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Homework Help: Photon energy, momentum, and velocity

  1. Sep 29, 2010 #1
    1. The problem statement, all variables and given/known data

    Suppose one photon has an energy of 200 MeV and it is traveling along the x-axis. Suppose another has an energy of 100 MeV and is traveling along the y-axis. (A) What is the total energy of this system. (The answer is 300 MeV) (B)If a single particle has this same energy and momentum, what would be its mass?

    The answer is 200 MeV, I am having trouble reaching that answer.

    2. Relevant equations

    [tex]p=\frac{E}{c}[/tex] for a photon
    [tex]p={\gamma}mu[/tex] for a particle with mass
    [tex]E=cp[/tex] for a photon
    [tex]E={\gamma}mc^{2}[/tex] for a moving particle with mass.

    3. The attempt at a solution

    Energy of the photon = energy of the moving particle:
    [tex]cp={\gamma}mc^{2}[/tex]
    [tex]300 MeV={\gamma}mc^{2}[/tex]

    Momentum of the photon = momentum of the moving particle:
    [tex]\frac{E}{c}={\gamma}mu[/tex]
    [tex]\frac{300 MeV}{c}={\gamma}mu[/tex]

    This is all I can do so far, after this I get stuck. If I continue, I get the result that u=c. The correct answer is u=.74c
     
    Last edited: Sep 29, 2010
  2. jcsd
  3. Sep 30, 2010 #2
    The total momentum of the system of the two photons is not 300 MeV. Momentum is a vector so you have to add the vectors in the correct way.
     
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