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Homework Help: Calculating the Recoil Shift.

  1. Jul 23, 2011 #1
    1. The problem statement, all variables and given/known data

    b) Calculate the recoil shift for the most energetic lyman line from a free H atom.

    c) Calculate the recoil shift for the emission of a 14.4keV gamma from a free atom of Fe-57.

    2. Relevant equations

    E = hc / [itex]\lambda[/itex] = h [itex]\nu[/itex]

    [itex]\Delta[/itex] E = E^2 / 2mc^2

    3. The attempt at a solution

    I'm still not sure I'm going about this correctly...

    b) start by finding the most energetic lyman line E = hc / [itex]\lambda[/itex] = (1.981E-16)/(912A) = 2.17E-19 (this is where I think my error is). Then find the recoil shift
    [itex]\Delta[/itex] E = E^2 / 2mc^2 = (4.72E-38)/(0.003) = 1.57E-35.

    c) calculate the recoil shift directly using the mass for Fe-57
    [itex]\Delta[/itex] E = E^2 / 2mc^2 = (207.36)/(1.89E-22)(2.99E8)^2 = 12.27MeV ...again this answer just feels wrong, how can a keV scale emission result in an MeV scale recoil?

    Quite clearly I've made some horrible mistake in here, I need some help to find what I did wrong.
  2. jcsd
  3. Jul 23, 2011 #2
    Ok, I've been able to answer part c:

    ((14.4keV)^2)/2(53.02GeV) = 0.002eV

    (sorry for not using tex with the equation, I've been spending way too much time with C++ lately)

    Still working on part b though.
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