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Homework Help: Simple special relativity

  1. May 12, 2014 #1
    1. The problem statement, all variables and given/known data
    High energy photon of energy E collides with a low energy photon of energy 1eV. It forms an electron-positron pair. I have found the threshold energy as E=261GeV.

    I am asked to find the speed of the centre of mass at this threshold energy.

    2. Relevant equations

    3. The attempt at a solution
    I can use conservation of energy to get the energy of the electron (or positron) say then use the above formula to find v from γ. I believe this then should be the CM speed. However it returns c. I don't believe that this is an acceptable solution (I don't have the answers though). Any thoughts would be helpful, thanks.
    Last edited: May 12, 2014
  2. jcsd
  3. May 14, 2014 #2
    I realise it may be a bit vague. Just in case, the full question is

    A high-energy photon γ1 of energy E traveling through space interacts with an
    infra-red photon γ2 of energy 1 eV to produce an electron-positron pair via the reaction
    By considering the total energy and the total momentum show that the threshold value of E required for this process is 261 GeV.

    What is the velocity of the centre of mass at this threshold?

    I have the 261GeV, but can only get speed c for the second bit (as outlined in my original post).
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