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Fractional change in wavelength

  1. Dec 27, 2013 #1

    utkarshakash

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    1. The problem statement, all variables and given/known data
    When a photon is emitted from an atom the atom recoils. The kinetic energy of recoil and the energy of photon come from the difference in energies between the states involved in the transition. Suppose a hydrogen atom changes its state from n=3 to n=2. Calculate the fractional change in wavelength of light emitted due to the recoil.

    2. Relevant equations

    3. The attempt at a solution

    Difference in energies of states = -13.6(1/4 - 1/9)

    This is equal to sum of KE of recoil and energy of photon(ΔE).

    [itex] \dfrac{mv^2}{2} + \delta E = -13.6 \left( 1/4 - 1/9 \right) [/itex]
    From this I can find energy of photon released only if I know the velocity v.
     
  2. jcsd
  3. Dec 27, 2013 #2

    haruspex

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    What else might be conserved?
     
  4. Dec 28, 2013 #3

    utkarshakash

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    Momentum.
    Using momentum conservation I can write

    ΔE/c=mv.

    Now if I plug v into energy conservation equation. I will get a quadratic in ΔE. Am I on the right track?
     
  5. Dec 28, 2013 #4

    haruspex

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    That's what I would do.
     
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