Мартыненко Т.П. и др. Практический курс физики. Квантовая физика. Элементы физики твёрдого тела и ядерной физики
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141
.108,7
1062,6
3741038,1
h
k
12
34
23
max
⋅=
⋅
⋅⋅
=
θ
=ν
−
−
(2)
.106,5108,71062,6hE
211234
maxmax
−−
⋅=⋅⋅⋅=ν⋅= (3)
(4.59 ):
max
max
v
h
p
ν
=
; (4)
v –
, v = ·ν. ν
max
min
= 2d,
d – .
v 2dν
max
(5).
(2), (3), (4) (5)
max
max
max
d2
p
ν
=
.
max
=5,16·10
–21
, ν
max
= 7,8·10
12
, d =3·10
–10
,
./101,1
108,71032
1016,5
p
24
1210
21
max
⋅⋅=
⋅⋅⋅⋅
⋅
=
−
−
−
4.26. ∆U
0 0,08⋅ .
<< .
0
0,08⋅ (4.72):
.dT)T(C
M
m
dT)T(C
M
m
U
08,0
0
m
T
0
m
θ
==∆ (1)
<< ,
(4.69)
3
4
m
T
R
5
12
C
θ
π=
. (2)
(2) (1),
=
θ
π
=
θ⋅
π
=∆
θ
θ
08,0
0
4
3
4
08,0
0
3
34
4
TR
5
12
M
m
5
dTRT12
M
m
U
( )
.)08,0(R
5
3
M
m
08,0
R
5
3
M
m
444
4
3
4
θ⋅π=θ
θ
π
=
(3)
142
(4.64)
θ= R
8
9
U
0
m
,
M
m
R
8
9
U
0
m
θ=
. (4)
(3) (4), :
.1017,2)08,0(
15
8
M
m
R95
8)08,0(R
M
m
3
U
U
344
44
−
⋅=π=
θ⋅⋅
⋅θ⋅⋅π
=
∆
4.27.
.
, d = 5,64·10
–10
5·10
3
/ , = 2,17·10
3
/
3
, = 58,5·10
–3
/ .
, . . .
,
.
,
( , ),
,
:
,vC
3
1
'
m
l=κ (1)
C
'
m
⋅ρ=
– , < l > –
, v –
.
m
= 50,58 /( · ) –
.
:
.K/1088,1
105,58
58,501017,2
M
C
36
3
3
m
'
m
⋅⋅=
⋅
⋅⋅
=
⋅ρ
=⋅ρ=
−
(1) < l >, v ,
'
m
C V
143
).K/(06,71051064,541088,1
3
1
3106
⋅⋅=⋅⋅⋅⋅⋅⋅⋅=κ
−
4.28. =129,8 ,
G = 48,33 , ρ = 8,90 /
3
.
.
(4.62):
k· = ·
max
(1)
(4.56):
,
v2v
n18
3
33
II
2
max
−
⊥
+
π
=ω (2)
n – n = N / ,
,
G
v
ρ
=
⊥
(3)
–
,
E
v
ρ
=
(4)
– . (2), (3)
(4) (1), .
.
G
M2
E
M
N18
k
)vv(M
N18
kk
3/1
2/32/3
A
2
3
33
||
A
2
max
ρ
+
ρ
ρπ
⋅=
+
ρπ
⋅=
ω⋅
=ω
−−−
⊥
−
(5)
, = 1,05·10
–34
⋅ , k = 1,38·10
-23
/ , = 8,9·10
3
/
3
,
N
A
= 6,02·10
23
–1
, = 64·10
–3
/ , G = 48,33·10
9
,
=129,8·10
9
(5)
= 334 .
4.29. <n
m
>
= 400
, = 200 ?
(4.61)
144
.
1)kT/exp(
1
n
i
i
−ν
=
(1)
ν
i
– , .
ν
i
= ν
m
,
(4.62)
max
= k (2), –
.
ν
max
(2), (1),
:
.
1e
1
1e
1
n
T/kT/k
i
−
=
−
=
θθ
/ = 200/400 = 0,5
.54,1
1
e
1
n
5,0
i
=
−
=
.
4.30.
= 0 , ,
.
= 19,3·10
3
/
3
, = 197·10
–3
/ .
4.31.
= 0 , ,
.
ρ = 2,69·10
3
/
3
, = 27·10
–3
/ .
4.32. n
1
/n
2
= 0 , ,
max1
= 7 ,
m 2
= 4, 72 .
4.33. N
1
/N
2
5
3
2
3
= 0 ,
,
,5,5E
Ag
F
=
.7E
u
F
=
4.34. ,
= 0 .
F
= 3,12 , ρ = 970 /
3
, =
23·10
–3
/ .
4.35.
0° ?
145
4.36.
m
= 0 , ,
.
.
= 540 /
3
, = 7·10
-3
/ .
4.37.
,
= 0 ?
,
. ρ = 10,5·10
3
/
3
,
= 108·10
-3
/ .
4.38.
, =0,01
, t = +18° ?
4.39.
,
0,01
T
1
=200 T
2
=300 ?
4.40.
,
=0,1
T
1
=1000 K T
2
=300 K?
4.41. ,
0,5
2%?
4.42. ( k ) ,
, ,
, 0,2 0,8.
4.43. ,
,
= 0,05
1)
1
= 300 , 2)
2
= 60 .
4.44.
, = 0,01
T
1
=1000 ,
T
2
= 500 ?
4.45. ( k )
,
0,1 0,9.
f( , ).
4.46. ,
,
∆ = 0,05
,
1
= 290 ,
2
= 50 K.
146
4.47. ,
,
∆E = 0,02 , 0,4?
,
, , 0,5?
4.48. <E>
= 0 ,
F
= 8 .
4.49.
T = 0 , ,
.
ρ = 860 /
3
, = 39·10
–3
/ .
4.50.
,
= 0 <E> = 4,2 .
4.51. ,
0,1
5%.
4.52.
1
3
= 0 . = 1,959·10
3
/
3
, = 133·10
–3
/ .
4.53. < >
, ?
= 0 ,
5 .
4.54. ,
, ,
= 0 .
ρ = 8,9·10
3
/
3
, = 64·10
–3
/ .
4.55. ,
= 0 (
).
4.56. 0
F
= 0 5
3
,
E
F
= 5,5 .
4.57. η
,
?
4.58. 0,5
.
E = 6 .
<∆E
i
>?
?
147
4.59. ∆E
i
.
1
3
, ∆E
i
( )
, ) 1 , ) 3 .
4.60. η
,
?
4.61.
, .
(
F
).
4.62.
= 0 . , ,
.
ρ = 0,54 /c
3
, = 7·10
–3
/ .
4.63. = 0
, ,
. , ,
.
ρ = 10,5·10
3
/
3
, = 108·10
-3
/ .
4.64. = 0 . ,
F
/4
F
/2
0
F
/2.
4.65. = 0 .
N/N,
4%.
4.66. n
1
= 0 ,
0,02
F
, n
2
,
0,5
F
.
4.67. n
1
= 0 ,
= 0,04
F
, n
2
,
= 0,04
F
.
4.68.
,
η = 2%, = 0 .
4.69.
= 0 ,
?
4.70.
,
148
= 0 ?
,
. = 19,3·10
3
/
3
, =
197·10
–3
/ .
4.71. ( )
= 0
, n =
·10
22
–3
, V = 5
3
.
4.72. < V > = 0 ,
,
. = 8,9·10
3
/
3
, =
64·10
–3
/ .
4.73. < V >
= 0 v
max
.
< V >
, E
F
=5,5 .
4.74. ,
= 0
0,75v
m
.
, ,
. =
1,84·10
3
/
3
, = 9·10
–3
/ .
4.75.
= 0 , ,
.
= 2,7·10
3
/
3
, = 27·10
-3
/ .
4.76.
, 1
3
= 0 , ,
.
= 0,54·10
3
/
3
, = 7·10
-3
/ .
4.77. , ,
= 0
0,7775·v
max
.
, 6 .
4.78.
= 0 . ,
.
ρ = 1,53·10
3
/
3
, = 40·10
-3
/ .
4.79. ,
<1/v> v
max
. <1/v>
.
4.80.
dn( ), dn(v)
, = 0 .
149
, v
max
/2 v
max
=
0 ,
F
= 5 .
4.81.
dn( ), dn(v)
, = 0 .
, = 0
η = 1,0 %.
4.82. ,
, v
m
/4 v
m
/2,
, 0 v
m
/4.
0 .
4.83. ,
,
= 0 , ,
. ρ = 19,3·10
3
/
3
, = 197·10
–3
/ .
4.84.
,
25% =0 . ,
. ρ =
1,84·10
3
/
3
, = 9·10
–3
/ .
4.85. ,
= 0
η=2%.
4.86. >v<
2
v
max
.
1
3
,
0 <v > = 0 .
F
= 6 .
4.87. dn( ),
dn(v).
v /2 v
0 v
/2.
.
4.88. , ,
t = 0° 1,8·10
9
.
3900
2
/( · ) 1900
2
/( · ).
= 5,33·10
3
/
3
,
= 73·10
–3
/ .
4.89. ,
, = 323 3·10
11
.
150
1340
2
/( · ) 460
2
/( · ).
= 2,33·10
3
/
3
, = 28·10
–3
/ .
4.90.
ρ = 0,48 ⋅ .
n- , µ
n
=
0,36
2
/(B· ), µ
p
= 0,16
2
/(B· ).
4.91. - ,
ρ = 0,3 ·
n
p
= 4·10
19
–3
.
4.92.
0,48 · . ,
, η = 0,67 .
,
. µ
p
= 0,39·
2
/(B· ).
4.93. n- 1,5
· R
x
= 5,4·10
3
3
/ .
.
4.94. n- ,
=1,6·10
–2
· 7·10
–3
3
/ .
4.95. σ = 112 / .
,
R = 3,66·10
-4
3
/ . ,
.
4.96. n-
Si, R = -2,7·10
–4 3
/ ,
n
= 0,16
2
/(B· ).
4.97. n
p
N
d
,
n
i
. n
p
,
n
i
T=300
4·10
19
-3
, n = 1,005N
d
.
4.98. 10 / .
,
10
28
–3
.
1 / .
4.99.
4,3·10
–4
/ .
? ,
?
n
= 0,135 =
0,048
2
/( · ).