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Why can't a photon transfer all of its energy to an electron?

  • Thread starter darrenhb
  • Start date
  • #1
7
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Homework Statement



Pretty straight forward, I just have to show why a photon can't transfer all of its energy to an electron. I understand this in theory but I'm stuck at how to show it.

Homework Equations



1) Ep + mec2 = Ep' + Ee

Where Ep is the energy of the photon, Ep' is the energy of the scattered photon, and the rest is obvious.

2) E = hf

3) p = p'cos([tex]\theta[/tex]) + pecos([tex]\phi[/tex])

4) p'sin([tex]\theta[/tex]) = pesin([tex]\phi[/tex])

p is the initial momentum of the photon, p' is the final momentum of the photon, pe is the momentum of the electron after scattering. [tex]\theta[/tex] is the angle of the scattered photon and [tex]\phi[/tex] is the angle of the scattered electron.

The Attempt at a Solution



I figure I have to use conservation of momentum and energy to show that it's a contradiction. I was going to assume [tex]\theta[/tex] and [tex]\phi[/tex] were 0, but I'm not sure if I can do that. I've hit a roadblock, I'm not sure how to go about this. A hint in the right direction would be much appreciated!
 

Answers and Replies

  • #2
45
0
Using the relativistic dispersion formula:
[tex]
E^2 = m^2 c^4 + p^2 c^2
[/tex]
you can prove that the conservation laws for energy and momentum can not be satisfied simultaneously if Ep'=0.
 
  • #3
7
0
Thanks! That equation was the missing link I think, I figured it out. :)
 

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