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Homework Help: Conservation of energy and momentum of a proton

  1. Feb 9, 2010 #1
    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 find p.


    2. Relevant equations
    massless: E=pc
    E=[tex]\gamma[/tex]mc2
    p=[tex]\gamma[/tex]mu
    Maybe relevant...but probably not : E=hf

    3. The attempt at a solution
    I'm assuming that p is 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 + mc2 = pc + [tex]\gamma[/tex]mc2
    Pnot=pe - 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 = pe - 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
     
  2. jcsd
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