12.5
12.6
12.7 Principal, n=1, 2, 3,...; angular momentum, l=0, 1, 2,...,
n−1; magnetic ml=l, l−1, l−2,... , −l.
12.8
12.9 n, Quantization of energy; l, quantization of total angular momen-
tum; ml: quantization of the zcomponent of angular momentum.
12.10
12.11
12.12
12.13
1
22
1
4
2
0
3
0
2
3
0
πa
r
a
era
a
⎛ − /
⎝
⎜
⎜
⎞
⎠
⎟
⎟
⎡
⎣
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
−
00
2
4 2
∞
∫ ()πrrd
1
224
2
(^32)
0
3
0
Z 2
a
r
a
e
i
ra
π
− /
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
∇
⎛
⎝
⎜⎜
⎞
⎠
∫
− 0 Z ⎟⎟
⎟ −
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
(^1) −
224
2
(^32)
0
3
0
Z (^202)
a
r
a
errra
π
/ dd dθ φφ
=−
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
∞
−
∫
(^1) /
8
2
0
3
3
0 0
2
0
a
r
r
a
errad
ψψτ
π
*drr
a
r
a
=−era/
⎛
⎝
⎜⎜
⎞
⎠
⎟⎟ −
∞
∫
1
16
1
2
2
0
3
0
2
0 0
0
∞∞
∫^4
πrr^2 d
λ
()(. )
==.
×
− =
9
8
9
829 11 10
2251122
ZRh cm
××= 10 −^8 cm 1 22. Å
ΔEZhcR
hc
=− h −
⎛
⎝
⎜⎜
⎞
⎠
(^222) ⎟⎟=
1
3
1
1 λ
λ
(. )
==.
×
− =×−
9
8
9
811 10
51 103 10^5
Rh cm
cmm
ΔEhcR
hc
=− h −
⎛
⎝
⎜⎜
⎞
⎠
⎟⎟=
1
3
1
(^221) λ
0
8
15
0
3
2
0
(^00)
=−/ ⎛
⎝
⎜⎜
⎞
⎠
− ⎟⎟ ==
a
er
r
a
ra or ra ..29 10× − (^10) m
04 = ()^2
d
d
*
r
πψψr
==×. −
3
2
(^0) 79 10 11
a
m
4
44
0
3
3
0
2
0
32
0
a re^0 r a xe x ae^0
ra x
∞
− −
∞
−
∫∫==
/ dd 22
32
(^20)
3
4
3
4
3
8
x⎛−− − −xxx
⎝
⎜⎜
⎞
⎠
⎟⎟
∞
ψψτ
π
*drr π d
a
= errra/
⎛
⎝
⎜⎜
⎞
⎠
⎟⎟ −
∞ ∞
∫∫
1
4
0
3
2
0 0
(^02) ==
∞
−
∫
(^4) /
0
3
3
0
(^20)
a
reradr
ANSWERS TO PROBLEMS 467
9781405124362_5_end.qxd 4/29/08 9:17 Page 467