797
Atomic Physics
CHAPTER OUTLINE
29.1
Early Structural Models of
the Atom
29.2
The Hydrogen Atom
Revisited
29.3
The Wave Functions for
Hydrogen
29.4
Physical Interpretation of
the Quantum Numbers
29.5
The Exclusion Principle
and the Periodic Table
29.6
More on Atomic Spectra:
Visible and XRay
29.7
Context Connection
Atoms in Space
ANSWERS TO QUESTIONS
Q29.1
Bohr modeled the electron as moving in a perfect circle, with zero
uncertainity in its radial coordinate. Then its radial velocity is always
zero with zero uncertainty. Bohr’s theory violates the uncertainty
principle by making the uncertainty product
∆ ∆
r p
r
be zero, less
than the minimum allowable
h
2
.
Q29.2
Fundamentally, three quantum numbers describe an orbital wave function because we live in three
dimensional space. They arise mathematically from boundary conditions on the wave function,
expressed as a product of a function of
r
, a function of
θ
, and a function of
φ
.
Q29.3
Bohr’s theory pictures the electron as moving in a flat circle like a classical particle described by
F
ma
∑
=
. Schrödinger’s theory pictures the electron as a cloud of probability amplitude in the
threedimensional space around the hydrogen nucleus, with its motion described by a wave
equation. In the Bohr model, the groundstate angular momentum is
1
h
; in the Schrödinger model
the groundstate angular momentum is zero. Both models predict that the electron’s energy is
limited to discrete energy levels, given by
−
13 606
2
.
eV
n
with
n
=
1
2
3
,
,
.
Q29.4
The term
electron cloud
refers to the unpredictable location of an electron around an atomic nucleus.
It is a cloud of probability amplitude. An electron in an
s
subshell has a spherically symmetric
probability distribution. Electrons in
p
,
d
,
and
f
subshells have directionality to their distribution. The
shape of these electron clouds influences how atoms form molecules and chemical compounds.
Q29.5
The direction of the magnetic moment due to an orbiting charge is given by the right hand rule, but
assumes a
positive
charge. Since the electron is negatively charged, its magnetic moment is in the
opposite direction to its angular momentum.
Q29.6
The deflecting force on an atom with a magnetic moment is proportional to the
gradient
of the
magnetic field. Thus, atoms with oppositely directed magnetic moments would be deflected in
opposite
directions in an inhomogeneous magnetic field.
Q29.7
Practically speaking, no. Ions have a net charge and the magnetic force
q
r
r
v
B
×
e
j
would deflect the
beam, making it difficult to separate the atoms with different orientations of magnetic moments.
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798
Atomic Physics
Q29.8
The SternGerlach experiment with hydrogen atoms shows that the component of an electron’s spin
angular momentum along an applied magnetic field can have only one of two allowed values. So
does electron spin resonance on atoms with one unpaired electron.
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 Spring '08
 DAFSF
 Physics, Atom, Atomic physics, ev

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