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Compton scattering

I'm looking at instructor notes for one of the problems in my textbook, the link is here:

On page (3), where it says "Part B" P'Max occurs when...., can you please explain to me how they got the equations directly below till the end of the Page (3).

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What you do is you write down the equation for conservation of momentum. You define an x-direction, so that the electron moves in the positive x-direction and the backscattered photon moves in the negative x-direction. The momentum of a photon of wavelength lambda is h/(lambda). The backscattered photon has a ...

Solution Summary

A detailed explanation is given.