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≤−aand x≥+ 3 a
(b)
(c)
(d)
10.12 (a)
(b)ψ(x) =0 at x=band x= 3 b
(c)
(d) λλ= 4 b
(e)
E
h
mb
V
()
=+
22
222 0
π
ψ
π
() sin
()
x
b
nx b
b
=
⎛ −
⎝
⎜⎜
⎞
⎠
⎟⎟
2
22
−+=
Z
2
2
mx^2 xVx Ex^0
d
d
ψψψ() () ()
λ==
24 ()
1
8
a
a
ψ
π
() sin
()
x ,,
a
nx a
a
= n
⎛ +
⎝
⎜⎜
⎞
⎠
⎟⎟ =
2
44
1 2 3...
−=
Z^22
2 mx^2 xEx
d
d
ψψ() ()
λ
(. )( )
.
==
hc ××−−
ΔE
663 10 3 10
42
(^34) Js (^8) m s 1
× 10 −^21 J
ΔE
(. )
(. )(
=
×
×
−
−−
663 10
8 9 11 10 10
34 2
31
Js
kg^882
43 4210^2221
m
J
)
().−= ×−
λ
()
== =
2210
4
20
4
L
n
nm
nm
λ
()
== =
2210
3
20
3
L
n
nm
nm
λ
(. )( )
.
==
hc ××−−
ΔE
663 10 3 10
14
(^34) Js (^8) m s 1
..
×
− =×− =
10
16 14 10^914
J
mnm
ΔE
(. )
(. )(
=
×
×
−
−−
663 10
8 9 11 10 10
34 2
31
Js
kg^1102
51 1410^2216
m
J
)
().−= ×−
λ
(. )( )
.
==
hc ××−−
ΔE
663 10 3 10
18
(^34) Js (^8) m s 1
.
×
− =×− =
10
17 1 1 10^811
J
mnm
ΔE
(. )
(. )(
=
×
×
−
−−
663 10
8 9 11 10 10
34 2
31
Js
kg^1102
21 1810^2217
m
J
)
().−= ×−
460 ANSWERS TO PROBLEMS
9781405124362_5_end.qxd 4/29/08 9:17 Page 460