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Pion decay (tell me if I'm approaching it correctly!)

  1. Aug 12, 2009 #1
    1. The problem statement, all variables and given/known data

    A neutral pion may decay into two photons. A particular pion is traveling along the x axis when it decays into two photos, the first going directly along the +x axis, the second going directly back along the -x axis. The energy of the photons is measured and it is found that E1 is n times more energetic than E2. Find the velocity u of the pion.

    2. Relevant equations

    1) relativistic momentum = gamma *m*u where u is velocity, m is mass
    2) momentum of a photon is h/wavelength = h*frequency/c (I'm denoting frequency by nu).

    3. The attempt at a solution

    I tried to do this using conservation of momentum. I'd like to know if my solution is correct.

    Pi = Pf (via conservation of momentum for isolated system)

    so

    gamma*m*u = h*nu1/c - h*nu2/c (the minus sign accounts for the fact that the photons move in opposite directions along the x axis)

    but as given above, E1 = n*E2, so

    gamma*m*u = h*nu2 (n - 1)/c

    Then I solved for u using algebra (I didn't forget about the u in gamma, I squared everything and solved for u afterwards).

    Can that be right? Or am I thinking way too simplistically here?
     
  2. jcsd
  3. Aug 13, 2009 #2

    tiny-tim

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    Hi quasar_4! :smile:

    (have a nu: ν :wink:)

    It's a bit difficult to tell without seeing your final calculations,

    but it looks as if you haven't used a conservation of energy equation. :confused:

    You need a conservation of momentum equation and a conservation of energy equation, just as in the Newtonian case (and ν needn't come into it). :wink:
     
  4. Aug 13, 2009 #3
    hello, tiny-tim! :-D

    I need both? Hmm, I thought that I could do it just with conservation of momentum OR conservation of energy. We only have one unknown, so two equations and one unknown! What am I missing here? Why do we need to use both the conserved quantities?

    (It's been a long, long time since I took any sort of modern physics class... I feel like such a dork for not remembering this!) :redface:
     
  5. Aug 13, 2009 #4

    kuruman

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    There are three equations and three unknowns. The equations are

    Momentum Conservation
    Energy Conservation
    E1=n E2

    The unknowns are
    u, E1 and E2.

    Your answer should come out in terms of n, c and the rest-mass of the pion.
     
  6. Aug 13, 2009 #5

    kuruman

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    Actually, the rest-mass of the pion drops out.
     
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