box with sides of length 3.5 Å and containing 6 7-electrons. What wavelength of light would be required to promote an electron from the ground state to the first excited electronic state? Answer 135 nm Hint: Use the result for the energy of a particle in a 2-d box: Enz ny (5.1) 2me L? 9.8 × 10-31kg You need with ng = 1, 2, 3... and ny = 1, 2, 3... and me the first 3 energy levels for the 6e¯, and the transition energy will be the enerov betwveen the HOMO and the LUMO (the 4th energy level).
box with sides of length 3.5 Å and containing 6 7-electrons. What wavelength of light would be required to promote an electron from the ground state to the first excited electronic state? Answer 135 nm Hint: Use the result for the energy of a particle in a 2-d box: Enz ny (5.1) 2me L? 9.8 × 10-31kg You need with ng = 1, 2, 3... and ny = 1, 2, 3... and me the first 3 energy levels for the 6e¯, and the transition energy will be the enerov betwveen the HOMO and the LUMO (the 4th energy level).
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Transcribed Image Text:2-d particle in a box problem. Benzene can be treated as a 2-d
box with sides of length 3.5 Å and containing 6 7-electrons. What
wavelength of light would be required to promote an electron from the
ground state to the first excited electronic state?
Answer
135 nm
Hint: Use the result for the energy of a particle in a 2-d box:
7²h?
Y
+
(5.1)
Nx,Ny
2me
L?
L3
1,2, 3... and те
9.8 × 10-31kg You need
with ng = 1,2, 3... and ny
the first 3 energy levels for the 6e¯, and the transition energy will be
the energy between the HOMO and the LUMO (the 4th energy level).
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