(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A photon whose energy equals the rest energy of the electron undergoes a Compton collision with an electron if the electron moves off at an angle of 40 degrees with the original photon direction, what is the energy of the scattered photon.

2. Relevant equations

E^{2}= (m_{0}c^{2})^{2}+ (pc)^{2}

[tex]\lambda'=\lambda_{c}(1-cos\phi)+\lambda[/tex]

3. The attempt at a solution

This problem has been bothering me for a while. I have tried several methods of solution but they all seem too complicated. One successful version (yet actually solved with a calculator) is this:

[tex]\theta=-40^{o}[/tex]

[tex]P_{x}=\frac{h}{\lambda}=\frac{h}{\lambda'}cos\phi+P_{e}cos\theta[/tex]

[tex]P_{y}=0=\frac{h}{\lambda'}sin\phi+P_{e}sin\theta[/tex]

Solve for the terms involving theta and divide the equations to eliminate the momentum of the electron

[tex]tan\theta=\frac{\frac{h}{\lambda'}sin\phi}{\frac{h}{\lambda'}cos\phi-\frac{h}{\lambda}}[/tex]

Then substitute in for lambda prime using the Compton equation to get

[tex]tan\theta=\frac{\frac{h}{\lambda_{c}(1-cos\phi)+\lambda}sin\phi}{\frac{h}{\lambda_{c}(1-cos\phi)+\lambda}cos\phi-\frac{h}{\lambda}}[/tex]

Now you have an equation involving only phi as a variable and 'can' solve for it, I had to use a calculator though. Is there a better method or a way to solve this equation analytically?

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# Angle of Photon after Compton Scattering

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