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CHEM 132B Study Guide - Quiz Guide: Spherical Harmonics, Term Symbol, Haplogroup R2AExam

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Eric Potma
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Chem 132B Practice Quiz 2 Key
Version B
Problem 1
Encircle all that are true regarding the spherical harmonic wavefunctions.
a) The energy associated with the spherical harmonic wavefunctions is inde-
pendent of the quantum number ml.True
b) The magnitude of orbital angular momentum is not quantized, but its
projection onto a chosen axis is. False
c) If we determine the angular momentum of the spherical harmonic wave-
function along x, then its projections along zand yare unknown. True
d) We cannot both determine the magnitude of orbital angular momentum
and its projection onto the z-axis at the same time. False
Problem 2
Encircle all that are true.
a) The groundstate of hydrogen is 2S0.False
b) The groundstate of helium is 1S0.True
c) The groundstate of He+is 2S1/2.True
d) The groundstate of His 2P1/2.False
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Problem 3
An excited hydrogen atom is the 2s1configuration.
a) Give an expression for
1) the radial part of the wavefunction (Rn,l(r)).
2) the angular part of the wavefunction (Yl,ml(θ, φ)).
R2,0(r) = 1
a03/2(2 r/a0)er/2a0
Y0,0(θ, φ) = 1
b) Determine the location (r > 0) along rwhere there is zero probability of
finding the electron (in units of a0).
Radial node is found when R2,0(r) = 0, which is when (2 r/a0) = 0.
This gives r= 2a0
c) Give the term symbol of the 2s1configuration.
l= 0, s =1
2, j =1
2, which gives 2S1/2
d) Can the atom decay to the ground state through the emission of a photon?
No, ∆l6=±1.
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