The Franck-Hertz Experiment

This picture is from a class (Experiments in Modern and Applied Physics) that I took at Rutgers back in my junior year.

It’s not a spaceship or alien technology; it’s a special mercury vapor triode I was using to recreate the famous Franck-Hertz experiment.

You can enjoy it as it is, or read further for an explanation of the physics behind the picture.

The Physics Behind the Picture

The glowing orange rectangle in the middle is called a cathode. It is a piece of metal so hot that electrons literally start falling out of it. There is a metal grate above the cathode, and then there is another piece of metal (the anode) above the grate that collects any electrons that pass through it. These three objects, along with a small amount of mercury vapor, are sealed inside a metal tube. The whole thing is knows as a mercury vapor triode. (The potential at all three locations – cathode, grid, and anode – can be independently controlled, hence the name triode. A diode only has a cathode and an anode.)

The main idea of the experiment is as follows:

  1. Set the potential at the grid higher than at the cathode. This will cause any electrons produced by the cathode to gently accelerate towards the grid.
  2. Set the potential at the anode a little bit lower than at the grid. This will only allow electrons with a certain minimum kinetic energy to pass through the grid and reach the anode.
  3. Measure the current produced in the anode for a variety of different cathode potentials.

So why is this interesting? You might think the following: “For low electron acceleration, they’ll just keep bumping into the mercury atoms, and very few of the electrons will make it to the anode. As we increase the acceleration, more and more will have enough energy to make it.” Sounds pretty boring.

It would be boring – but that’s not what happens! It happens at first, but then something strange occurs. All of a sudden, the current in the anode drops to zero.

The only way to explain this is through quantum mechanics. Quantum mechanics tells us that the mercury atoms can only absorb certain quantized amounts of energy from the electrons. If an electron is moving too slowly when it bumps into a mercury atom, it cannot transfer any energy to it. However, if it gains enough speed, it will be able to transfer energy. So if our accelerating potential is chosen so that the electrons transfer all of their energy to mercury atoms right before they reach the grid, none of them will make it to the anode.

As we increase the potential further, the current will increase again for a while until it drops again. This time, the electrons transferred their energy to the mercury atoms halfway along their path and then once more right before the grid.

As we increase the potential even further, the same thing keeps happening over and over again. If you make a graph, it will look something like the following picture. (The two lines correspond to different triode temperatures… can you guess which is higher?)

So what happens to the mercury atoms? Well, when they absorb energy from a travelling electron, they enter into an excited state. But they don’t like to be there, so they soon release this extra energy in the form of a photon. The first time there is a dip in the current, there will be a line of glowing atoms right below the grid. The second time, there will be lines of glowing atoms right before the grid and halfway to the grid. Et cetera, et cetera.

My picture actually shows something a little bit more complicated than that. The first excited mercury state produces UV light, which is invisible to a human eye or a camera. To make this picture, I had to make the tube and cathode far hotter than normal. This produced far more collisions than normal. So many, in fact, that some mercury atoms were excited into their second excited states. When the atoms decay from their second excited state to their first, they produce the blue lines seen in the picture.

Pretty cool, right?

This experiment is a direct validation of quantum mechanics, but it’s interesting to note that James Franck and Gustav Ludwig Hertz first performed it in 1914- years before quantum mechanics became prevalent in the physics community. In fact, Franck and Hertz didn’t even know about quantum mechanics when they did this! It was only later that people realized the importance of their experiment, which eventually resulted in the 1925 Nobel prize in physics.

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