The early years of quantum physics, from Einstein’s explanation of the photoelectric effect in 1905 through the introduction of the Schrödinger equation in 1926, was a remarkable time for science and filled with novel ideas, speculations, and experiments. In the teaching of physics, some of these results get more attention, and some absolutely beautiful experiments are not discussed as often as others, as they are not essential to understanding the phenomena, even if they were essential in proving them.

One example of this I’ve had on my mind for some time is the Franck-Hertz experiment, reported in 1914. This experiment was the first demonstration that the energy levels of atoms are quantized, and that an atom can only absorb or emit energy in discrete amounts referred to as “quanta.” I did the Franck-Hertz experiment as an undergraduate, and it has always stuck with me. A few years ago, I tried to track down the original paper, but found to my surprise that it was extremely difficult to find — even an attempt to acquire it through Interlibrary Loan failed! This week, however, I took another look, and managed to get the original paper in German and translate it, and wanted to share a description of it here.

First, a little background: one of the big puzzles of the late 19th century was the existence of discrete absorption and emission spectra for atoms. A general beam of light can be decomposed into its different colors by using a prism, just like Pink Floyd’s classic Dark Side of the Moon album cover illustrates:

The color pattern can then be projected onto a screen, to determine which colors are present and how bright each of them are. If one does this for sunlight, you get a nearly continuous rainbow pattern.

There are, however, dark lines spotted throughout the spectrum. It was quickly recognized that these dark lines represent discrete colors that are absorbed by the different atomic elements in the sun. Each element has its own unique discrete set of lines at which it will absorb light, and if heated, that element will emit light with the same spectral lines. For example, hydrogen has four lines that can be observed in the visible part of the spectrum.

So the spectral lines of each element clearly tell us something about the atomic structure of that atom, but what do they tell us? This was an unexplained puzzle for many years, until Niels Bohr argued in 1913 that the electrons of an atom can only orbit the nucleus at discrete orbital positions, and that an atom can only absorb or emit light energy by jumping from one of these orbital positions to another.

This model has one very important consequence: it suggests that an atom cannot in general absorb an arbitrary amount of energy, but can only absorb energy equal to that required to make an electron “jump.” If an atom is hit with a photon (light particle) or an electron with an energy lower than the amount required to make the smallest jump, that photon or electron will not transfer energy to the atom — it suffers what is known as an elastic collision.

It is important to note that Bohr’s model is not a very good picture of what electrons are actually doing in an atom; one might say that it is a transition model that allowed physicists to break out of their classical physics way of thinking and embrace the new quantum physics. More realistically, an electron has wave-like properties, as first predicted by Louis de Broglie, and the “discrete orbital positions” that Bohr envisioned are really standing waves of the electron surrounding the nucleus, as illustrated below.

But Bohr’s basic vision holds: an electron normally stays in one of these “stationary states” of discrete energy, and can only jump from one state to another by absorbing or emitting a characteristic transition energy.

None of this, ironically, was known to the German physicists James Franck and Gustav Hertz¹ when they did their experiments and published their results in 1914,² even though Bohr’s work had been released a year earlier. As James Franck later said in an interview, with some humor, in 1961,³

It might interest you that when we made the experiments that we did not know Bohr’s theory. We had neither read nor heard about it. We had not read it because we were negligent to read the literature well enough– and you know how that happens. On the other hand, one would think that other people would have told us about it. For instance we had a colloquium at that time in Berlin at which all the important papers were discussed. Nobody discussed Bohr’s theory. Why not? The reason is that fifty years ago one was so convinced that nobody would, with the state of knowledge we had at that time, understand spectral line emission, so that if somebody published a paper about it, one assumed, ‘Probably it is not right.’

Franck and Hertz were interested in studying the ionization of atoms, i.e. the removal of an electron from the atom. It was well-known at that time, and had been studied by many researchers, that a fast-moving electron, if its energy was high enough, could collide with an atom and liberate one of its bound electrons. Franck and Hertz had done earlier experiments to measure how much energy was required to liberate electrons from gases of various atoms, but in 1914 they introduced a new technique to determine this ionization energy with much higher precision.

They made three assumptions, based on earlier experiments, that seemed reasonable to them:

• Electrons that hit an atom with energy much lower than the ionization energy are unlikely to transfer energy to the atom.
• If the electron can cause ionization, it will give all of its energy to the atom to free the bound electron.
• If the electron has energy equal to or greater than the ionization energy, it is almost certain to cause ionization in a collision.

In a stroke of good luck, though these assumptions do not apply to ionization energy, they apply to the discrete transition energies of an atom!

An illustration of their experiment, which is somewhat different from modern iterations, is shown below.

A sealed glass container contains a few drops of liquid mercury, and the entire container is heated, producing a controllable density of mercury vapor throughout. A platinum wire runs through the center of the chamber, thinner along a portion of its length. When a current is run through this wire, the thinner portion heats up and emits slow-moving electrons. A positive electrical potential difference is set up between the wire and the platinum mesh (let’s call it the wire-mesh potential), causing electrons to be accelerated towards the mesh; between the mesh and the ground, a small negative potential difference is set up, which will repel the electrons.

It can help by drawing a picture of what the potential energy of the electron looks like as the electron leaves the wire. We can imagine the electron rolling down a hill as it approaches the mesh, gaining speed (kinetic energy) as it goes. If nothing obstructs it, the electron will be moving very fast when it reaches and passes through the mesh; it will lose a little bit of energy going “uphill” to the ground, but not enough to stop it. We therefore have a current flowing from the wire to the ground.

Now let us imagine that the mercury vapor is present, and we turn up the voltage V of the wire-mesh potential from zero. If nothing happens to an electron in transit from the wire to the mesh, the energy of it at the mesh will simply be V electron volts.

When V is small, and smaller than the smallest transition energy of the mercury atoms, the electrons will basically bounce off of the mercury atoms in elastic collisions. The electrons might change direction, and some of them might not make it to the ground because of this, but overall most of the electrons will reach the ground plane. As V is increased, more electrons will make it to ground, and the current will increase.

But when V matches the transition energy of mercury, the electrons reaching the mesh will have just enough energy to excite a mercury atom, and they will donate all their energy to the mercury. Those electrons will be stopped dead at the mesh, and won’t have enough energy to reach the ground. The measured current will drop. If V is increased, those electrons will dump their energy into mercury closer to the wire, and will then be able to gain enough speed continuing “downhill” to reach the ground; the current starts to increase again. When V reaches twice the transition energy of mercury, however, the electrons will be stopped dead again right at the mesh, and won’t be able to make it to ground. Again, we will see a dip in current. And this process will repeat as V is increased further, to three times the transition energy, and so on.

The key plot from the paper by Franck and Hertz is shown below. The horizontal axis is the wire-mesh potential, and the vertical axis is the measured current. As the potential is increased, we see the current increase right up to the level of about 4.9 volts, when there is a big drop; another big drop happens at roughly 9.8 volts, and again at 14.7 volts. This indicates that the mercury atoms have a lowest energy transition of 4.9 electron volts; this image shows the discrete nature of atomic energy levels.

It is worth noting that the actual ionization voltage of mercury is 10.39 electron volts, significantly larger than the lowest transition energy.

The observation of discrete energy transitions in atoms was impressive enough, but Franck and Hertz had one more significant observation to make. Other researchers had noted that mercury vapor has a natural emission/absorption line, like those discussed for hydrogen above, with a wavelength of λ = 253.6 nanometers. In his explanation of the photoelectric effect, Einstein hypothesized that the energy E of a photon is given by

,

where c is the speed of light and h is another fundamental constant known as Planck’s constant. In Bohr’s model of the atom, he predicted that atoms would radiate photons according to this same rule. Franck and Hertz noted that, with the choice λ = 253.6 nanometers, the calculated energy of the photon is 4.84 electron volts, incredibly close to their calculated transition energy of 4.9 electron volts! They had found evidence that the atomic excitation of mercury observed with electrons is the same excitation seen with photons.

Franck and Hertz went even further in a follow-up paper. If the electrons are exciting mercury atoms into a higher energy state, then those mercury atoms must eventually release that energy in the form of a photon, and that photon should have the wavelength 253.6 nanometers. They could not see such radiation directly, as it lies in the invisible ultraviolet part of the spectrum, but when they set up an experiment to detect ultraviolet light, they found that their mercury vapor was emitting at exactly the wavelength predicted.

So Franck and Hertz not only demonstrated the existence of discrete atomic energy levels in atoms, they verified that an atom can reradiate light with a wavelength exactly as Bohr had predicted. This was a dramatic and concrete verification of Bohr’s basic ideas, and gave great impetus to the fledgling quantum theory. Franck and Hertz won the 1925 Nobel Prize in Physics “for “for their discovery of the laws governing the impact of an electron upon an atom.”

Today, the Franck-Hertz experiment is often done in undergraduate physics labs. Instead of having a cathode wire in the center of the apparatus and the grounded anode on the boundary of the glass cylinder, the cathode, mesh, and anode are placed in a line along the length of the tube. Mercury, which is a toxic substance, is usually replaced with neon gas, and the critical voltage to cause a drop in the current is 18.7 volts. One particularly nice advantage of using neon is that the photon emission from the neon gas is in the visible range⁴, allowing experimenters to see the exact positions at which the energy of the electrons matches the transition energy of the neon atoms.

To me, the Franck-Hertz experiment is particularly beautiful because of its simplicity — it is easy to understand how it works, and it provides tremendous insight into the quantum nature of matter.

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1. Gustav Hertz is the nephew of Heinrich Hertz, the discoverer of radio waves.
2. J. Franck, G. Hertz, “Über Zusammenstöße zwischen Elektronen und Molekülen des Quecksilberdampfes und die Ionisierungsspannung desselben,” Verhandlungen der Deutschen Physikalischen Gesellschaft 16 (1914), 457–467.
3. G. Holton, “On the recent past of physics,”.Am. J. Phys. 61 (1961), 805–810.
4. If a photon was emitted with 18.7 electron volts, it would be in the UV range and not visible to the eye. In neon, however, the atom actually transitions to an intermediate energy level and releases a visible photon.