(a) A photon of energy \(E_{0}\) strikes a free electron at rest in the lab. ("Free" here means the electron is not bound inside an atom.) Is it possible for the photon to be absorbed by the electron? If so, find the energy and momentum of the final electron. If not, explain why not.

(b) A free electron of energy \(E_{0}\) is moving in the lab. Is it possible for the electron to emit a photon, so that after the emission there is a photon and an electron moving more slowly than before? If so, find the final energy and momentum of both the photon and the electron. If not, explain why not.