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## Homework Statement

Consider Compton scattering of a photon by a moving electron. Before the collision the photon has a wavelength λ and is moving in the positive x direction. The electron is moving in the negative x direction with a total energy E ( including rest energy mc^2). The photon and electron collide head on. After the collision both are moving in the negative x direction.

Derive an expression for the wavelength λ' of the scattered photon. Show that if E>>mc^2, where m is the rest mass of the electron, your result reduces to

λ'=(hc\λ)(1+m^2c^4/4hcE)

## Homework Equations

λ'-λ=h/mc(1-cosθ)

## The Attempt at a Solution

I've tried many things to manipulate the Compton equation and conservation of energy but I can't seem to get anywhere.