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Photon beam is incident on a proton target produces a particle

  1. Sep 20, 2016 #1
    1. The problem statement, all variables and given/known data
    A photon beam is incident on a proton target (at rest). Particle X (and nothing else) with rest mass M=1.232GeV/c2 is then produced. Use m_p =0.938GeV/c2 as the proton mass.

    a) What is the energy of the photon beam, in terms of GeV?

    b) What is the momentum of the moving particle X, in terms of GeV/c? c) What is the energy of the moving particle X, in terms of GeV?

    c) What is the speed of the moving particle X, in terms of c? (i.e, βX=?

    2. Relevant equations
    E = γ*m*c^2

    P = γ*m*u

    γ = 1/sqrt(1-β^2)

    β = u/c
    3. The attempt at a solution
    Using the conservation of mass-energy law
    E_1 = E_2

    the energy before the light hits the proton is E_1 and the energy afterwards is E_2

    E_1 = P*c(the energy due to the photon beam) + m_p*c^2(the rest energy of the proton) = γ*M*c^2(the energy of particle X) = E_2

    P*c + m_p*c^2 = γ*M*c^2

    can somebody let me know if i got this equation right so far?
     
  2. jcsd
  3. Sep 20, 2016 #2

    TSny

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    Homework Helper
    Gold Member

    Yes, your energy equation looks good.

    It might be easier to approach the problem using energy-momentum four-vectors, if you are familiar with them.
     
  4. Sep 20, 2016 #3
    No I haven't gotten learn about 4-vectors yet, unfortunately. But since you said my equation looked good I tried the following...
    Ok so then I can write

    P*c + m_p*c^2 = sqrt( (P_x*c)^2 + (M*c^2)^2 )

    using conservation of momentum

    P + P_p = P_x where P, P_p, and P_x are the photon, proton, and X particle momentum's, repectively.

    --> P + 0 = P_x
    --> P = P_x

    using the fact that the momentum of particle X is the same as the photon's

    P*c + m_p*c^2 = sqrt( (P*c)^2 + (M*c^2)^2 )

    --> E_γ + m_p*c^2 = sqrt( (E_γ)^2 + (M*c^2)^2 ) where E_γ is the energy of the photon

    rearranging this equation for E_γ

    E_γ = 0.5*( 1/m_p * (M*c)^2 -m_p*c^2 )

    after plugging in the numbers I get

    E_γ = 0.340 GeV
     
  5. Sep 20, 2016 #4

    TSny

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    Gold Member

    That looks very good.
     
  6. Sep 20, 2016 #5
    Woohoo! thanks!
     
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