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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