Compton Effect Derivation

  • Thread starter gotojason
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  • #1
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oK SO.... I have been given the task of deriving the Compton effect equ. ( [tex]\lambda\prime-\lambda=\frac{h}{m_ec}(1-cos\theta)[/tex])
exactly from the 3 following:
1) [tex]\frac{h}{\lambda}=\frac{h}{\lambda\prime}cos\theta +\gamma m u cos\phi[/tex]

2) [tex]0=\frac{h}{\lambda\prime}sin\theta-\gamma mu sin\phi[/tex]

3) [tex]\frac{hc}{\lambda}=\frac{hc}{\lambda\prime}+(\gamma-1)mc^2[/tex]

I found the link
http://en.wikipedia.org/wiki/Compton_scattering
however I am having a hard time going from my equations to momentum and energy conservation
any ideas where to go ... I have been at it for 4+hrs and its driving me nuts
Thanks
 

Answers and Replies

  • #2
Astronuc
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To get rid of term of [tex]\phi[/tex], try

[tex]\frac{h}{\lambda}\,-\,\frac{h}{\lambda'}cos\theta\,=\,\gamma m u cos\phi[/tex]


[tex]\frac{h}{\lambda'}sin\theta\,=\,\gamma mu sin\phi[/tex]


Square both equations and add.

Now, IIRC, [itex]\beta[/itex] = u/c and [itex]\gamma[/itex] = [tex]\frac{1}{\sqrt{1-\beta^2}}[/tex]
 
  • #3
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1 and 2 are from momentum conservation and 3 from energy conservation.

First you need to eliminate Phi from the two first equations using the indentity cos^2(phi)+sin^2(phi)=1. Yes, you need to square up these equations after moving all other terms to one side except one with Phi.
 

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