29-1
A
TOMS
, M
OLECULES
,
AND
S
OLIDS
29
Answers to Multiple-Choice Problems
1.
A, C
2.
A, D
3.
B, D
4.
B
5.
A, D
6.
A, B, E
7.
B
8.
C
9.
C
10.
D
Solutions to Problems
29.1.
Set Up:
1,
Solve:
0,
1, 0,
There is one state for
three for
and five for
The total number of states is
29.2.
Set Up:
Solve: (a)
The largest
is for
and is
(b)
L
is larger than the maximum possible
(c)
For
and
For
and
For
and
For
and
For
and
For
and
For
and
29.3.
Set Up:
1,
Solve: (a)
0,
0,
(b)
In each case
not defined.
Reflect:
There is no state where
is totally aligned along the
z
axis.
29.4.
Set Up:
1,
Solve: (a)
0,
0,
0,
0,
(b)
not defined.
(c)
The minimum angle is
and occurs for
The maximum angle is
and occurs for
m
l
5 2
4
l
5
4,
153.4°
m
l
5 1
4.
l
5
4,
26.6°
153.4°.
132.1°,
116.6°,
102.9°,
90.0°,
77.1°,
63.4°,
47.9°,
26.6°,
L
5
2
"
5
U
:
150.0°.
125.3°,
106.8°,
90.0°,
73.2°,
54.7°,
L
5
2
"
3
U
:
144.7°.
114.1°,
90.0°,
65.9°,
35.3°,
L
5
"
6
U
:
135.0°.
90.0°,
45.0°,
L
5
"
2
U
:
u
L
5
0:
2
4
U
.
2
3
U
,
2
2
U
,
2
U
,
U
,
2
U
,
3
U
,
L
z
5
4
U
,
L
5
2
"
5
U
,
l
5
4:
2
3
U
.
2
2
U
,
2
U
,
U
,
2
U
,
L
z
5
3
U
,
L
5
2
"
3
U
,
l
5
3:
2
2
U
.
2
U
,
U
,
L
z
5
2
U
,
L
5
"
6
U
,
l
5
2:
2
U
.
L
z
5
U
,
L
5
"
2
U
,
l
5
1:
L
z
5
0.
L
5
0,
l
5
0:
cos
u 5
L
z
/
L
.
6
l
.
6
2,
c
,
6
1,
m
l
5
0,
n
2
1.
2,
c
,
l
5
0,
L
z
5
m
l
U
.
L
5
"
l
1
l
1
1
2
U
.
L
S
144.7°.
114.1°,
90.0°,
65.9°,
35.3°,
L
5
"
6
U
:
135.0°.
90.0°,
45.0°,
L
5
"
2
U
:
u
L
5
0:
cos
u 5
L
z
/
L
.
2
2
U
.
2
U
,
U
,
L
z
5
2
U
,
L
5
"
6
U
,
l
5
2:
2
U
.
L
z
5
U
,
L
5
"
2
U
,
l
5
1:
L
z
5
0.
L
5
0,
l
5
0:
cos
u 5
L
z
/
L
.
6
l
.
6
2,
c
,
6
1,
m
l
5
0,
n
2
1.
2,
c
,
l
5
0,
L
z
5
m
l
U
.
L
5
"
l
1
l
1
1
2
U
.
u 5
150.0°.
cos
u 5
2
3
U
2
"
3
U
L
z
5 2
3
U
,
u 5
125.3°.
cos
u 5
2
2
U
2
"
3
U
L
z
5 2
2
U
,
u 5
106.8°.
cos
u 5
2
U
2
"
3
U
L
z
5 2
U
,
u 5
90.0°.
cos
u 5
0
L
z
5
0,
u 5
73.2°.
cos
u 5
U
2
"
3
U
L
z
5
U
,
u 5
54.7°.
cos
u 5
2
U
2
"
3
U
L
z
5
2
U
,
u 5
30.0°.
cos
u 5
3
U
2
"
3
U
L
z
5
3
U
,
L
z
.
L
5
"
3
1
3
1
1
2
U
5
2
"
3
U
5
3.46
U
.
L
z
5
3
U
.
m
l
5
3
L
z
cos
u 5
L
z
/
L
.
L
5
"
l
1
l
1
1
2
U
.
6
l
.
6
2,
c
,
6
1,
m
l
5
0,
L
z
5
m
l
U
.
1
1
3
1
5
5
9.
l
5
2.
l
5
1,
l
5
0,
2
2.
2
1,
m
l
5
2,
l
5
2:
2
1.
m
l
5
1,
l
5
1:
m
l
5
0.
l
5
0:
6
l
.
6
2,
c
,
6
1,
m
l
5
0,
n
2
1.
2,
c
,
l
5
0,