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Quantum Well with Infinite Barriers

  1. Sep 18, 2012 #1
    1. The problem statement, all variables and given/known data
    An electron is in a one-dimensional rectangular potential well
    with barriers of infinite height. The width of the well is equal to L = 5 nm.
    Find the wavelengths of photons emitted during electronic transitions from the
    excited states with quantum numbers n = 2, λ21, and n = 3, λ31, to the ground
    state with n = 1. (Answer: λ21 ≈ 1.15 µm and λ31 ≈ 0.43 µm.)


    2. Relevant equations

    E1 = (∏^2)*h^2/2meL^2 = 0.3737/L^2 eV

    ΔE = En+1 − En = (2n + 1)E1

    ε = hf

    3. The attempt at a solution

    I found the ground state energy to be 0.0149 eV. Then using the ΔE equation for n=2,3 I found the energies of the emitted photons to be 0.0745 eV and 0.1043 eV, respectively.
    Using these energies in plancks formula is getting me the wrong wavelengths, what am I doing wrong?

    Please help!
     
    Last edited: Sep 18, 2012
  2. jcsd
  3. Sep 18, 2012 #2

    TSny

    User Avatar
    Homework Helper
    Gold Member

    This formula will only work for jumping between two neighboring states. So, it should work for E2-E1. But what value should you use for n in the formula for this case? (It's not n = 2.)

    For the jump from the n = 3 to the n = 1 case you might just want to calculate the energies of each state separately and then subtract.
     
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