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Wavelength of a photon

  1. Jan 15, 2013 #1
    1. The problem statement, all variables and given/known data
    Calculate the shortest wavelength photon that is emitted in the hydrogen atom.

    Energy when n = 1 = -13.6 eV

    2. Relevant equations

    E = hc/λ
    λ = hc/E

    3. The attempt at a solution
    Well as far as I understand, when the electron is in the n = 1 energy level it has it's lowest energy, which is -13.6 eV. I believe this is where the shortest wavelength will be...
    λ = hc/E
    = (4.14 x 10^-15 eV*s)(3.00 x 10^8 m/s) / -13.6 eV
    = approx 9.13 x 10^-8 m

    Was my method correct? I would really just like a second opinion. Thank you!
     
  2. jcsd
  3. Jan 15, 2013 #2

    ehild

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    The method is correct, but the photon energy is positive: 13.6 eV, the same the electron loses when it becomes bounded to the hydrogen atom. You divided by -13.6 eV, then ignored the sign, which is wrong.

    ehild
     
  4. Jan 15, 2013 #3
    Are n't photons produced when an electron jumps between energy levels not stay on one level? The shortest wavelength photon will be the one with least energy produced by an electron transition of the smallest energy. If the electron is to end up at n=1, the shortest wavelength photon comes from a jump from n=2 to n=1 (-3.4eV to -13.6eV).
     
  5. Jan 15, 2013 #4

    ehild

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  6. Jan 15, 2013 #5
    Sorry I have just realized my mistake. Shortest wavelength comes from the largest energy not the smallest.
     
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