Relativistic Collision of an Electron and a Photon

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Homework Statement

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.

Homework Equations

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?

Thanks

 

[bon]

any ideas?

 

[bon]

anyone?