# Compton Scattering Energy Equation?

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Could anybody point me in the right direction as to how one would derive the equation below?

$E_{\gamma}'=\frac{E_{\gamma}}{1+\frac{E_{\gamma}}{m_0 c^2} \left(1- \cos \theta \right)}$

I read it in my lab manual along with the Compton Wavelength equation (which I know how to derive) and I'm wondering where it comes from.

Thanks.

Edited by x(x-y)
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The expression results from conservation of momentum and energy.

Remembering that both the x and y components of momentum have to be conserved.

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Take your derivation of the compton scattering (which you say you are happy with) - at one point you will have

$\lambda_{f} - \lambda_{i}= \frac{h}{m_{e}c}(1-\cos \theta)$

replace wavelength with hc/E ie planck relation

divide both sides by hc

subtract Ei from both sides

take reciprocals of each side

multiple top and bottom of RHS by Ei

clean up - and you have your equation. It's just a simple algebraic mix up of the standard equation and use of planck. Let me know if it doesnt work out when you try

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Yep that works - but you can skip a few of those last steps actually and get to the answer easily from

$\frac{1}{E_2} - \frac{1}{E_1} = \frac{1}{m_e c^2} \left(1-\cos \theta \right)$

Anyway, thanks for the help.

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