(adsbygoogle = window.adsbygoogle || []).push({}); "high school" algebra -> relativistic conservation of momentum and energy

1. The problem statement, all variables and given/known data

Consider a head-on, elastic collision between a massless photon (momentump_{o}and energyE_{o}) and a stationary free electron. (a) Assuming that the photon bounces directly back with momentump(in the direction of -p_{o}) and energyE, use conservation of energy and momentum to findp.

2. Relevant equations

E=[tex]\gamma[/tex]mc^{2}

p=[tex]\gamma[/tex]mu

massless: E=pc

rest mass: E=mc^{2}

E^{2}=(pc)^{2}+(mc^{2})^{2}

v/c=pc/E

[tex]\gamma[/tex]=1/[tex]\sqrt{1+(v/c)^2}[/tex]

3. The attempt at a solution

Note:First of all I know that this is relativity, but it boils down to just plain algebra. I can't figure it out and help is hard to find, so if you can help I would really appreciate it.

I assume thatpis the momentum of the electron. m=mass of the electron u=velocity of the electron c=speed of light

conserving energy:p_{o}c+mc^{2}=pc+[tex]\gamma[/tex]mc^{2}

p_{o}+mc=p+[tex]\gamma[/tex]mc

p_{o}=p+[tex]\gamma[/tex]mc-mc

conserving momentum:p_{o}=p-p=[tex]\gamma[/tex]mu-p

Plugging the result I got in conserving energy into the momentum equation:

p-p=p+[tex]\gamma[/tex]mc-mc

p=2p+mc([tex]\gamma[/tex]-1)

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# High school algebra -> relativistic conservation of momentum and energy

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