What really happens with the electron gas in the famous Franck-Hertz experiment?

Abstract

The interpretation of the anode current characteristics obtained in the famous Franck-Hertz experiment of 1914 led to the verification of Bohr's predictions of quantised atomic states. This fundamental experiment has been often repeated, and nowadays is generally part of the curriculum in modern physics education. However, the interpretation of the experiment is typically based upon significant simplifying assumptions, some quite unrealistic. This is the case especially in relation to the kinetics of the electron gas, which is in reality quite complex, due mainly to non-uniformities in the electric field, caused by a combination of accelerating and retarding components. This non-uniformity leads to a potential energy valley in which the electrons are trapped. The present state of understanding of such effects, and their influence upon the anode characteristics, is quite unsatisfactory. In this article a rigorous study of a cylindrical Franck-Hertz experiment is presented, using mercury vapour, the aim being to reveal and explain what really happens with the electrons under realistic experimental conditions. In particular, the anode current characteristics are investigated over a range of mercury vapour pressures appropriate to the experiment to clearly elaborate the effects of elastic collisions (ignored in typical discussions) on the power budget, and the trapping of electrons in the potential energy valley. Show more