Consider an isolated electron and a photon of energy 'hf' suffers collision with it. Then will the electron absorb all the energy of the photon or some amount is absorbed? If so, then does the photon after collision has less frequency than the previous one?
When a photon scatters off a free electron, it can either scatter elastically, i.e. no change in the frequency of the outgoing, or undergoes what is called Compton scattering. The distributions of the outgoing photonh can be calculated using the expansion in Feynman diagrams to first order :
The outgoing photon will have a smaller frequency as the incoming transferred part of its momentum and energy to the electron. For the history see here.