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CHEM 132B Study Guide - Quiz Guide: Wave Function, Spherical Harmonics, Momentum OperatorExam

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Eric Potma
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Chem 132B Quiz 2 Key
Version A
Problem 1 (16 points)
Consider the 2pzorbital shown in the image above. Indicate whether the fol-
lowing statements are True or False. (4 points each)
a) The electron is located on either side of the nodal plane, and not on both
sides simultaneously. False
b) There is a nonzero chance of finding the electron outside of the shaded
volume. True
c) The sign reversal along zcorresponds to a spin flip of the electron. False
d) It is less likely to find the electron on the side with negative amplitude
than on the side with positive amplitude. False
Problem 2 (16 points)
Consider the wavefunction of an atomic system. Indicate whether the following
statements are True or False. (4 points each)
a) If the spin state is symmetric, then the orbital wavefunction must be anti-
symmetric. True
b) If the spin state is in a singlet state, then the orbital wavefunction is
symmetric. True
c) If the spin state is in a triplet state, then the electrons must occupy
different orbital wavefunctions. True
d) If the spin state is anti-symmetric, then the electrons must occupy the
same orbital wavefunction. False
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Problem 3 (34 points)
The wavefunctions of the hydrogen atom can be written as |Ψn,l,mli=|n, l, mli
a) The atom is in de excited state |2,1,1i. Give the full expression for the
wavefunction in terms of coordinates (r, θ, φ). (8 points)
Ψ2,1,1(r, θ, φ) = 3
24 1
rer/2a0sin θ e
This can be simplified to:
Ψ2,1,1(r, θ, φ) = 1
rer/2a0sin θ e
b) How many angular planar nodes does |2,1,1ihave? (8 points)
One angular node is found at θ= 0, which is the same plane defined
by θ=π. No nodes along φ.
c) Consider b
l2|2,1,1i. What is the magnitude of orbital angular momen-
tum of this state, and what is its projection onto the z-axis?
(5+5=10 points)
l2|2,1,1i=l(l+ 1)¯h2|2,1,1i= 2¯h2|2,1,1i
Magnitude of orbital angular momentum is h.
Since b
lz|2,1,1i=ml¯h|2,1,1i=¯h|2,1,1i, projection is ¯h.
d) Can the atom be excited from |2,1,1ito |4,0,1i? Explain. (8 points)
Yes, ∆l=1, which is a valid transition, since allowed transition have
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