An ultra relativistic electron collides head on with a very low energy photon of the cosmic microwave background. No new particles are created. Show that the energy of the photon after the collision is given by:
E = [(E1+p1c)E2]/[(E1-p1c) + 2E2]
Where E1 and p1 are respectively the energy and the magnitude of the momentum of the incident electron and E2 is the energy of the initial photon.
The Attempt at a Solution
I tried solving this by labeling the final energy and momentum of the electron E' and p' and using the invariant E^2 - c^2p^2...but couldn't get the answer out..
is it right to assume that after the collision the rest mass of the electron is the same..
i.e. E1^2 - c^2 p1^2 = E'^2 - p'^2c^2?