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Electron in 1-D box: photon absorbed?

  1. Mar 20, 2016 #1
    I don't know where I'm going wrong with this problem - I was so sure I had it right but the online grader tells me otherwise :oldfrown:

    1. The problem statement, all variables and given/known data
    An electron in a one-dimensional box has ground-state energy 2.60 eV. What is the wavelength of the photon absorbed when the electron makes a transition to the second excited state?

    2. Relevant equations
    En = n2h2 / 8mL2
    hf = hc / λ
    ⇒ λ = hc / hf

    3. The attempt at a solution

    The ground-state energy in Joules is (2.60 eV)⋅(1.602⋅10-19 J/eV) = 4.165668⋅10-19 J

    First I calculated the length of the box by rearranging the energy level equation above:
    L = √(n2h2 / 8mEn)

    For n=1, this gives:
    L = √{(6.626⋅10-34)2 / 8(9.109⋅10-31)(4.165668⋅10-19)}
    = 3.80294⋅10-10 m

    Then I used this L to find the energy of the n=2 level:
    En=2 = {(2)2(6.626⋅10-34)2} / {8(9.109⋅10-31)(3.80294⋅10-10)2}
    = 1.66627⋅10-18 J

    The difference in these energy levels is:
    1.66627⋅10-18 J - 4.165668⋅10-19 J = 1.2497⋅10-18 J

    I took this to be equal to the energy of the photon absorbed, i.e. equal to hf. Then:
    λphoton = {(6.626⋅10-34)(2.99⋅108)} / 1.2497⋅10-18 J
    = 158.532 nm

    I corrected it to 3 significant figures to input the answer; I tried both 159nm and 158nm in case it was a rounding error but Computer Says No. Can anyone spot where I'm going wrong? Thanks in advance!
     
  2. jcsd
  3. Mar 20, 2016 #2

    blue_leaf77

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    n=2 is the first excited state, not the second one.
     
  4. Mar 20, 2016 #3
    Ack, of course! Thanks so much, I completely missed that. :)
     
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