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Nuclear Excitation

  1. Feb 16, 2014 #1
    1. The problem statement, all variables and given/known data
    A nucleus of mass m initially at rest absorbs a gamma ray (photon) and is excited to a higher energy state such that its mass is now 1.01 m.

    Find the energy of the incoming photon needed to carry out this excitation.


    2. Relevant equations

    [itex]m^{2} = E^{2}-P^{2}[/itex] possibly

    [itex]E_{sys}= KE+E_{o}+E_{\gamma}[/itex]

    3. The attempt at a solution

    Equating energy before and after.

    [itex]m+E_{\gamma}=1.01m+KE[/itex]

    [itex]E_{\gamma}=.01m+KE[/itex]


    Is there a way to find the exact energy required? I think it may have something to do with the momentum but they do not give any info about the motion of the final particle.
     
  2. jcsd
  3. Feb 16, 2014 #2

    Dick

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    The motion of the final particle is fixed by conservation of momentum. They don't have to specify it.
     
  4. Feb 16, 2014 #3
    So the momentum before and after is E_gamma? I still have that kinetic energy value that I cannot do anything with.
     
  5. Feb 16, 2014 #4

    Dick

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    Sure it is. At least in units where c=1. Use ##m^{2} = E^{2}-P^{2}## on the final state.
     
  6. Feb 16, 2014 #5
    I think I may have solved it. I made a diagram.

    Using the second portion

    [itex](E_{\gamma}+m)^{2}-(E_{\gamma})^{2}=(1.01m)^{2}[/itex]

    [itex]2E_{\gamma}+m^{2}=1.0201m^{2}[/itex]

    [itex]E_{\gamma}=0.51005m[/itex]

    This seems to make sense but I am not sure if it is correct.
     

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  7. Feb 16, 2014 #6

    Dick

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    I'm not really familiar with that kind of diagram. But the solution looks correct.
     
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