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Math Help - Initial and final state of a hydrogen atom

  1. #1
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    Initial and final state of a hydrogen atom

    Hi dudes! I hope you can help me with this problem; it was on my modern physics exam but I got it wrong; however, the teacher didn't tell me what the right answer was. Anyway, here is the problem:

    In a hydrogen atom a photon of wavelength 95 nm is emitted. What are the initial and final states of the hydrogen atom?

    My solution:

    The energy of the photon is hc/λ = 1240 eV*nm / 95 nm = 13.05 eV, which is the energy difference between the final and initial states. So I get

    E = 13.05 eV = Ei - Ef = -E0/ni^2 - (-E0 /nf^2) = -13.6 eV(1/ni^2 - 1/nf^2)

    So I get this equation with 2 unknowns, and after a few guesses I came to the conclusion that the initial state must be ni=5 and the final state is nf=1, because after substituting those values I get 13.056 eV, which is a close approximation to the value of 13.05 eV I got earlier.

    Where is the mistake? Thanks in advance!
    Last edited by Cesc1; June 6th 2013 at 01:23 PM.
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  2. #2
    Forum Admin topsquark's Avatar
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    Re: Initial and final state of a hydrogen atom

    Quote Originally Posted by Cesc1 View Post
    Hi dudes! I hope you can help me with this problem; it was on my modern physics exam but I got it wrong; however, the teacher didn't tell me what the right answer was. Anyway, here is the problem:

    In a hydrogen atom a photon of wavelength 95 nm is emitted. What are the initial and final states of the hydrogen atom?

    My solution:

    The energy of the photon is hc/λ = 1240 eV*nm / 95 nm = 13.05 eV, which is the energy difference between the final and initial states. So I get

    E = 13.05 eV = Ei - Ef = -E0/ni^2 - (-E0 /nf^2) = -13.6 eV(1/ni^2 - 1/nf^2)

    So I get this equation with 2 unknowns, and after a few guesses I came to the conclusion that the initial state must be ni=5 and the final state is nf=1, because after substituting those values I get 13.056 eV, which is a close approximation to the value of 13.05 eV I got earlier.

    Where is the mistake? Thanks in advance!
    Looks good to me. What is the given correct answer?

    -Dan
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  3. #3
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    Re: Initial and final state of a hydrogen atom

    Quote Originally Posted by topsquark View Post
    Looks good to me. What is the given correct answer?

    -Dan
    The teacher didn't tell me what was the right answer, he said he was busy I guess I'll go to complain about this, because I also think the answer is correct.
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