delta}{\ensuremath{\nu}}_{E}$ and $\ensuremath{\Delta}{\ensuremath{\nu}}_{D}$ respectively ($\ensuremath{\Delta}{\ensuremath{\nu}}_{D}=\mathrm{Doppler}\mathrm{broadening}$), the absorption of a slab of thickness $l$ is calculated as a function of $\ensuremath{\kappa}({\ensuremath{\nu}}_{0})l$, where $\ensuremath{\kappa}({\ensuremath{\nu}}_{0})$ is the absorption coefficient for the center of any one of the components. From experimental values of the absorption, $\ensuremath{\kappa}({\ensuremath{\nu}}_{0})$ is found to be consistent with the theoretical value $1.41\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}N$ (where $N$ is the number of Hg atoms per cc) provided $\frac{\ensuremath{\Delta}{\ensuremath{\nu}}_{E}}{\ensuremath{\Delta}{\ensuremath{\nu}}_{D}}$ is taken to be 1.21 in these experiments, 1.46 in Orthmann's, 1.50 in Hughes and Thomas', 1.15 in Kunze's, and 1.15 in Kopfermann and Tietze's.Lorentz collision broadening of the absorption line. A theoretical expression is obtained for the absorption coefficient when collision broadening is superimposed upon Doppler broadening, and is evaluated for different values of the frequency and of $\frac{\ensuremath{\Delta}{\ensuremath{\nu}}_{C}}{\ensuremath{\Delta}{\ensuremath{\nu}}_{D}}$ where $\ensuremath{\Delta}{\ensuremath{\nu}}_{C}$ is the Lorentz collision breadth and $\ensuremath{\Delta}{\ensuremath{\nu}}_{D}$ is the Doppler breadth. With $\ensuremath{\kappa}({\ensuremath{\nu}}_{0})l$ and $\frac{\ensuremath{\Delta}{\ensuremath{\nu}}_{E}}{\ensuremath{\Delta}{\ensuremath{\nu}}_{D}}$ equal to the values found for these experiments, the absorption is calculated as a function of $\frac{\ensuremath{\Delta}{\ensuremath{\nu}}_{C}}{\ensuremath{\Delta}{\ensuremath{\nu}}_{D}}$. From experimental values of the absorption of mercury vapor in the presence of ${\mathrm{H}}_{2}$, ${\mathrm{N}}_{2}$, A, CO, N${\mathrm{H}}_{3}$, He, C${\mathrm{H}}_{4}$, and ${\mathrm{C}}_{3}$${\mathrm{H}}_{8}$, $\ensuremath{\Delta}{\ensuremath{\nu}}_{C}$ is found as a function of the pressure of each gas. The curves of $\ensuremath{\Delta}{\ensuremath{\nu}}_{C}$ against pressure yield the effective broadening radius of each molecule, which is found to be directly proportional to the square root of the molecular diamagnetic susceptibility. On the basis of the Langevin theory this means that the effective broadening area of a molecule varies at the product of the number of outer electrons and the mean square radius of all the electronic orbits. The same result is obtained from the experiments of F\"uchtbauer, Joos and Dinkelacker.