Consider Compton scattering of a photon by a moving electron

[Albi Mema]

Homework Statement

Consider Compton scattering of a photon by a moving electron. Before the collision
the photon has wavelength λ and is moving in the +x-direction, and the electron is
moving in the −x-direction with total energy E (including its rest energy mc2). The
photon and the electron collide head-on. After the collision, both are moving in the
−x-direction (that is, the photon has been scattered by 180◦).
(a) Derive an expression for the wavelength λ′ of the scattered photon. Show that if
E ≫ mc2, where m is the rest mass of the electron, your result reduces to
λ′ =hc/E(1 +m^2c^4λ/4hcE)

Homework Equations

Energy Coservation and Momentum Conservation law. Energy of a particle moving particle and energy of the photon.

The Attempt at a Solution

Using the given equations above the same strategy as the one to find the Compton scattering is used. The problem is that the last formula is not the same as the one stated above.

 

[kuruman]

I worked it out and got the quoted expression. Perhaps if you showed what you did, I will be able to guide you. There are several places where one can make a wrong turn.