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Finding the energies of 2 photons from a decay of a travelling mass

  1. May 10, 2012 #1
    1. The problem statement, all variables and given/known data
    Mass M travelling at v=c/3 decays into 2 photons in x and -x directions.

    Mass M orginally formed by mass m travelling at v=3c/5 hitting a stationary mass m.
    This gives M v=c/3 and M=3m/√2.

    2. Relevant equations

    E=K + mc^2

    p = gamma m v
    E = gamma m c^2

    K = (gamma -1) mc^2

    E^2 - p^2 c^2 = m^2 c^4

    3. The attempt at a solution

    I am confused how the photons form from a moving mass. How would I find out the ratio of the energies of the photons?
     
  2. jcsd
  3. May 10, 2012 #2

    collinsmark

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    Use your E2 - p2c2 = m2c4 formula to find the relationship of a given photon's momentum and its energy. Set m = 0. Then solve for p.

    Then set up the following simultaneous equations (noting that the photons fly off in opposite directions on the x-axis):
    • (Energy of one photon) + (Energy of the other photon) = (The original energy of the system)
    • (|Momentum of one photon|) - (|Momentum of the other photon|) = (|Original momentum of the system|)

    "Original energy of the system" above is the original total energy of the system; not just its kinetic energy. You have two equations and two unknowns. You can take it from there.
    Your above calculations kinda worry me. Is this intermediate step something you are explicitly told to calculate? If so, I don't think it's correct: According to my calculations, (total) energy and momentum are not conserved in your calculations (as they should be). If you are not required to perform this intermediate step, then I don't think it's necessary.
     
    Last edited: May 10, 2012
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