Say a photon hits some atom.
What determines whether there will be a photoelectric effect (photon is absorbed, electron is released) or whether there will be a Compton scattering (the photon is scattered at some angle, and the electron is released with another direction)?
Best Answer
For a given system that the electron is in, the primary determinant is the energy of the photon. As @DJBunk points out, this is a quantum mechanical process, so the "choice" is fundamentally random. A given interaction will occur with a probability proportional to its cross section. Figure 1 of this lecture shows how the cross section for each possible process varies with photon energy. This plot is for the interaction of photons with electrons in copper. At low energies, the photoelectric effect is the dominant effect. From about 200 keV to about 10 MeV, Compton scattering is the dominant effect. Above 10 MeV, the dominant effect is pair production. At a given photon energy, the relative probability of two processes would be the ratio of their cross sections.
The dependence of each cross section on photon energy should be similar in form for any system; the exact numbers will vary from system to system. Table 2 of that lecture gives the dependence on the atomic number, for example.