Frank-Hertz experiment. Why only intervals of 4.9ev?

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The Frank-Hertz experiment demonstrates that free electrons excite mercury atoms primarily at intervals of 4.9 eV due to the likelihood of these interactions at specific temperatures and energies. Higher energy levels are accessible, but the mean free path of electrons is affected by pressure, which limits their ability to collide with mercury atoms before losing energy. As electrons are accelerated to higher energies, they can reach higher excited states, but this becomes less probable under certain conditions. The 4.9 eV interactions remain dominant until around 100 eV, where other effects start to play a role. Understanding these dynamics is crucial for interpreting the results of the experiment.
JaktheAce
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I was presenting my data on the Frank-Hertz lab to a lab class when I was asked by the professor why the interactions only happened in intervals of 4.9eV. Why weren't the free electrons exciting the mercury atoms to other energy levels?

My answer was that I suspected at these temperatures and energies, this interaction was simply much more likely than other interactions, but I could not explain this physically. Researching online, the only information that I could find relevant to this was that the 4.9eV interactions occur up 100ev, after which other effects become significant.

I was hoping someone here had a substantive answer why the electrons only seem to interact with mercury in intervals of 4.9ev. Thank you!
 
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Pressure is also important here, as it will affect the mean free path of the electrons. Basically, you would need to accelerate an electron to higher energies, in order to reach higher excited states in Hg, before it collides with an atom.
 

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