Franck-Hertz: Overall behaviour of the current

[greypilgrim]

Hi.

The blue curve shows the idealized behaviour of the detected current vs. the acceleration voltage in a Franck-Hertz experiment:

1. It appears that the underlying behaviour is quadratic, why? I calculated the time for an electron to reach the grid at distance ##d## from the hot cathode to be $$t=d\cdot\sqrt\frac{2m_e}{U_B\cdot e}\enspace.$$ Now I'm not sure how to use this. How many electrons are released at the hot cathode per second? Does this depend on ##U_B## as well? I think so, otherwise there shouldn't be an overall increase of the blue curve at all.
2. Why isn't the first drop at exactly 4.9 V? Is there still energy needed to release electrons even from a hot cathode? This would probably agree with 1., but is there a simple quantitative relation?

 

[Charles Link]

What is the gas that was used as the medium? You can expect the current to increase with voltage. Whether it can be expected to be a quadratic dependence is something I'm not sure of. The places where the current drops considerably are where the gas has atomic transitions and absorbs energy. ## \\ ## Edit: I googled it=if mercury (Hg) is used as the medium, 4.9 volts is the place where the first dip occurs. Perhaps you had something other than mercury. ## \\ ## As for the temperatures on the graphs=is that the cathode temperature for different cases? I don't have sufficient expertise with this particular experiment to know whether T=190 C is a suitable cathode temperature. As plasma arcs go, that is a very cool cathode, but perhaps it is sufficient for the Franck-Hertz experiment.