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

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SUMMARY

The Frank-Hertz experiment demonstrates that free electrons excite mercury atoms at specific energy intervals of 4.9 eV. This phenomenon occurs due to the likelihood of interactions at these energy levels, particularly at lower temperatures and energies. Beyond 100 eV, other interactions become significant, complicating the excitation process. Additionally, pressure influences the mean free path of electrons, necessitating higher energies to achieve excitation of higher states in mercury before collisions occur.

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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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