The Franck–Hertz experiment was the first electrical measurement to clearly show the quantum nature of atoms. It was presented on 24 April 1914, to the German Physical Society in a paper by James Franck and Gustav Hertz. Franck and Hertz had designed a vacuum tube for studying energetic electrons that flew through a thin vapour of mercury atoms. They discovered that when an electron collided with a mercury atom, it could lose only a specific quantity (4.9 electron volts) of its kinetic energy before flying away. This energy loss corresponds to decelerating the electron from a speed of about 1.3 million metres per second to zero. A faster electron does not decelerate completely after a collision, but loses precisely the same amount of its kinetic energy. Slower electrons merely bounce off mercury atoms without losing any significant speed or kinetic energy.
These experimental results proved to be consistent with the Bohr model for atoms that had been proposed the previous year by Niels Bohr. The Bohr model was a precursor of quantum mechanics and of the electron shell model of atoms. Its key feature was that an electron inside an atom occupies one of the atom's "quantum energy levels". Before the collision, an electron inside the mercury atom occupies its lowest available energy level. After the collision, the electron inside occupies a higher energy level with 4.9 electronvolts (eV) more energy. This means that the electron is more loosely bound to the mercury atom. There were no intermediate levels or possibilities in Bohr's quantum model. This feature was "revolutionary" because it was inconsistent with the expectation that an electron could be bound to an atom's nucleus by any amount of energy.
In a second paper presented in May 1914, Franck and Hertz reported on the light emission by the mercury atoms that had absorbed energy from collisions. They showed that the wavelength of this ultraviolet light corresponded exactly to the 4.9 eV of energy that the flying electron had lost. The relationship of energy and wavelength had also been predicted by Bohr because he had followed the structure laid out by Hendrik Lorentz at the 1911 Solvay Congress. At Solvay, Hendrik Lorentz suggested after Einstein's talk on quantum structure that the energy of a rotator be set equal to nhv. Therefore, Bohr had followed the instructions given in 1911 and copied the formula proposed by Lorentz and others into his 1913 atomic model. Lorentz had been correct. The quantisation of the atoms matched his formula incorporated into the Bohr model. After a presentation of these results by Franck a few years later, Albert Einstein is said to have remarked, "It's so lovely it makes you cry."
On 10 December 1926, Franck and Hertz were awarded the 1925 Nobel Prize in Physics "for their discovery of the laws governing the impact of an electron upon an atom".
Franck and Hertz's original experiment used a heated vacuum tube containing a drop of mercury; they reported a tube temperature of 115 °C, at which the vapour pressure of mercury is about 100 pascals (about a thousandth of the atmospheric pressure). A contemporary Franck–Hertz tube is shown in the photograph. It is fitted with three electrodes: an electron-emitting, hot cathode; a metal mesh grid; and an anode. The grid's voltage is positive relative to the cathode, so that electrons emitted from the hot cathode are drawn to it. The electric current measured in the experiment is due to electrons that pass through the grid and reach the anode. The anode's electric potential is slightly negative relative to the grid, so that electrons that reach the anode have at least a corresponding amount of kinetic energy after passing the grid.
The graphs published by Franck and Hertz (see figure) show the dependence of the electric current flowing out of the anode upon the electric potential between the grid and the cathode.
At low potential differences—up to 4.9 volts—the current through the tube increased steadily with increasing potential difference. This behaviour is typical of true vacuum tubes that do not contain mercury vapour; larger voltages lead to larger "space-charge limited current".
At 4.9 volts the current drops sharply, almost back to zero.
The current then increases steadily once again as the voltage is increased further, until 9.8 volts is reached (exactly 4.9+4.9 volts).
At 9.8 volts a similar sharp drop is observed.
While it is not evident in the original measurements of the figure, this series of dips in current at approximately 4.9 volt increments continues to potentials of at least 70 volts.
Franck and Hertz noted in their first paper that the 4.9 eV characteristic energy of their experiment corresponded well to one of the wavelengths of light emitted by mercury atoms in gas discharges. They were using a quantum relationship between the energy of excitation and the corresponding wavelength of light, which they broadly attributed to Johannes Stark and to Arnold Sommerfeld; it predicts that 4.9 eV corresponds to light with a 254 nm wavelength. The same relationship was also incorporated in Einstein's 1905 photon theory of the photoelectric effect. In a second paper, Franck and Hertz reported the optical emission from their tubes, which emitted light with a single prominent wavelength 254 nm. The figure at the right shows the spectrum of a Franck–Hertz tube; nearly all of the light emitted has a single wavelength. For reference, the figure also shows the spectrum for a mercury gas discharge light, which emits light at several wavelengths besides 254 nm. The figure is based on the original spectra published by Franck and Hertz in 1914. The fact that the Franck–Hertz tube emitted just the single wavelength, corresponding nearly exactly to the voltage period they had measured, was very important.
Modelling of electron collisions with atoms
Franck and Hertz explained their experiment in terms of elastic and inelastic collisions between the electrons and the mercury atoms. Slowly moving electrons collide elastically with the mercury atoms. This means that the direction in which the electron is moving is altered by the collision, but its speed is unchanged. An elastic collision is illustrated in the figure, where the length of the arrow indicates the electron's speed. The mercury atom is unaffected by the collision, mostly because it is about 400,000 times more massive than an electron.
When the speed of the electron exceeds about 1.3 million metres per second, collisions with a mercury atom become inelastic. This speed corresponds to a kinetic energy of 4.9 eV, which is deposited into the mercury atom. As shown in the figure, the electron's speed is reduced, and the mercury atom becomes "excited". A short time later, the 4.9 eV of energy that was deposited into the mercury atom is released as ultraviolet light that has a wavelength of 254 nm. Following light emission, the mercury atom returns to its original, unexcited state.
If electrons emitted from the cathode flew freely until they arrived at the grid, they would acquire a kinetic energy proportional to the voltage applied to the grid. 1 eV of kinetic energy corresponds to a potential difference of 1 volt between the grid and the cathode. Elastic collisions with the mercury atoms increase the time it takes for an electron to arrive at the grid, but the average kinetic energy of electrons arriving there is not much affected.
When the grid voltage reaches 4.9 V, electron collisions near the grid become inelastic, and the electrons are greatly slowed. The kinetic energy of a typical electron arriving at the grid is reduced so much that it cannot travel further to reach the anode, whose voltage is set to slightly repel electrons. The current of electrons reaching the anode falls, as seen in the graph. Further increases in the grid voltage restore enough energy to the electrons that suffered inelastic collisions that they can again reach the anode. The current rises again as the grid potential rises beyond 4.9 V. At 9.8 V, the situation changes again. Electrons that have travelled roughly halfway from the cathode to the grid have already acquired enough energy to suffer a first inelastic collision. As they continue slowly towards the grid from the midway point, their kinetic energy builds up again, but as they reach the grid they can suffer a second inelastic collision. Once again, the current to the anode drops. At intervals of 4.9 volts this process will repeat; each time the electrons will undergo one additional inelastic collision.