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Homework Help: How much mass does an atom lose when it emits a photon?

  1. Dec 15, 2008 #1
    1. The problem statement, all variables and given/known data

    An atom initially at rest emits a photon with frequency f. Explain why the mass of the atom decreases, and by an amount greater than hf/c^2.

    2. Relevant equations

    E= mc^2
    E = hf

    3. The attempt at a solution

    So I know that the atom must lose mass when the photon is emitted because in order for it to emit energy it must lose mass (by E = mc^2), but I don't understand why it should be more than hf/c^2, since from these 2 equations:

    E = mc^2 = hf

    therefore m = hf/c^2

    Why is this wrong?

  2. jcsd
  3. Dec 15, 2008 #2


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    Science Advisor

    The atom is initially at rest. Is it at rest after it emits the photon?
  4. Dec 15, 2008 #3
    Ok, I see. So the atom recoils with the opposite momentum of the photon (-hf/c), since momentum is conserved. Thanks, I was just thinking about energy conservation.
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