Editing Franck–Hertz experiment (section)

== Modelling of electron collisions with atoms ==
[[File:FHcollisions.svg|thumb|upright=0.5|Elastic and inelastic collisions of electrons with mercury atoms. Electrons travelling slowly change direction after elastic collisions, but do not change their speed. Faster electrons lose most of their speed in inelastic collisions. The lost kinetic energy is deposited into the mercury atom. The atom subsequently emits light, and returns to its original state. |alt=Drawing showing three circles, each with a label "Hg" inside. The top circle is labelled "elastic collision". It is next to two arrows of equal length, one pointing towards the circle, and one pointing away. The middle circle is labelled "inelastic collision", and has a longer arrow pointing towards it, and a shorter arrow leading away. The lowest circle is labelled "light emission", and is next to a squiggly arrow that points away.]]

Franck and Hertz explained their experiment in terms of [[elastic collision|elastic]] and [[inelastic collision]]s between the electrons and the mercury atoms.<ref name=FH1 /><ref name=Lemmerich /> Slowly moving electrons collide elastically with the mercury atoms. This means that the direction in which the electron is moving is altered by the collision, but its speed is unchanged. An elastic collision is illustrated in the figure, where the length of the arrow indicates the electron's speed. The mercury atom is unaffected by the collision, mostly because it is about 400,000 times more massive than an electron.<ref name=Melissinos /><ref name=Demtroeder />

When the speed of the electron exceeds about 1.3 million metres per second,<ref name=Nuffield /> collisions with a mercury atom become inelastic. This speed corresponds to a kinetic energy of 4.9&nbsp;eV, which is deposited into the mercury atom. As shown in the figure, the electron's speed is reduced, and the mercury atom becomes "excited". A short time later, the 4.9&nbsp;eV of energy that was deposited into the mercury atom is released as ultraviolet light that has a wavelength of 254&nbsp;nm. Following light emission, the mercury atom returns to its original, unexcited state.<ref name=Melissinos /><ref name=Demtroeder />

If electrons emitted from the cathode flew freely until they arrived at the grid, they would acquire a kinetic energy proportional to the voltage applied to the grid. 1 eV of kinetic energy corresponds to a potential difference of 1 volt between the grid and the cathode.<ref name=Thornton /> Elastic collisions with the mercury atoms increase the time it takes for an electron to arrive at the grid, but the average kinetic energy of electrons arriving there is not much affected.<ref name=Demtroeder />

When the grid voltage reaches 4.9&nbsp;V, electron collisions near the grid become inelastic, and the electrons are greatly slowed. The kinetic energy of a typical electron arriving at the grid is reduced so much that it cannot travel further to reach the anode, whose voltage is set to slightly repel electrons. The current of electrons reaching the anode falls, as seen in the graph. Further increases in the grid voltage restore enough energy to the electrons that suffered inelastic collisions that they can again reach the anode. The current rises again as the grid potential rises beyond 4.9&nbsp;V.  At 9.8&nbsp;V, the situation changes again.  Electrons that have travelled roughly halfway from the cathode to the grid have already acquired enough energy to suffer a first inelastic collision. As they continue slowly towards the grid from the midway point, their kinetic energy builds up again, but as they reach the grid they can suffer a second inelastic collision. Once again, the current to the anode drops.  At intervals of 4.9 volts this process will repeat; each time the electrons will undergo one additional inelastic collision.<ref name=Melissinos /><ref name=Demtroeder />