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Expression for frac photon energy from Compton Scattering

Starting from the expression (Klein-Nishina) for the change in wavelength for a photon experiencing Compton Scattering an expression relating the fractional change of the photons energy is derived

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Starting with the Klein-Nishina expression for Compton Scattering [1]

Lamda' - Lamda = {h/mc}*{1 - cos(theta)} (1)

Where h is Plancks constant and m is the mass of the electron

We note that in general the energy of a photon may be expressed as

E = h*mu = hc/Lamda (2)

Thus by re-arrangement of (2) we get

Lamda = hc/E (3)

On ...

Solution Summary

A derivation of the fractional change in the energy of a photon due to Compton Scattering. Show that the fractional energy change of the photon undergoing Compton Scattering is given by

f = {h/lamda'*mc}*{1 - cos(theta)}

Where m is the mass of the scattering centre electron, c is the speed of light, h is plancks constant, lamda' is the scattered photon wavelength and theta is the angle that the scattered photon makes with the axis of the incoming photon