How gamma radiation causes ionization
A gamma photon only causes a single ionization directly
A given source produces gamma photons with one particular energy or a few well-defined energies. Energy is proportional to the frequency of the gamma photon. The higher the frequency the higher the energy.
Gamma photons interact with electrons in several different ways. We’ll look at the simplest one which is straight ionization.
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A gamma photon can knock out an electron from an atom’s electron shell. It doesn't need to be an electron in the outer shell. All of the energy of the gamma photon is transferred to this electron and the gamma photon is annihilated. In other words the gamma photon disappears and all that is left is its energy.
So strictly speaking the gamma photon causes only a single ionization directly.
The knocked-out electron can cause lots of secondary ionizations
But the energy needed to cause the actual ionization is quite small compared with the energy of the gamma photon so the electron ends up with kinetic energy similar to the energy of the photon. This means it’s moving about as fast as a beta particle with the same energy as the gamma photon.
This fast-moving electron causes a series of secondary ionizations and free-radical formations and it is these that do the damage.
However the gamma photon can easily pass through a person without interacting with them. In this case there are no ionizations, no free radicals and so no damage.
A gamma photon acts a bit like a beta particle that might suddenly be called into existence in the middle of your body.