a photon and electron collision

1. The problem statement, all variables and given/known data
Consider a photon colliding with an electron and scattered directly backward. If the electron is initially at rest and the incident photon has frequency f, determine the frequency of the back-scattered photon

2. Relevant equations

3. The attempt at a solution
Since the photon has no rest mass, then it should always move in speed of light. Therefore the frequency before and after the collision must be the same.

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