Why is it that a photon can't transfer all its energy to a free electron?
It's imposible to conserve both energy and momentum in such a process. You need another particle or object in order to do this.
It's not the same thing, but there is a classical analogue of that fact: a ball of mass m cannot transfer all its kinetic energy to a ball of mass M=/=m.
The only way for a photon to interact with a free electron (other than photoproduction at very high energies) is via Compton scattering.
Ok, I've got it. This explains it really well: http://188.8.131.52/search?q=cache...can't+absorb+photon&cd=1&hl=en&ct=clnk&gl=us"
Separate names with a comma.