Elastic electron-atom collision effects in the Franck--Hertz experiment

In the Franck--Hertz experiment one observes the effect of inelastic collisions in which fixed quanta of energy are exchanged between electrons and atoms. It is shown here that one can also readily demonstrate with a Franck--Hertz apparatus energy-dependent features of the elastic collision cross section. For mercury vapor of sufficiently high pressure, elastic electron--atom collisions between the grid and the anode are able to energy analyze the electrons so that the characteristic peaks and troughs in the anode current are still observed without the traditional retarding field to separate off the lowest-energy electrons. This is because in mercury vapor the most energetic electrons have the longest mean free path, are more penetrating through the gas, and are the most likely electrons to reach the anode. The electron transport theory for this effect is developed and applied to a crude determination of the electron energy distribution. Not surprisingly, the electron energy distribution in this experiment consists of two electron groups separated in energy by 4--5 eV consistent with the known 61S-63P energy-level separation in mercury of 4.9 eV