Mathematics of the Compton effect

Collision of a photon with a stationary electron; deriving the Compton formula relating change in wavelength to scattering angle of the photon:

incident photon

electron scattered photon incident photon electron

When a photon of a given momentum is scattered elastically through an angle d, the energy loss is uniquely defined.

Assume the incoming photon has energy E = hf and momentum p = hf/c, the scattered photon has energy E' = hf' and momentum p' = hf '/c, and pe is the momentum of the recoil electron.

Momentum vector triangle:

From the cosine rule and multiplying across by c2, pi c2 = (hf )2 + (hf 02 - 2h2ff' cos 0

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