Мартыненко Т.П. и др. Практический курс физики. Квантовая физика. Элементы физики твёрдого тела и ядерной физики
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191
)
4,12
; /1062,6
24
⋅⋅
−
; 1021,2
32−
⋅ ;
)
24,1
;
/1062,6
22
⋅⋅
−
;
1021,2
30−
⋅
.
1.52 )
960
; )
106,1
4
⋅
)
106,1
10
⋅
.
1.53 )
19
105⋅
; )
13
10
.
1.54
3
106,7
mTk8
h
N ⋅=
π
⋅⋅
⋅
λ
= , m – ,
k – .
1.55 745
k
m
8
h
2
2
=
λ
⋅
⋅
⋅π
= , m – .
1.56
117
1053,4
−
⋅=ν .
1.57
1036,2
sinb
ch
3−
⋅=
ϕ⋅
⋅
=
,
/1026,1
30
⋅⋅=
−
.
1.58 07,2
)sin(sind
ch
12
=
ϕ−ϕ
⋅
= .
1.59
4F
=
,
19
10N =
.
1.60
313
1052,2
ch)1(
n
−
⋅=
⋅⋅ρ+
λ
⋅
=
,
1221
1
1056,7nn
−−
⋅⋅=⋅=
.
1.61
6,4
=
`.
1.62
2
/5,1J =
.
1.63
10F
10−
=
.
1.64
/10
7
⋅=
−
.
1.65
7,11F
=
.
1.66
15
109N ⋅=
.
1.67
18
1
1077,3N ⋅=
.
1.68
312
10n
−
=
.
1.69
11
=
.
1.70 7,0
1
=
,
35,0
2
=
.
1.71
197
=
λ
; 175
0
=
λ
.
1.72 /1045,3p
25
max
⋅⋅=
−
.
1.73 517
Li0
=λ , 540
Na0
=λ , 620
K0
=λ , 660
Cs0
=λ .
1.74 5,4
min
=
ε
.
1.75 5,4
=
;
/101,9
5
max
⋅=υ
; 38,2108,3T
19
max
=⋅=
−
.
1.76 )
s
: /103,1
6
max
⋅=υ ;
Pt
: /1005,7
5
max
⋅=υ . )
s
: /1005,6
5
max
⋅=υ ;
Pt
.
1.77 15,2
min
=
ε
.
192
1.78
73,1V
=
.
1.79 1076,3x
4−
⋅=
1.80 2,24
=
λ
.
1.81 26,0=ε
′
; /103,9
12
⋅⋅=
′
−
.
1.82
1,0
=
ε
.
1.83 57
1
=
λ
.
1.84
°
=
θ
120
°
=
θ
240
.
1.85 224,0=ε
′
;
176,0
=
.
1.86
/108,2
22
⋅⋅=
′
−
.
1.87 0,5
1.88
0
4
60
′
°
=
θ
.
1.89
37,0=ε
.
1.90 70%.
1.91 8,4108,4
12
=⋅=λ∆
−
106,2
15−
⋅=λ∆
.
1.92
0
90=θ
, 0,24
=
′
.
1.93
2sin2
2sin2ch
2
c
2
c
e
θ⋅λ+λ
θ⋅λ⋅
λ
⋅
=ε
′
,
cm
h
e
c
⋅
=λ
, 184,118
e
=
ε
′
255 .
1.94
0
50=θ
.
1.95
/106,1p
22
e
⋅⋅=
′
−
.
1.96 1035,1
12−
⋅=λ∆ ,
0
4
63
′
°
=
θ
.
1.97
λ⋅⋅+
θ
=ϕ
cmh1
2
ctg
tg
e
.
1.98 03109
′
°
=
ϕ
+
θ
.
1.99 102,1
cm2
h
12
e
−
⋅=
⋅
=λ .
2.
2.17. 39 0,91 ; 0,15 0,082 .
2.18. 15,0m/)1(2
2
=∆⋅−η⋅π=λ
2.19.
132m2/2 =⋅⋅⋅π=λ
, – ; m –
.
2.20.
(
)
30
m2
BRe
T
p
2
2
p
== , – .
2.21.
38,0m2m2
2222
=−λ⋅π=∆
.
2.22. )
2
m21
1
m2
2
⋅+
⋅
⋅
⋅
π
=λ
;
193
)
≤
37
20
−
−
2.23.
(
)
21,0m12
2
=⋅⋅−=
;
2.24.
( )
−λ+⋅> 1L1cm
2
C
2
, 2,1Lcm
C
2
ee
=λ⋅⋅>
6,0
>
c
λ
– .
2.25. 3,3m1 =⋅πλ⋅⋅+λ=λ ,
λ
–
.
2.26.
( )
λ
−λλϕ
−
2
4
a
exp~
,
mkT2
h
a
2
= ;
89
Tkm
2
a
=
⋅⋅
⋅π
==λ
.
2.27.
/100,1xmbL4
6
⋅=∆⋅⋅⋅⋅π=υ
.
2.28.
(
)
24mxd/L2
2
=∆⋅⋅⋅π=
.
2.29.
(
)
15,0sin1dLm2U
2
2
222
0
=θ−η⋅⋅⋅⋅π= .
2.30.
(
)
21,0
2
cosm2d =
α
⋅⋅⋅⋅⋅π=
,
4
=
2.31. )
( )
Etpx
i
t
2
i2
AA)t,(
−
ν−
π
⋅⋅π
⋅=⋅=ψ
)
( )
Etrp
i
t
2
r
i2
AA)t,r(
−
ν−
π
⋅⋅π
⋅=⋅=ψ .
2.32.
104
14−
⋅=λ
.
2.33.
6
1027,7 ⋅
/1096,3
3
⋅
, 150 0,082 .
2.34. 2,1
e
=
λ
; 66,0=λ
2.35. 108,7
m2
m
Em2
h
15
H
0e
H
−
⋅≈⋅
⋅
≈λ∆ ,
H
m
– .
2.36.
18,0
RH
h
0
=
⋅⋅⋅µ
=λ
.
2.37.
( )
103,306,0
d
m
2
h
T
3
2
2
−
⋅÷≈
⋅
>
.
2.38.
( )
2
mc2/eU1meU2 +
=λ
2.39.
0
2
m4
λ
λ∆
⋅≈
; ) 20,4 ; ) 37,5 ; ) 150 .
2.40.
1007,2
T
ch
16−
⋅=
⋅
≈λ
. – .
194
2.41.
2
22
e
2
n
sindm8
h
U
υ⋅⋅⋅⋅
=
;
3,2,1n
=
U
= 26,1; 104,5; 235 .
2.42.
0
2b ≈⋅πλ=ϕ
.
2.43.
/102
2
e
⋅=υ∆
;
/1,0=υ∆
.
2.44.
/101
6
⋅=υ∆
; /102,2
6
1
⋅=υ .
2.45.
2
e
2
min
Lm2/T ≈ ,
4T
≈
.
2.46.
42
e
102,1TLm22
−
⋅=⋅⋅⋅⋅≈υυ∆ .
2.47.
224
Lm102 ⋅⋅⋅≈ .
2.48.
3cx
=
τ
⋅
≈
∆
,
8
1032
−
⋅≈τ⋅⋅πλ≈λλ∆
.
2.49.
( )
6,13
42
m
2
2
0
4
=
ε⋅π
⋅
=
;
53
m
4
r
2
2
0
=
⋅
⋅πε
=
.
2.50. .7,0
mE22
l
min
=≈
2.51. 1)
2
102,1
p
p
−
⋅=
∆
, 2)
2,1
p
p
=
∆
.
.
2.52. 1)
0
E
=
∆
, 2)
03,0E
≈
∆
.
2.53. )
,
a
2
A
π
=
) 0x = , )
,
4
a
x
2
2
=
) kp
x
= .
2.54.
2ax
⋅
=
∆
.
2.55.
2
2
22
n
n
L
m
2
E ⋅
⋅
⋅π
=
,
,...;2,1n
=
L
xn
sin
L
2
)x(
n
⋅⋅π
⋅=ψ .
2.56.
5,2L
=
.
2.57.
109,2
5
⋅=
.
2.58.
⋅π⋅
⋅
=
E2
mL
dE
dN
;
1
108,0
dE
dN
7
⋅=
.
2.59.
%2%,21%,78EE
nn
=∆
.
2.60. n = 3·10
9
. .
2.61.
L
3
1
1
=
;
L
3
2
2
=
;
( )
L
2
3
x
2
=ψ
.
2.62.
475,0P
=
.
2.63.
091,0P
=
.
2.64. )
b
yn
sin
a
xn
sin
ba
4
)y,x(
21
nn
21
⋅⋅π
⋅
⋅⋅π
⋅
⋅
=ψ
;
195
)
+⋅
⋅π
=
2
2
2
2
2
1
22
nn
b
n
a
n
m2
E
21
;
)
( ) ( )
−−
2
2
1
1
n2
b
1k2:
n2
a
1k2
;3n
;2n
2
1
=
=
.3,2,1k
.2,1k
2
1
=
=
2.65. P = 0,67.
2.66. )
a2
1
A
⋅π
=
; )
2
a
r >=<
.
2.67. )
0
r
2
1
)
⋅π
−
22
2
0
n2
3
1r
3
1
; )
⋅π
−
22
2
0
n
6
1r
12
1
.
2.68.
2
42
8
m⋅⋅
−=
;
0
4
1
ε⋅π
=
.
2.69. ) −
1
2
3
1
r
r2
expr
r
4
; ) 0,323; ) 0,238.
2.70.
1
rr = ;
1
r
2
3
r >=<
;
1
r
2
3
=σ .
2.71. )
3rr
1
2
=><
, )
1
r
1
r
1
>=<
;
10
2
r4
U
⋅ε⋅π
−>=<
,
)
2
1
2
r
2
r
1
>=< ;
2
10
2
r4
2
F
⋅ε⋅π
>=<
, )
677,0L5P
2
1
==
,
)
(
)
15
3
12
105,6rrP
−
⋅== .
2.72.
1
r21a ⋅=β−=
,
1
r –
9,52m4r
22
01
=⋅ε⋅π=
,
1
E
4
1
E −=
,
6,13
h8
m
E
22
0
4
1
=
ε
⋅
=
,
2
n
=
.
2.73.
3
1
r81 ⋅π=
.
2.74.
2
22
L
m
3
2
T
⋅
π⋅
⋅=
.
2.75.
2
m
ω
=β ;
2
E
ω
=
,
m
k
=ω .
2.76. ) 0; ) 0; )
2
0
x
2
1
,
(
)
ω⋅= mx
0
.
2.77. )
4
ω
⋅
; )
4
ω
⋅
.
2.78.
m
k
2
3
E ⋅=
.
196
2.79.
016,0R
=
;
77,0n
=
.
2.80.
2
n1
n1
R
+
−
=
.
2.81.
172,0n
1
=
; 83,5n
2
=
.
2.82.
2
E
U
16
1
R =
2.83. 2%.
2.84. 1,03.
2.85.
(
)
2
n1n4D +=
.
2.86.
384,0n
1
=
, 61,2n
2
=
.
2.87. D=0,2.
2.88. ) 1; )
( )
2exp
4
2
2
2
2
1
2
1
2
−
+
=ψ
.
2.89.
2
0
0
UEE
UEE
R
++
+−
=
; )
0
U
E
41R ⋅−=
; )
2
0
E4
U
R =
.
2.90.
( )
EUm22
x
0
.
−
=
; 1,0x
.
= .
2.91 ) 0,122; ) 42,9 .
2.92. )
( )
−
⋅
−≈
2/3
0
0
EU
U3
m2L4
expD ;
)
( )
−
⋅π
−≈ EU
U
m2L
expD
0
0
.
3. .
3.19
2
n
=
,...5,4,3n
=
′
)
656
1
=λ
; 365
=
λ
∞
;
) :
656
1
=λ
,
486
2
=
λ
,
434
3
=λ
,
410
4
=
λ
.
3.20
97,0
=
;
28,1
=
λ
.
3.21 )
8,40U
1
=
; )
8,91U
1
=
.
3.22 )
4,30
1
=λ
; )
5,13
=
λ
.
3.23
254
=
λ
.
3.24
775U
=
.
3.25 4,54U
=
; 122U
Li
=
.
3.26
3
n
=
.
3.27
3
n
=
; 6,102
1
=
λ
;
5,121
2
=λ
656
3
=λ
.
197
3.28
45
2
)1n(n
N =
−
=
.
3.29 , .
3.30
4
n
=
.
3.31
544,0
−
=
;
5n
=
.
3.32 B2,10U
12
=
; 6,13E
1
=
; 5,121
12
=
λ
; 2,91
1
=
λ
∞
;
115
12
1047,2
−
⋅=ν ;
115
1
1029,3
−
∞
⋅=ν ;
14
12
1023,8
−
⋅=ν ;
14
1
1097,10
−
∞
⋅=ν .
3.33
53
=
λ
.
3.34 397,0 ;
114
1055,7
−
⋅
.
3.35
17
1009,1R
−
⋅=
.
3.36
6,13
1
ch
3
4
1
i
=
λ
⋅=
.
3.37 2743; 2916, 686 439
1−
; 30,4, 292, 1055
2590 .
3.38 –
(
)
2327
→
→
, –
(
)
310 →
.
3.39
1005,1
c
em
5632
15
34
31
2
0
3
4
⋅⋅≈
⋅ε⋅π
⋅
⋅
λ∆⋅
=
−
.
3.40
4
4sindR
sindR
2n =
−ϕ⋅⋅
ϕ⋅⋅
⋅=
.
3.41 1950 .
3.42
5,52
=
λ
.
3.43
/107v
5
⋅=
. .
3.44
106,6
cM2
h
1
cM2
h
16−
⋅=
⋅
≈
ν
ν∆
−
⋅
=λ∆
1
<<
ν
ν
∆
,
ν
′
−
ν
=
ν
∆
, – .
/26,3M4Rh3v =⋅=
.
3.45
3
23
105,1N/N
−
⋅= .
3.46
12
nn →
,
Zn
1
=
, ,...;Z4,Z3,Z2n
2
=
(
Z
–
).
3.47 .
3.48
/101,3v
6
⋅=
.
3.49
1005,1
4
10
2
2
0
1
−
⋅=
⋅µ
⋅ε⋅π
=
,
µ
– .
8,6E
i
=
.
3.50 1085,2
13
1
−
⋅= ;
654,0
12
=λ
.
3.51
19
1007,2R
−
⋅=
;
92,1U
12
=
; 56,2U
i
=
.
198
3.52
2L =∆
,
(
)
62 −±
,
(
)
126 −
.
3.53
1064,312L
34
⋅⋅==
−
; 1015,33L
34
maxz
⋅⋅==
−
.
3.54
38,3E
p2
−=
;
1048,12L
34
⋅⋅==
−
;
/103,1
23−
⋅=µ
.
3.55
1091,0
34
⋅⋅
−
;
1005,2
34
⋅⋅
−
.
3.56
0
8,61
.
3.57
0
9,65
,
0
7,144
.
3.58
0
12,28=ϕ
.
3.59 4,4mvL
z
22
=
∂
∂
µ=∆ .
3.60 l = 4.
3.61
105,1L
34
⋅⋅=∆
−
;
2
.
3.62
0
26,35
.
3.63
0
5,10
.
3.64 32;
1004,2
34
⋅⋅
−
;
1091,0
34
⋅⋅
−
.
3.65
1046,0
23−
⋅±
.
3.66
3
1
µ
;
3
52
µ
.
3.67
0L
Z
=
,
34
1005,1
−
⋅±
,
101,2
34
⋅⋅±
−
.
3.68
nS
-
0L
=
,
np
-
34
105,12L
−
⋅==
⋅
.
3.69 1) ; 2) ; 3) 2(2l + 1) ;
4)
2
n
2
.
3.70 32 .
n
4
n
=
l
0 1 2 3
m
0 – 1,0,+1 –2, –1,0,1,2 –3, –2, –1,0,1,2,3
S
m
±
1/2
±
1/2
±
1/2
±
1/2
3.71
45=θ
, 90º, 135º.
3.72 ) 9, ) 2, ) 3, ) 5.
3.73
32622
p3s3p2s2s1
;
15N
=
.
3.74
46
N
=
3.75 ) 7, ) 3.
3.76
17
103
−
⋅
.
3.77
4
1014,1
−
⋅
.
3.78
30
10
−
.
3.79
3
103,2
−
⋅
.
199
3.80 5,75 .
3.81 Li, Na.
3.82 69,6 .
3.83 2,45 .
3.84
3 µ⋅=µ
.
3.85 – : 2/3 4/3, D – 4/5 6/5.
3.86 0;
/1031,1
23−
⋅
;
/1027,2
23−
⋅
.
3.87
247
1092,1I ⋅⋅=
ω∆
=
−
, 1012,1d
10−
⋅= .
3.88 2 3
3.89
113
c109,112
I
−
⋅==ω (I – ).
3.90 5,3
2
Edm
L
2
=
⋅⋅
= , m – .
3.91
111
c1024,7
−
⋅=ω∆ .
3.92 48,1E
=
∆
.
3.93 3,3
=
.
3.94 035,1L
−
=
∆
.
3.95
( )
247
12
21
106,2
c2
I ⋅⋅=
λ−λ⋅π
λ
⋅
λ
⋅
=
−
.
3.96 8J
m
=
.
3.97
392
=
.
3.98
111
109,24
81
Tk4
−
⋅=
⋅
=ω∆ .
3.99
347
=
.
3.100 13 .
3.101
30
N
≈
.
3.102 36
E
E
r
=
υ
.
3.103
2
r
107,1
E
E
⋅=
υ
.
3.104 67,1
N
N
0J
1J
=
=
=
.
3.105
4
101,3
N
N
−
⋅= .
3.106 1082,0
11−
⋅= ; /1089,1k
3
⋅= .
3.107 1012,1d
10−
⋅=
3.108 740
3lnk
=
⋅
ω
⋅
= .
3.109
K630T
=
.
200
4.
.
4.30.
max
= 5,49 ; v
max =
1,39·10
6
/c.
4.31.
F
= 11,55 ; v
max
= 2·10
6
/c.
4.32. n
1
/n
2
= 1,8.
4.33. N
1
/N
2
= 1,74.
4.34. ,
, 0,995.
4.35. n = 1,66·10
25
-3
.
4.36
max
= 4,68 ;
F
= 5,43·10
4
.
4.37. = 2,51·10
4
.
4.38. f (E,T) = 0,6.
4.39. ∼1,08 .
4.40. ∼11,63 .
4.41. = 1491 .
4.42. ∆
1
= 1,39 kT, ∆
2
= –1,39 kT.
4.43.
1
=300 ; f
1
(E,T
1
) = 0,128; f
2
(E,T
1
) = 0,87;
2
=60 ; f
1
(E,T
2
) = 6,8⋅10
-5
; f
2
(E,T
2
) = 1.
4.44.
.07,1
)T,E(f
)T,E(f
2
1
=
4.45. ∆
1
= 2,2 kT; ∆
2
= –2,2 kT.
4.46. ∆
1
= –0,05
,881,0
)T,E(f
)T,E(f
22
11
=
∆
1
= +0,05
.1029,1
)T,E(f
)T,E(f
4
24
13
⋅=
4.47. = 572 , 2) .
4.48. < > = 4,8 .
4.49.
max
= 2,029 ; < > = 1,217 .
4.50.
max
= 7 .
4.51. = 394 .
4.52. = 1,32 .
4.53. . < > = 3 .
4.54. = 3,3 ·10
4
.
4.55.
.E
m2
2
V
)E(g
2/3
22
⋅
π
=
4.56. N=3·10
23
.
4.57.
.65,0)5,01(
N
N
2/3
max
=−=
∆
=η
4.58. <∆
i
> = 2·10
-23
, <∆
i
> η .