Chemistry 120A Problem Set 6
(due March 17, 2010)
1. Problems 643, 644 and 645 in McQuarrie and Simon. These problems lead you
through the textbook’s treatment of orbital magnetization in the hydrogen atom.
You might find them helpful as background for Problem 2 below.
2. The orbital motion of the electron in a hydrogen atom produces a magnetic moment
in the
z
direction,
μ
z
=

(
e/
2
m
e
c
)
L
z
,
where

e
and
m
e
are, respectively, the charge and mass of an electron,
c
is the speed
of light, and
L
z
is the differential operator giving the
z
component of the angular
momentum. The energy of a magnetic moment in a static magnetic field,
~
B
=
B
ˆ
z
,
is
E
mag
=

μ
z
B
.
Use first order perturbation theory for the energy and calculate the expectation
values for the energy when the hydrogen atom is in the states (
n, ‘, m
)=(2,1,1),
(2,1,0), and (2,1,1). Compare your results with the magnetic energies discussed in
lecture.
3. The instantaneous dipole moment of a hydrogen atom is
~μ
=

e~
r
, where
~
r
is the
position of the electron relative to that of the nucleus. The energy of a dipole in an
electric field,
~
E
, is
E
elec
=

~μ
·
~
E
.
With this formula in mind, you will consider the Hamiltonian for a hydrogen atom
perturbed by an electric field and use first order
degenerate
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 Spring '10
 DAVIDCHANDLER
 Hydrogen atom

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