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Can anyone explain to me how the Franck-Hertz experiment works? (in term of electric current and voltage changes) I am getting all confused.

More specifically, why is an accelerating grid (or mesh grid) needed in the experiment, and what is the accelerating grid? And why would the accelerating grid exhibit positive charge at first?

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The experiment basically collides electrons with mercury atoms and measures how much the electrons are scattered. Can you be a bit more specific about what aspects of the experiment you don't understand? –  John Rennie Jun 26 '12 at 16:23

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In the experiment, the cathode was held at some voltage $V_C$ and the anode was held at a voltage $V_A>V_C$, so that electrons would be emitted from the cathode and strike the anode. In a vacuum, the amount of kinetic energy an electron arriving at the anode had would be proportional to the difference in voltage $V_A-V_C$. But the experiment was conducted in a tube filled with mercury vapor, with which electrons might collide and thus lose energy. The experiment was designed to measure this loss, so they needed some way to distinguish between electrons with different amounts of kinetic energy. This is where the grid comes in. The grid was held at a voltage $V_G>V_A$, and so electrons passing through the grid (it was assumed only a small fraction collided with it) did one of two things:

  • If they had enough kinetic energy to overcome the potential difference $V_G-V_A$, they would continue on to the anode, thus contributing to the current between the cathode and the anode.
  • If they had too little kinetic energy, they would eventually fall to the grid and contribute to the current between the cathode and the grid.

Thus by comparing the two currents, Frank and Hertz were able to determine what fraction of electrons had less than a certain amount of kinetic energy. By calculating the expected amount of kinetic energy the electrons would have in a vacuum, they were able to determine what fraction of electrons had lost a certain amount of energy to collisions. Since almost all of this energy loss was due to inelastic collisions which raised the energy level of n electron in the Mercury atom, they were able to predict this using the Bohr model. The agreement of these predictions with the experiment provided support for the Bohr model.

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It's actually a myth that you need the deccelerating grid, at least for Hg. If you ever have the chance to do the experiment turn off the grid voltage and you should still be able to get Franck-Hertz curves. It has to do with the fact that $e^{-}+\text{Hg}$ has an enormous elastic scattering resonance at low energies. The proper transport theory (based on the Boltzmann equation) is able to explain all of this, but not as intuitively as your explanation. Read the work of Nicoletopoulos, Robson or R.D. White. The latter two work at my university and coached me through this experiment. :) –  Michael Brown Jan 2 '13 at 0:27
    
The key insight regarding the elastic scattering is that the picture of electrons freely streaming through the Franck-Hertz tube except for the occasional inelastic collision is completely wrong. The transport is dominated by elastic collisions (diffusion, essentially), and the potential just gives a slight bias to the motion. –  Michael Brown Jan 2 '13 at 0:30

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