Мартыненко Т.П. и др. Практический курс физики. Квантовая физика. Элементы физики твёрдого тела и ядерной физики
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91
.
.
3.62. ,
,
.
d - .
3.63. n = 4,
.
,
.
3.64. ,
= 97,2 . : )
; )
.
3.65.
= 0,5 .
.
3.66. p - .
( ).
3.67.
L
( d - ).
3.68. L
, : 1) S - ; 2) P-
.
3.69. , ,
: 1) n, l, m, m
S
2) n, l, m 3) n, l 4) n.
3.70.
n = 4. .
3.71. - .
, ,
L
Z.
3.72. M - ,
: ) m
S
= +1/2; ) m
l
= – 2; ) m
S
= – 1/2
m
l
= 0; ) m
S
= +1/2 l = 2.
3.73. , K L
, 3s- 3p- .
.
92
3.74. , K -,
L - , M - , 4s-, 4p- 4d- .
3.75.
: ) m
l
= 0, ) l = 1, m
S
= +1/2.
.
3.76.
n = 2
= 3000 ?
3.77.
3P
= 2400 . 3P 3S = 589 .
3.78.
t = 27ºC,
= 694 . .
3.79.
2 = 3000 .
(2 2S) = 670,8 .
3.80. K L
. K L
1
= 1
2
= 7,4 .
3.81.
K - L -
?
3.82.
, K -
.
3.83.
= 65 K - .
.
3.84.
S - ( ).
3.85.
P - D – .
3.86. ,
, = 12,09 .
3.87.
,
112
c1050,5
−
⋅=ω∆ .
93
3.88. HCl
, = 7,86 .
HCl 10275,1d
10−
⋅= .
3.89.
113
c1064,1
−
⋅=ω .
.
1012,1d
10−
⋅= .
3.90. ,
= 2,16 .
2
10207,1d
10−
⋅= .
3.91.
10128,1d
10−
⋅= .
.
3.92. N
2
.
N
2
1010,1d
10−
⋅= .
3.93. NO ,
,
. NO
1015,1d
10−
⋅= .
3.94.
1250
=
λ
,
.
N
2
1010,1d
10−
⋅= .
3.95.
HCl 117
1
=
λ
156
2
=
λ
. HCl.
3.96. J
O
2
= 300 . O
2
10207,1d
10−
⋅= .
3.97. , I
2
,
J = 60.
I
2
10667,2d
10−
⋅= .
.
94
3.98. , ,
= 384,5 .
J = 4.
.
3.99. , NO,
J
1
= 5 J
2
= 12 ?
NO 1015,1d
10−
⋅= .
3.100. HF ,
. HF
10917,0d
10−
⋅= ,
114
c10796,7
−
υ
⋅=ω . .
3.101. ,
CO.
10128,1d
10−
⋅= ,
114
c10088,4
−
υ
⋅=ω .
3.102. H
2
,
.
H
2
114
c10279,8
−
υ
⋅=ω ,
10741,0d
10−
⋅= . .
3.103. ,
HI
. HI
114
c10350,4
−
υ
⋅=ω ,
10604,1d
10−
⋅= . .
3.104.
J = 1
= 300 .
H
2
10741,0d
10−
⋅= .
3.105.
1
=
υ
, J = 0,
0
=
υ
, J = 1
= 880 .
2
10741,0d
10−
⋅= ,
114
c10279,8
−
υ
⋅=ω .
95
3.106.
,
.
.
114
c1008,4
−
υ
⋅=ω .
3.107. –
CH, ,
J = 0,
113
c101,1
−
⋅=ω∆ . .
.
3.108.
:
1
Tk
exp
2
−
⋅
ω⋅
ω
⋅
+
ω
⋅
=ε
,
,
.
114
c10064,1
−
υ
⋅=ω .
3.109.
, ,
0
=
υ
, J = 5.
114
c10977,2
−
υ
⋅=ω ,
10207,1d
10−
⋅= .
96
4.
.
.
,
,
. ,
,
.
d.
1
3
10
22
- 10
23
, d ≅ 3⋅10
–8
. ,
.
1
,
2
,
3
...,
n
1
, n
2
, n
3
, ( .4.1).
.
. ,
d
(∼ 3⋅10
-8
), ,
,
- .
.
,
( . 4.2).
.
(n ),
E
E
1
E
2
E
3
n=1
n=3
n=2
. 4.1
d
. 4.2
97
D.
τ.
" " ,
τ = ∞.
,
τ = 1/ω⋅ D, ω –
, D –
. , ,
, D , τ .
≥
∆
⋅
∆
t
E
(
π
=
2/h
– ,
1005,1
34
⋅⋅=
−
) ∆t τ,
∆E→0, . .
.
τ 10
-15
,
1
/106,110
101,05
1915
34
≅
⋅⋅
⋅⋅
=
−−
−
,
∆E ( . 4.3).
.
,
,
.
∆E
1
∆E
2
E
2
-E
1
,
∆E .
N – (
).
∆E
i
= ∆E/N, ∆E – . ,
∆E
i
= 1 /10
22
= 10
-22
.
= kT (k=1,38⋅10
-23
/ ),
( =300 ) 0,025 .
. .
d
.4.3
98
,
E)m2(V4
)2(
3/2
3
i
π
π
=∆
(4.1)
m – , V – , – .
,
.
,
. ,
n = 2, 8 (2n
2
),
, , N, ,
n = 2 8N .
: 1) . 2)
.
4- .
.
: "
2-
, ".
,
, ,
. , ( )
, .
, .
.
,
( . 4.4).
–
– :
, .
E
E
. 4.4
99
.
.
,
, ,
,
,
d ,
.
.
.
,0E
m2
zyx
22
2
2
2
2
2
=Ψ+
Ψ
+
Ψ
+
Ψ
(4.2)
– , m – , –
.
– ,
, –
, , z L (L – ).
:
)Lz,y,x()z,y,x(
)z,Ly,x()z,y,x(
);
z
,
y
,
L
x
(
)
z
,
y
,
x
(
+Ψ=Ψ
+Ψ=Ψ
+
Ψ
=
Ψ
(4.3)
(4.2) .
,
, , z.
(x) =
x
, ( ) =
y
, (z) =
z
.
)z()y()x()z()y()x(
zy
Ψ⋅Ψ⋅Ψ=Ψ⋅Ψ⋅Ψ=Ψ
(4.4)
2
z
2
yx
2
2
2
y
2
zx
2
2
2
x
2
zy
2
2
dz
d
z
;
dy
d
y
;
dx
d
x
Ψ
⋅Ψ⋅Ψ=
Ψ
Ψ
⋅Ψ⋅Ψ=
Ψ
Ψ
⋅Ψ⋅Ψ=
Ψ
(4.2)
.0E
m2
dz
d
dy
d
dx
d
xyx
22
z
2
yx
2
y
2
zx
2
x
2
zy
=Ψ⋅Ψ⋅Ψ⋅+
Ψ
⋅Ψ⋅Ψ+
Ψ
⋅Ψ⋅Ψ+
Ψ
⋅Ψ⋅Ψ
100
xyx
1
ΨΨΨ
,
,E
m2
dz
d
·
1
dy
d
·
1
dx
d
·
1
22
z
2
z
2
y
2
y
2
x
2
x
−=
Ψ
Ψ
+
Ψ
Ψ
+
Ψ
Ψ
(4.5)
,kE
m2
2
2
=
k - =
λ
π
2
–
.
(4.5) ,
, (4.2) ,
:
2
x
2
x
2
x
k
dx
d
1
−=
Ψ
⋅
Ψ
0k
dx
d
x
2
x
2
x
2
=Ψ⋅+
Ψ
(4.6)
2
y
2
y
2
y
k
dy
d
1
−=
Ψ
⋅
Ψ
0k
dy
d
y
2
y
2
y
2
=Ψ⋅+
Ψ
(4.7)
2
z
2
z
2
z
k
dz
d
1
−=
Ψ
⋅
Ψ
0k
dz
d
z
2
z
2
z
2
=Ψ⋅+
Ψ
(4.8)
,kkkk
2
z
2
y
2
x
2
++=
(4.6 ÷ 4.8)
,eA
xik
x
x
⋅=Ψ
,eB
yik
y
y
⋅=Ψ
,eC
zik
z
z
⋅=Ψ
, , – .
(4.3)
,ee
)Lx(ikxik
xx
+
=
,1e
Lik
x
=
,n2Lk
xx
π=⋅
,...)2,1,0n(
x
±±=
,
,ee
)Ly(ikyik
yy
+
=
,1e
Lik
y
=
,n2Lk
yy
π=⋅
,...)2,1,0n(
y
±±=
,
,ee
)Lz(ikzik
zz
+
=
,1e
Lik
z
=
,n2Lk
zz
π=⋅
,...)2,1,0n(
z
±±=
,
n
x
, n
y
, n
z
– , .
,
( )
2
z
2
y
2
x
2
2
z
2
y
2
x
2
nnn
L
2
kkkk ++
π
=++=
.
2
2
kE
m2
=
, ,
(
)
22
z
2
y
2
x
nnnn =++
,
:
2
2
2
n
n
L
2
m2
E ⋅
π
=
(4.9)