42
Atomic Physics
CHAPTER OUTLINE
42.1
Atomic Spectra of Gases
42.2
Early Models of the Atom
42.3
Bohr’s Model of the
Hydrogen Atom
42.4
The Quantum Model of the
Hydrogen Atom
42.5
The Wave Functions of
Hydrogen
42.6
Physical Interpretation of the
Quantum Numbers
42.7
The Exclusion Principle and
the Periodic Table
42.8
More on Atomic Spectra:
Visible and Xray
42.9
Spontaneous and Stimulated
Transitions
42.10 Lasers
ANSWERS TO QUESTIONS
Q42.1
If an electron moved like a hockey puck, it could have
any arbitrary frequency of revolution around an atomic
nucleus. If it behaved like a charge in a radio antenna,
it would radiate light with frequency equal to its own
frequency of oscillation. Thus, the electron in hydrogen
atoms would emit a continuous spectrum, electromagnetic
waves of all frequencies smeared together.
*Q42.2
(a)
Yes, provided that the energy of the photon is
precisely
enough to put the electron into one of the
allowed energy states. Strangely—more precisely
nonclassically—enough, if the energy of the
photon is not sufF
cient to put the electron into a
particular excited energy level, the photon will not
interact with the atom at all!
(b)
Yes, a photon of any energy greater than 13.6 eV
will ionize the atom. Any “extra” energy will go
into kinetic energy of the newly liberated electron.
*Q42.3
Answer (a). The 10.5eV bombarding energy does not match the 10.2eV excitation energy
required to lift the atom from state 1 to state 2. But the atom can be excited into state 2 and the
bombarding particle can carry off the excess energy.
*Q42.4
(i) b (ii) g
±rom Equations 42.7, 42.8 and 42.9, we have
−=
− =
+ − =+
E
ke
r
r
r
KU
ee
e
e
22
2
.
Then
KE
=
and
UE
e
=−
2
.
489
Note
:
In chapters 39, 40, and 41 we used
u
to represent the speed of a particle with mass. In this
chapter 42
and the remaining chapters we go back to using
v
for the symbol for speed.
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Chapter 42
*Q42.5
In
∆
E
nn
if
= (
)
−
⎛
⎝
⎜
⎞
⎠
⎟
13 6
11
22
.e
V
for
∆
E
>
0 we have absorption and for
∆
E
<
0 we have emission.
(a)
for
n
i
=
2 and
n
f
=
5,
∆
E
=
286
V
(absorption)
(b)
for
n
i
=
5 and
n
f
=
3,
∆
E
=−
0 967
V
(emission)
(c)
for
n
i
=
7 and
n
f
=
4,
∆
E
0 572
V
(emission)
(d)
for
n
i
=
4 and
n
f
=
7,
∆
E
=
0 572
V
(absorption)
(i)
In order of energy change, the ranking is
a > d > c > b
(ii)
E
hc
=
λ
so the ranking in order of decreasing wavelength of the associated photon is c = d > b > a.
*Q42.6
(a) Yes. (b) No. The greatest frequency is that of the Lyman series limit. (c) Yes. We can imagine
arbitrarily low photon energies for transitions between adjacent states with
n
large.
Q42.7
Bohr modeled the electron as moving in a perfect circle, with zero uncertainty 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
∆∆
rp
r
be zero, less than the
minimum allowable
h
2
.
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 Spring '11
 williams,frank
 Atom, Energy, Mass, Photon, Atomic orbital, ev

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