## Compton effect

By 1923, the photoelectric effect and Einstein’s explanation were accepted. Compton tried doing it with X-rays—he expected the photoelectrons to go much faster due to the higher frequency of X-rays. There was a problem: since X-rays can penetrate into metal, most electrons would be stopped or slowed down a lot by the time they reached the edge of the plate. To avoid this, Compton used thin metal foil for the target.

Still, he didn’t get the results he was expecting. Instead of a fast electron shooting out straight ahead, he found that a lower energy X-ray and a photoelectron both exited the other side of the foil at an angle to the original X-ray. He suggested that the X-ray photons could have momentum. Using E = mc^2, E = hf, and p = mv, he derived an equation for the momentum of a photon:

p = (hf)/c = h/lambda.

As it turns out, there are five possible photon–matter interactions. From lowest energy to highest energy, they are the following:

1. E < W\ => reflection
2. E > W\ => photoelectric
3. E ≫ W => Compton
4. With even more energy, we have excitation of inner electrons. The photoelectric and Compton effects deal with valence electrons.
5. With insane amounts of energy, we get pair production. The photon interacts with the nucleus to create an electron and a positron.