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Photon-electron collision with pair production

  1. Mar 18, 2017 #1
    1. The problem statement, all variables and given/known data
    photon collides with an electron producing a electron-positron pair, the three particles ( two electrons and one positron) move together in the same direction of the original photon.
    calculate the energy of each particle.

    2. Relevant equations
    photon:
    Ep=hf
    p=E/c
    electron/positron
    1) E=Ke+me*c^2

    3. The attempt at a solution
    so 2)Ep + me*c^2=3E : photon energy plus electron rest energy equals the energy of the 3 remaining particles and since mass and direction is the same the energy is the same, same goes for momentum
    3)Ep/c=3p
    so 2 equations 3 unkowns so i wrote eq 2) with 1) and substituted k for 1/2*me*v^2 and in eq 3) i substituted p for me*v, this did not yield a correct answers.
    how should i do this?
     
  2. jcsd
  3. Mar 18, 2017 #2

    mfb

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    2016 Award

    Staff: Mentor

    You cannot use the nonrelativistic kinetic energy and momentum formulas here. The particles will move at significant speed. You have to use the relativistic formulas.
     
  4. Mar 18, 2017 #3
    so K= m*c2*(1/(1-v2/c2)0.5)-m*c2
    and p=m*v*(1/(1-v2/c2)0.5)
    thanks!
     
  5. Mar 18, 2017 #4

    mfb

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    2016 Award

    Staff: Mentor

    I wouldn't introduce the velocity at all. ##E^2 = m^2 c^4 + p^2 c^2##
     
  6. Mar 18, 2017 #5
    ok! got the correct answer now... thanks!
     
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