Photo electron effect on free electron Suppose there is light of high enough frequency so it causes photoelectric effect (in a piece of metal). Does such light cause photoelectric effect on free electrons as well?
 A: The photoelectric effect occurs when an atom (or ion) absorbs the energy of a photon and an electron is emitted. Some of the photon energy is used to liberate the electron, the rest goes into the electron kinetic energy.
The same thing cannot happen when light interacts with a free electron (e.g. see Free electron can't absorb a photon ). A simple proof shows that a free electron cannot absorb all the energy of a photon and simultaneously conserve linear momentum.
Instead, part of the photon energy is given to the electron and a photon of lower energy is scattered. This is known as the Compton effect.
A: The photoelectric effect - ejection of electrons from matter due to light - is a phenomenon that occurs when light shines on a piece of metal. I do not think such phenomenon was observed with free electrons in vacuo.
( Compton scattering is often described as if electrons interacting with the light were free, but it actually refers to an experiment where the electrons are bound to nuclei in matter. )
A: We can prove that photoelectric effect does not happen for free electron.
we look at the hypothetical process in the center-of-mass system, which is defined as that system in which the initial momentum is zero. From the conservation of energy.
E initial = E final
hv +Mc^2  = Mo c^2
( Mo is the rest mass)
( M is the relativistic mass)
or
which implies Mo> M
Since this cannot be true the process can't occur.
The electrons participating in the photoelectric effect are not free. The heavy matter present takes off momentum but absorbs a negligible amount of energy.
