Мартыненко Т.П. и др. Практический курс физики. Квантовая физика. Элементы физики твёрдого тела и ядерной физики
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201
4.59.
;
E)m2(V4
)2(
E
2/1
i
2/3
3
i
π
π
=∆
) 1,5·10
-22
, ) 0,85·10
-22
.
4.60.
.54,0)6,01(
N
N
2/3
max
i
=−=
∆
∆
=η
4.61. E ≥ E
F
, E ≥ 0,63E
F
.
4.62. E = E
F
(1–0,54)
2/3
= 2,8 .
4.63. E = E
F
(1–0,5)
2/3
= 3,44 .
4.64. ∆N
1
/∆N
2
= 0,65.
4.65. ∆N/ N= [1– (1–0,04)
3/2
] = 0,06.
4.66.
.086,0
)5,0(
)02,01(1
n
n
2/3
3/2
2
1
=
−−
=
∆
∆
4.67.
[
]
.424,7
)04,0(
)04,01(1
n
n
2/3
2/3
2
1
=
−−
=
∆
∆
4.68.
.03,0)1(1
n
n
2/3
1
=η−−=
∆
4.69.
;54,0)6,0(1
n
n
2/3
1
=−=
∆
%.54
n
n
1
=
∆
4.70.
K.25434
k
5
E2
T
F
==
4.71.
.104
)n3(mV
2
E
23
3/12
22
−
⋅=
π
π
=∆
4.72.<v> = 1,18·10
6
/ .
4.73. <v> = 1,05·10
6
/ .
4.74. <v> = 1,676·10
6
/ .
4.75. <v> = 1,52·10
6
/ .
4.76. < > = 0,04 · / .
4.77. <v > = 1,14·10
6
/ .
4.78. <v > = 9,9·10
5
/ , v = 1,27·10
6
/ .
4.79.
;
v2
3
v
1
max
=
.125,1
v
1
/
v
1
=
4.80.
;dvv
h
m
)v(dn
2
32
3
π
=
[
]
.105,4)5,0(1
3
vm
n
3283
32
3
max
3
−
⋅=−
π
=∆
4.81.
;dvv
h
m
)v(dn
2
32
3
π
= .03,0
n
n
1
=
∆
4.82.
.7
n
n
2
1
=
∆
∆
4.83.
,c/1008,1
m5
E6
v
6
F
⋅==
,c/1005,1
m8
E9
v
6
F
⋅==
202
./c1008,1
E8
m9
v
1
6
F
−
⋅==
4.84.
.10423,1n
329 −
⋅=∆
4.85. ∆N/N = 0,56.
4.86.
;v6,0v
max
⋅=
,
3
vVm
N
3
32
3
⋅
π
=∆
.101,3N
22
⋅=∆
4.87.
.7
n
n
2
1
=
∆
∆
.
4.88. σ = 2,26 / .
4.89. ρ ≅ 208 · .
4.90. n = 2,5 ·10
19
-3
.
4.91. µ
p
= 0,52
2
/(B·c) n = 4 ·10
19
-3
.
4.92. n = 2,24 ·10
19
-3
.
4.93. n = 1,36 ·10
21
-3
; µ
n
= 0,306
2
/(B·c).
4.94. µ
n
= 0,37
2
/(B·c).
4.95. µ
p
= 3,2 ·10
-2
2
/(B·c), n
p
= 1,7·10
22
-3
.
4.96. σ = 6,98·10
2
/ .
4.97.
;1
N
n
41
2
N
n
2/1
2
d
id
p
−+=
n = 2,82 ·10
18
-3
.
4.98. <λ> = 71 .
4.99. n = 1,47 ·10
16
-3
; 2) .74,0
j
j
pn
n
=
+
4.100.
18,0
lRnq
1
e
pn
=
η∆
−
η
=µ+µ
2
/(B·c).
4.101. ∆ϕ =1,2 B.
4.102. n = 3,69 ·10
21
-3
; 2) µ
p
= 0,85
2
/(B·c).
4.103.1) R = 2·10
–3
-3
/K ;
2) – ;
3) n = 3,125·10
21
-3
; 4) µ
n
=0,079
2
/(B·c).
4.104.1)
315
xe
e
105
lq
dUB
n
−
⋅=
ϕ∆⋅ρ⋅⋅
⋅
⋅
=
2)
( )
cB/05,0
dUB
l
2
x
e
⋅=
⋅⋅
ϕ
∆
⋅
=µ
.
4.105.
.102,4
q8
aBj3
n
317
Xe
−
⋅=
ϕ
=
4.106.
.25,56
aBR
U
X
X
=
ρ
ϕ
∆
=
l
203
4.107. n = 1,14 ·10
29
-3
; 2) µ
= 3,24·10
–2
2
/(B·c).
4.108. R = 1330 O .
4.109.
.O1007,1
T
1
T
1
k
E
exp
5
12
F
12
⋅⋅=−ρ=ρ
−
4.110. σ
2
/σ
1
= (4,83) = 125,7.
4.111.
.75,0
/1/1
10lnk2
E
21
=
τ−τ
=∆
4.112. n
1
/n
2
= 1332; 2) n
2
= 6,03·10
16
-3
2
= 400 .
4.113.
.33,0ln
TT
TkT2
E
12
21
=η
−
=∆
4.114.
.315,3
TkT2
TE
exp
T
T
n
n
21
3
2/3
1
2
2
1
=
∆∆
=
4.115.
.
R
R
ln
TT
TkT2
E
2
1
12
21
3
−
=
4.116. .K308
2lnkT2E
TE
T
1
1
2
−∆
∆
=
4.117. 1)
2
kT
2
E
−=α ; 2) .K1043,6
13
Si
−−
⋅−=α
4.118. = – 0,048 K
-1
.
4.119. E = 0,14 .
4.120. 1) λ ≤ λ
min
= 1,66 , 2)
.K05,0
kT
c
1
max
2
−
−=
λ
π
−=α
4.121. 1) λ
1
= 19,096 , 2) λ
1
= 0,2482 .
4.122. 1) λ
max
= 6200 , 2) α = –8,33·10
-3
K
-1
.
4.123. 1) ν = 1,57·10
15
, 2) λ = 191 , 3) α = –0,942 K
-1
.
4.124. ν = 2,6·10
14
-1
.
4.125. α = –0,071 K
-1
.
4.126.
.360
Rl)(nq1
R
R
pne
0
=
µ+µ∆−
=
4.127.
( )
lRRq
RR
nn
0pne
0
pn
⋅⋅⋅µ+µ
−
≈∆≈∆
4.128. 1) λ = 2,03·10
-6
, 2) ∆E = 0,6096 .
4.129. E
1
= – 1,03 , E
2
= –2,472 , E
3
= – 4,12 .
E n → ∞,
.
4.130.
.865,9
ln
t
1
2
20
10
=
ρ
ρ
⋅
ρ−ρ
ρρ
=τ
204
. .
4.131. 1) = 445 /( ·K);
2) = 425 /( ·K).
4.132. c
.
=17,53 /( · ).
4.133. c
2
/ c
1
= 62,6.
4.134. c = 1,08 /( · ).
4.135. 1)
66,5
M
M
3
c
c
3
2
Al
Ag
Al
Ag
Ag
Al
=
ρ
ρ
⋅⋅=
=2 .
2)
4
c
c
Ag
Al
=
t=200º .
4.136. M = 0,107 / , – .
4.137. ∆T = 66,43 K.
4.138. . ~ T
3
. θ = 409,46 K.
4.139. ∆U = 1,33 ; U
0
= 1963 .
4.140. 1)
./1013,6
vv
n18
13
3
33
||
2
max
⋅=
+
π
=ω
−
⊥
−
2) θ = 466,41 K.
4.141. θ = 1415 K.
4.142. 1) E
max
= 2,86⋅10
-21
; 2) θ = 207 ; 3) λ = 6,95⋅10
–5
.
4.143. 1) v
max
= 3422 / ; 2) ω
max
= 5,99⋅10
13
c
-1
;
3) p
max
= 3,68⋅10
–24
( · )/ .
4.144. 1)
./2622
N6
Mk
v
3
A
2
=
ρπ
θ
=
2)
.46,0
N
M
2d2
3
A
min
=
ρ
==λ
4.145.
/3126
h
dk2
v =
θ
=
.
4.146. 1) E
max
= 2,28⋅10
-21
. 2) p
max
=8,3·10
–25
( · )/ .
4.147. U
0
= 18,35 .
4.148.
3698
kd
2
v
R
8
9
U
0
=
⋅
⋅=
4.149.
/10
v
k1,0
p
25
⋅=
θ
⋅
⋅
=
−
.
4.150.
( )
,55,32TT
5
3
E4
kT
R
M
m
U
4
1
4
2
3
2
F
2
1
2
=−
θ
π
+π=∆
T
1
= T
0
= 2K, T
2
= 20K.
4.151.
,6,411T)T(c
M
m
U
v
=∆⋅=∆
c
v
(T) = 242,84 / · .
4.152.
,0124,0)T30(
5
3
T
E4
k
9
8
U
U
4
0
4
3
2
2
0
F
2
0
=−
θ
π
+
θ
π
=
∆
T
0
= 3 K.
205
4.153.
1068,2
C5
R12Tk
13
3
4
max
⋅=
π
⋅
⋅
=ω
µ
4.154. 1) ω
max
= 1,05 ⋅10
14
/ ; 2) v = 3,6·10
3
/ .
4.155. θ = 164 K.
4.156.
.37,99T)T(c
M
m
U
1v
=∆⋅=∆
4.157.
.57,586T)T(c
M
m
U
1v
=∆⋅=∆
4.158.
.K27,331
MQ5
)TT(Rm3
3
4
1
4
2
4
=
−π
=θ
4.159.
.1026,1
)TT(E12
kT5
Q
Q
2
4
3
4
4
2
F
32
2
2
1
−
⋅=
−π
θ
=
4.160.
.
)TT(5
)TT(
U
U
,1022,3
U
U
3
34
4
1
4
2
4
2
1
3
2
1
θ−
−π
=
∆
∆
⋅=
∆
∆
−
4.161.
;1099,9
Q
Q
2
2
1
−
⋅=
∆
∆
.
T5
)TT(
Q
Q
3
4
1
4
2
4
2
1
θ⋅∆
−π
=
∆
∆
4.162.
;
45
)TT(24
U
U
4
4
1
4
2
4
0
θ
−π
=
∆
.102,5
U
U
3
0
−
⋅=
∆
4.163. θ
D
= 443 K.
4.164. 1) E
max
= 2,28⋅10
-21
; 2)
;1057,2
N
M
d
10
3
A
−
⋅=
ρ
=
3) < n > = 1,37.
4.165. < l > = 4 .
4.166.
.28,2
n
n
max
i
=
4.167.
.1016,1
n
n
4
2
1
−
⋅=
4.168.
;
Rv
xM
l
ρ
=
< l > = 1,39⋅10
–7
.
4.169.
;
vl
xM
c
v
ρ
=
v
= 44,15 /( ⋅ ).
4.170. a) T >> θ – , U = 3N
A
kT;
) T << θ – ,
.T
v5
Vk4
U
4
33
45
⋅
π
=
5.
. .
5.24. m = 7,014 . . . = 6533,88 .
206
5.25. m
e
/ m
a
= 2·10
–2
%.
5.26.
1
H
3
;
3
Li
7
;
7
N
15
.
5.27. 5,2 ; 7,8 ; 10,4 ; 13 ; 15,6 .
5.28. V /V
a
= 2,49 · 10
–14
.
5.29. <ρ > ≅ 0,18 · 10
18
/
3
.
5.30. F
1
= 0,59 · 10
-33
H, F
2
= 0,18· 10
3
H, F
2
/ F
1
= 0,312·10
36
.
5.31. ∆m = 4 · 10
-30
; E
= 2,24 .
5.32. ∆E
.
= 7,42 / .
5.33. σ
1
/σ
2
= 3,36.
5.34. ∆E
.1
= 2,661 / , ∆E
.2
= 2,235 / ;
1
H
3
.
5.35. M
a
= 3,0141 . . .
5.36. M
a
= 5,0113 . . .
5.37. E
min
= 39,27 .
5.38. E
min
= 10,55 .
5.39. E
min
= 15,45 .
5.40. ∆E
. .
= 5,376 / .
5.41. E
min
= 7,3 .
5.42. E = 12,4 .
5.43 E
.
= 8,2 / .
. .
5.44. δ = 0,71.
5.45. t = 16 .
5.46. (0) = 1,1 · 10
13
/ =300 .
5.47. ∆t ≅ 9,96 .
5.48. ∆N/N = 10
–4
.
5.49. 10
6
.
5.50. T
1/2
= 6 .
5.51. N
α
= 8, N
β
= 6.
5.52.
)./ln(
2
t
21
21
λλ
λ−λ
=∆
5.53. t = 4104,9 .
5.54.
.
e1e1
N)t(N
21
t
12
21
103
21
λ
−
−
λ
−
λ−λ
λλ
=
λ−λ−
5.55. T
1/2
= 5,3 .
5.56.
82
Pb
206
.
5.57. v
α
= 3·10
5
/ .
5.58. Q = 1,862 .
5.59. Eγ = 0,0155 .
5.60. E
n
= 930,9 ; E
e
+ = –7,6 .
207
5.61. τ = 86,5 .
5.62. η = 1/9.
5.63. I = 0,69 /
2
.
5.64. (0) = 3·10
14
/ , ( t) = 0,4·10
13
/ .
5.65. E
.
= 2,24 .
5.66.
3
Li
7
.
5.67. .
5.68.
84
Po
216
; v
Po
= 2,96·10
5
/ .
5.69. ∆N/N = 0,35.
5.70. T
1/2
= 1579,36 .
5.71. x
1/2
= 14,75 .
5.72. Q = 3,296·10
12
.
5.73. x
1/2
= 1,33 .
5.74. . Q = – 933,49 .
5.75. .
5.76. E/E
0
= 10
-3
.
5.77. . Q = 17,35 .
5.78. E
γ
= 0,75 ,
λ
= 1,65 .
5.79.
.
m/m1
c)mmmm()m/m1(T
Cn
2
nCBeC
n
+
−−++−
=
αα
5.80. E = 3,55 .
5.81.
.1035,1N
m
QE
23
A
⋅=
µ
=
5.82. m
Li
6
= 6,0134 . . .
5.83.
.29,11
2
QT
T
d
=
+
=
α
.4,87;045,0
Tm4
Tm
cos
dd
°=ϕ==ϕ
αα
5.84. . Q = – 1,28 .
5.85. E
γ
= 9,45 .
5.86. .1053,5m
5
OH
2
⋅=
5.87. Q = 2,3 · 10
4
⋅ .
5.88. Q = 6,82 .
5.89. m = 6,01514 . . .
5.90. T
α
= 5,26 ; T
n
= 0,44 .
5.91. T = 6,7 .
5.92. Q = –11 .
5.93. E = 11,9 .
5.94. m
C
= 10,0135 . . .
5.95.
;cosTT
m
mm
2T
m
m
1T
m
m
1Q
p
2
0
p
0
p
0
p
θ⋅−−−+=
α
α
α
α
Q = –1,2 .
208
5.96. T
p
= –2,15 .
5.97. T
α
= 9,1 ; ϕ = 170,5°.
5.98.
.3,3
m
)mm(E
T
2
2
H
H
p
p
=
+
≥
5.99.
...0842,222
m5,931
T
1)mm(m
0
0
p
px
=
⋅
++=
α
5.100.
.1023,4QN
m
Q
14
1A
He
He
⋅=
µ
=
5.101.
.28,55,931
mm
)mmmm(m
T
C
CnBeC
n
=⋅
+
−
−
+
=
α
α
5.102.
.39,4Q
m
mm
T
Li
Li
,
=⋅
+
=
α
α
5.103.
.2,2E
mm
mm
)mm(T
mm
1
T
Cn
BeC
nBe
Be
=
+
−−
+
=
α
α
209
.
∞
π
=
−
⋅
0
x
6
1e
dxx
=
−
⋅
1
0
x
3
225,0
1e
dxx
∞
=
−
⋅
0
x
2
405,2
1e
dxx
=
−
⋅
2
0
x
3
18,1
1e
dxx
∞
=
π
=
−
⋅
0
4
x
3
494,6
15
1e
dxx
.
x << 1,
,x1
x1
1
=
±
x21)x1(
2
±=±
,
x
2
1
1)x1( ±=±
,
,x
2
1
1
x1
1
=
±
,x1e
x
+=
.x)x1ln(
=
+
210
1.
,
. .
( ) 0 n 1,00867
1
1
H 1,00783
2
H 2,01410
3
H 3,01605
2
3
H 3,01603
4
H 4,00260
3
6
Li
6,01513
7
Li
7,01601
4
7
Be 7,01693
9
Be 9,01219
10
Be 10,01354
5
9
B 9,01333
10
B 10,01294
11
B 11,00931
6
10
C 10,00168
11
C 11,00114
12
C 12,00000
13
C 13,00335
14
C 14,00324
7
13
N 13,00574
14
N 14,00307
15
N 15,00011
8
16
O 15,99491
17
O 16,99913
18
O 17,99916
9
19
F 18,99840
11
22
Na 21,99444
23
Na 22,98977