To demonstrate, through the study of collisions between electrons and gas molecules, that the energy is indeed quantized in atomic interactions.


A mercury-filled Franck-Hertz tube, an electric oven, a neon-filled Franck-Hertz tube, a control unit providing various power supplies and a DC current amplifier, and digital oscilloscope.


Simplified Circuit for Franck-Hertz Experiment

In an oven-heated vacuum tube containing mercury gas, electrons are emitted by a heated cathode, and then accelerated toward a grid that is at a potential, Va, relative to the cathode. The anode (plate) is at a lower potential, Vp = Va - DV. If electrons have sufficient energy when they reach the grid, some will pass through and reach the anode. They will be measured as current Ic by the ammeter. If the electrons do not have sufficient energy when they reach the grid, they will be slowed by DV, and will fall back to the grid.  As long as the electron/molecule collisions are elastic, the collector current depends only on Va and DV since the electrons lose no energy. However, Franck and Hertz discovered that Ic went through a series of maxima and minima as Va was varied. This implies that the gas molecules absorb energy from the electrons only at specific electron energies (resonant energies).

For example, the first excited state of mercury is 4.9 eV above the ground state. This is thus the minimum energy that mercury atoms can absorb from the accelerated electrons. Hence, if Va< 4.9 volts, any collisions are elastic and if Va >
DV, many electrons pass through the grid and reach the anode, to be measured as Ic. If Va= 4.9 volts, the electrons gain enough kinetic energy to collide inelastically with the mercury atoms just when they reach the grid. In these interactions, the mercury atoms absorb 4.9 eV. Thus, the electrons lose the same amount and no longer have sufficient energy to overcome DV. They fall back to the grid and Ic is a minimum. As Va is raised beyond 4.9 volts, Ic increases again. However, when Va reaches 9.8 volts, the electrons can lose all their energy in two collisions with mercury atoms in two inelastic collisions between the cathode and grid. Again, these are pushed back onto the grid, and Ic falls to a minimum. Current minimum are found whenever Va is a multiple of 4.9 volts.

This simplified description neglects contact potentials. Therefore, Va will need to be somewhat higher than 4.9 volts when the first minimum occurs. Nevertheless, all successive current minima should differ by multiples of 4.9 volts from the first minimum.  The spectral frequency corresponding to this energy is 1.18 x 10-15 Hz and the wavelength is 253.7 nm.
  In their original experiments, Franck and Hertz verified the presence of the ultraviolet radiation with the aid of a quartz spectrometer.

Neon has 10 energy states in the range between 18.3eV and 19.5eV.  From these excited levels, the Ne atoms decay to other excited states. These intermediate states decay to the ground state by emitting visible radiation and can be seen in a tube with the room darkened.