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

Consider a head-on, elastic collision between massless photon (momentum Pnot and energy Enot) and a stationary free electron. Assuming that the photon bounces directly back with momentum p (in the direction of -Pnot) and energy E, use conservation of energy and momentum to findp.

2. Relevant equations

massless: E=pc

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

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

Maybe relevant...but probably not : E=hf

3. The attempt at a solution

I'm assuming thatpis the momentum of the electron, because it is the only momentum not denoted in the problem. Note: Pnot is momentum of photon before collision, p is momentum of photon after collision, and m is the mass of the electron. I've set up this:

(Pnot)c + mc^{2}= pc + [tex]\gamma[/tex]mc^{2}

Pnot=p_{e}- p

I remove a c from the top equation and isolate Pnot on the left side.

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

I plug this into the second equation

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

From here I try a couple different things, but my main method seems to be putting p on one side and pulling things out

2p= m([tex]\gamma[/tex]u - [tex]\gamma[/tex]c + c)

thanks for any help

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# Homework Help: Conservation of energy and momentum of a proton

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