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Quantum Well with Infinite Barriers

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Homework Statement


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.)


Homework Equations



E1 = (∏^2)*h^2/2meL^2 = 0.3737/L^2 eV

ΔE = En+1 − En = (2n + 1)E1

ε = hf

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!
 
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Answers and Replies

  • #2
TSny
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ΔE = En+1 − En = (2n + 1)E1
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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