The usual schematic representing the setup of Frank-Hertz experiment is the following:

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However, sometimes, you can see a bit different schematic:

enter image description here

My question is: what function does $V_{G_1K}$ serve?

I understand that this constant offset is irrelevant to the experiment (because what matters is the difference in accelerating potential, not its absolute value), but I'm curious and want to check my intuition.



The gate G1 is there to help pull electrons off the cathode, increasing the overall current. This exploits the so called Schottky effect to lower the effective surface barrier ("work function") of the metal cathode. Electrons are emitted by thermionic emission, which is exponentially sensitive to the barrier because the probability of an electron to have a given energy $E$ inside the metal due to the temperature $T$ is proportional to $\exp(-E/k_B T)$. So anything you do to reduce the barrier to emission helps increase the overall current greatly. With an applied field to increase emission people speak of "field enhanced thermionic emission."

  • $\begingroup$ Why can't electrode $G_2$ serve this function? $\endgroup$ – Vasiliy Jul 25 '13 at 2:57
  • $\begingroup$ @VasiliyZukanov In principle it could, only I believe it would be impractical given tube sizes and voltages etc. Also, you don't want the Franck-Hertz oscillations and the Schottky effect to get jumbled together in your data. :) $\endgroup$ – Michael Brown Jul 25 '13 at 4:22
  • $\begingroup$ @VasiliyZukanov By the way, if you are doing the classic Franck-Hertz experiment with mercury, I strongly recommend you try unplugging G2. You don't even need it to see Franck-Hertz curves, in contradiction to all the textbooks! If you want to understand what is really going on look up the papers by P. Nicoletopoulos, or R. Robson and R.D. White. It has to do with the elastic collision cross section which, in Hg, has a huge resonance right at low energies where it needs to be to ruin the textbooks. It doesn't work for neon because the elastic cross section is better behaved. :) $\endgroup$ – Michael Brown Jul 25 '13 at 4:26
  • $\begingroup$ thx. It was my intuition that the function of $G_1$ is to screen the cathode from the changing potential on $G_2$. It is not that the emission will be larger in presence of $G_1$, on contrary - it will be smaller, but constant during the whole experiment. Please edit your answer so I can accept it. $\endgroup$ – Vasiliy Jul 25 '13 at 8:59

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