10.8
10.9
10.10 (a) n = 3
(b)
(c) n = 4
(d)
(e)
= 4.74 × 10
−5 m = 47,400 nm
10.11 (a) The wavefunction is zero at x ≤ −a and x ≥ +3a
(b)
(c)
(d)
10.12 (a)
(b) ψ(x) = 0 at x = b and x = 3b
(c)
(d) λ
λ = 4b
(e) E
h
m b
V
( )
=
+
2 2
2
0
2 2
π
ψ
π
( )
sin
(
)
x
b
n x b
b
=
−
⎛
⎝
⎜ ⎜
⎞
⎠
⎟ ⎟
2
2
2
−
+
=
Z
2
2
2
0
m x
x
V x
E x
d
d
ψ
ψ
ψ
( )
( )
( )
λ =
=
( )
2 4
1
8
a
a
ψ
π
( )
sin
(
)
, ,
x
a
n x a
a
n
=
+
⎛
⎝
⎜ ⎜
⎞
⎠
⎟ ⎟
=
2
4
4
1 2 3 . . .
−
=
Z
2
2
2
2m x
x
E x
d
d
ψ
ψ
( )
( )
λ
( .
)(
)
.
=
=
×
×
−
−
hc
E
Δ
6 63 10
3 10
4 2
34
8
1
Js
m s
×
−
10
21 J
ΔE
( .
)
( .
)(
=
×
×
−
−
−
6 63 10
8 9 11 10
10
34
2
31
Js
kg
8 8
2
2
2
2 1
4
3
42 10
m
J
)
(
)
.
−
=
×
−
λ
(
)
=
=
=
2
210
4
20
4
L
n
nm
nm
λ
(
)
=
=
=
2
210
3
20
3
L
n
nm
nm
λ
( .
)(
)
.
=
=
×
×
−
−
hc
E
Δ
6 63 10
3 10
1 4
34
8
1
Js
m s
.
.
×
=
×
=
−
−
10
1 4 10
1 4
16
9
J
m
nm
ΔE
( .
)
( .
)(
=
×
×
−
−
−
6 63 10
8 9 11 10
10
34
2
31
Js
kg
1 10
2
2
2
1 6
5 1
14 10
m
J
)
(
)
.
−
=
×
−
λ
( .
)(
)
.
=
=
×
×
−
−
hc
E
Δ
6 63 10
3 10
1 8
34
8
1
Js
m s
.
×
=
×
=
−
−
10
1 1 10
11
17
8
J
m
nm
ΔE
( .
)
( .
)(
=
×
×
−
−
−
6 63 10
8 9 11 10
10
34
2
31
Js
kg
1 10
2
2
2
1 7
2
1
18 10
m
J
)
(
)
.
−
=
×
−
460
ANSWERS TO PROBLEMS
9781405124362_5_end.qxd 4/29/08 9:17 Page 460