Let's take the mercury atom 20280Hg into consideration. Its valence electron when in the ground state has the energy of Ep=-10,42eV. The energy of the first state of excitation equals E1=-5,54eV. To empower the electron to jump up to the excited state we need the energy of:
And what would happen if shooting a beam of electrons through the gaseous mercury? Well, if the energy of those electrons is lower than 4.88eV, then we will see nothing special happening. But if their energy exceeds 4.88eV, then they can collide with the mercury atoms giving them 4.88eV of energy - and that means exciting them. After such collision the energy of the electron will be lower by 4.88eV. So if the electron initially had more energy than 2*4.88eV, it can cause more than one excitation.
In 1914 James Franck and Gustav Hertz confirmed the phenomenon experimentally. Their scientific equipment consisted of a vessel filled with gaseous mercury. A net divided the inside of the vessel into two parts. At one end there was a source of electrons (the cathode), and at the opposite end there was the anode. The electrons leaving the cathode were speeded up by an electric field between the cathode and the net. And they were slowed down between the net and the anode (Some of them were, of course, completely stopped.). There was an electrometer connected to the vessel and measuring the current flow through the vessel. The higher the accelerating voltage, the more current flow. That is because more electrons can pass the area of the moderating voltage. But when the accelerating voltage achieves some multiple of 4.88V, then the current flow drops. All because some of the electrons can collide the Hg atoms giving them energy. Having given the energy away, these electrons can't get through the moderating area. That was the effect observed by Hertz and Franck. And it also was another proof for Bohr's theory.
In 1925 the both scientists were awarded the Nobel Prize.
