Мартыненко Т.П. и др. Практический курс физики. Квантовая физика. Элементы физики твёрдого тела и ядерной физики
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171
,
.
:
t
1
2
eC
⋅λ−
.
t
2
1
eC
⋅λ−
.
,
C
2
:
,eCeCeN
t
21
t
22
t
01
111
⋅λ−⋅λ−⋅λ−
λ−=λ−λ
.
N
C
12
01
2
λ−λ
⋅
λ
=
:
.e
N
eCeCeCN
t
12
01
t
1
t
2
t
12
1212
⋅λ−⋅λ−⋅λ−⋅λ−
λ−λ
⋅
λ
+=+=
, t = 0 N
2
=0,
.
N
C
12
01
1
λ−λ
⋅
λ
=
:
(
)
.ee
N
N
tt
12
01
2
21
⋅λ−⋅λ−
−
λ−λ
⋅
λ
=
5.8. 1/4
, 24
?
(5.9):
,eNN
t
0
⋅λ−
⋅=
N – .
,eNNN
4
1
t
T
2ln
000
⋅−
−=
,eNN
4
3
t
T
2ln
00
⋅−
=
,t
T
2ln
4
3
ln ⋅−=
.97,924
693,0
098,1386,1
T
2ln
3ln4ln
t =⋅
−
=⋅
−
=
5.9. ,
38
Sr
80
10 , 100 .
172
A
(5.13):
.
dt
dN
A −=
"–" , N
.
,eN
dt
dN
t
0
λ−
λ−=
t
0
eN
λ−
λ
– t, A
0
–
t = 0:
A
0
= ⋅N
0
.
3
38
Sr
80
.
28 8,83⋅10
8
. , ∆t
1
∆t
2
.
λ=
λ=
∆λ−
λ−
,eNA
,eNA
)t(
02
t
01
.e10
A
A
1
t
2
1
∆λ−
==
;t
T
2ln
t10ln
11
∆=∆λ=
;
2
ln
T·10ln
t
1
=∆
.93c1031,29
693,0
1083,83,2
t
8
8
1
=⋅=
⋅⋅
=∆
:
,100
A
A
3
1
=
,
2ln
T100ln
t
2
⋅
=∆
.186t2t
12
=
∆
=
∆
5.10. -
6
11
.
+
- (5.16 ):
.eB
0
0
0
1
11
5
11
6
ν++→
+
+
-
Z – 1 . ,
+
e
0
, .
.
, γ - :
+1
e +
–1
e = γ + γ
173
+
-
2
c
·
m
E
=
∆
, ∆m – :
∆m = m
C
– m
B
– m
e
;
).mmm(
...
5,931E
eBC
−−=
:
...0114,11m
11
6
C
=
...0093,11m
11
5
=
m = 0,00055 . . .
,
+
- :
.44,1)00055,00093,110114,11(
...
5,931E =−−=
5.11. , , -
5,46 ,
84
218
.
m
P
= 218,07676 . . .
- (5.15):
Z
X
A
→
84
o
218
+
2
4
.
:
.
2
vm
2
vm
cmcmcm
22
PoPo
2
0
2
Po
0
2
X
αα
α
+++=
:
.
2
vm
2
vm
c)mmm(
22
PoPo
2
0
Po
0x
αα
α
+=--
:
0 = m
Po
v
Po
+ m
α
v
α
.
:
,
m
vm
v
Po
Po
αα
=
,
m
m
1E
m2
vmm
2
vm
c)mmm(
Po
2
Po
22
Po
2
2
0
Po
0x
+=+=−−
α
α
αααα
α
,
5,931m
E
1)mm(
m
m
1
5,931
E
mmm
Po
Po
Po
0
Po
0x
⋅
++=+++=
α
α
αα
α
=
⋅
++=
5,93107676,218
46,5
1)00149,407676,218(m
x
222,08424 . . .
174
5.12.
82
b
206
92
U
238
. ,
10
9
.
t
1
.
– N
0
. t
1
, t
1
t
1
=
U
= 4,5⋅10
9
. t = 10
9
( )
(5.9)
.eNN
)tt(
T
2ln
0U
1
−−
=
:
.e1NeNNN
)tt(
T
2ln
0
)tt(
T
2ln
00U
11
−=−=∆
−−−−
:
N
Pb
= ∆N
U
.
t
.1e
e
)e1(
N
N
)tt(
T
2ln
)tt(
T
2ln
)tt(
T
2ln
U
Pb
1
1
1
−=
−
=
−
−−
−−
.72,01e
N
N
N
N
)10105,4(
105,4
693,0
U
U
U
Pb
99
9
=−=
∆
=
−⋅
⋅
5.13. , 2,5
32,86
40,54
3
.
84
210
.
84
210
.
,
. ,
175
V (p
0
= 1,013·10
5
/
2
,
0
= 273 ), p
0
= n
0
k , ∆N = n
0
V,
p
0
V = ∆Nk . k = 1,38·10
–23
/ – .
.
kT
Vp
N
0
0
=∆
( . (5.9))
;eNN
t
T
2ln
0
−
⋅= ).e1(NNNN
t
T
2ln
00
−
−=−=∆
N
0
–
)N
M
m
N(
A0
=
, :
).e1(N
M
m
N
t
T
2ln
A
−
−=∆
, :
);e1(N
M
m
kT
Vp
t
T
2ln
A
0
0
−
−=
;
mRT
VMp
TmkN
VMp
e1
0
0
0A
0
t
T
2ln
==−
−
kN
A
=R = 8,31 /( ⋅ );
;
mRT
VMp
1e1
0
0
t
T
2ln
−=−
−
;
mRT
VMp
1lnt
T
2ln
0
0
−=−
;
mRT
VMP
1ln
t2ln
T
0
0
−
⋅
−=
.138
27331,8105,2
102101054,4010013,1
1ln
86,32693,0
T
3
365
=
⋅⋅⋅
⋅⋅⋅⋅⋅
−
⋅
−=
−
−−
5.14. , 1
88
R
226
,
, , -
5,3
.
- (5.15)
.RnRa
4
2
222
86
226
88
α+→
α
176
- -
86
Rn
222
,
:
.
2
vM
2
vM
EEE
2
RnRn
2
Rn
+=+=
αα
α
, v
. :
.vMvM
Rn
Rn
−=
α
α
.
M
M
vv
Rn
Rn
α
α
=
:
.
M
M
1
2
vM
M2
MvM
2
vM
E
Rn
2
2
Rn
22
Rn
2
+=+=
ααααααα
,
, :
,
2
vM
E
2
αα
α
=
.
M
M
1EE
Rn
+=
α
α
1 R
226
Q = E = E· N,
∆N – ,
τ.
∆N , (5.9):
,eNeNN
t
0
t
0
τ
−
λ−
== . . ;
1
τ
=λ (5.10 )
;N
M
m
N
A
Ra
0
=
;1002,6N
123
A
−
⋅=
);e1(NeNNNNN
1
0
t
000
−λ−
−=−=−=∆
(
)
;e1N
M
m
N
1
A
Ra
-
−=∆
.1068,1
7182,2
1
1
10226
1002,610
N
18
3
236
⋅=−
⋅
⋅⋅
=∆
−
−
Q =5,3⋅10
6
⋅1,6⋅10
-19
⋅1,68⋅10
18
= 1,45⋅10
6
.
177
5.15. Ir
192
γ
= 129 , , γ-
. γ- ,
.
Ir
= 192,2 . . .
Ir
192
E
0Ir
.
γ -
γ
= 129 ; ,
Ir ,
M
Ir
⋅v
2
/2; γ - ω.
,
E
E
ω
ω
∆
=
∆
:
.
2
vM
E
2
Ir
ω+
⋅
=
γ
,
c
vM0
Ir
ω
+⋅=
0 – Ir; M
Ir·
v –
; ω/ – γ - .
ω = – M
Ir
⋅v⋅c.
γ
.cvM
2
vM
E
Ir
2
Ir
⋅⋅−
⋅
=
γ
:
.1
cM
E2
1cv
2
Ir
−
⋅
+⋅=
γ
2
Ir
cM
E2
1
⋅
+
γ
,
2
Ir
cM2
E2
1
⋅
+
γ
.
.
cM
E
v
2
Ir
⋅
≅
γ
Ir
192
γ
= 129 . γ -
,
Ir
·v
2
/2
178
.
2
vM
E
2
Ir
⋅
−=ω
γ
γ - ,
.
cM2
2
vM
E)(
2
Ir
2
2
Ir
⋅
=
⋅
=ω−=ω∆
γ
γ
,
:
.106,3
1091066,12,1922
106,110129
cM2
E
)(
7
1627
193
2
Ir
−
−
−
γ
γ
⋅=
⋅⋅⋅⋅⋅
⋅⋅⋅
=
⋅
=
ω∆
5.16.
,
32 ?
γ - ,
, (5.18):
J = J
0
⋅e
-µx
,
J
0
– , ; J –
, x; –
(
).
γ
.
, , ,
1,02 – -
.
γ - . ,
2 .
(5.18),
,
2
1
J
J
0
1
=
32
1
J
J
0
2
=
,eJJ
2/1
d
01
µ−
=
d
1/2
– ;
179
,eJJ
d
02
µ−
=
d – ;
;e
2
1
J
J
2/1
d
0
1
µ−
==
,d2ln
2/1
µ
=
;e
32
1
J
J
d
0
2
µ−
==
.d32ln
µ
=
, , :
;
2ln
32ln
d
d
2/1
=
µ
µ
.d5d
693,0
466,3
d
2/12/1
=⋅=
5.17. ,
7
N
14
+
2
He
4
→
8
O
17
+
1
1
. 1.
(5.20):
).mm(cE
2
1k
k
2
1i
i
2
==
−=∆
,
...00567,18...)00260,400307,14(mmm
HeN
2
1i
i
=+=+=
=
...00641,18...)00728,199913,16(mmm
pO
2
1k
k
=+=+=
=
,
m . . .
, 1 . . .= 931,5 , :
Q = (18,00567 – 18,00641)⋅931,5 = – 0,689 .
.
5.18.
:
3
Li
7
+
1
H
1
→
4
7
+
0
n
1
.
(5.20 ).
:
Q = (7,01601 + 1,00783 – 7,01693 – 1,00867)⋅931,5 = –1,64 .
180
.
(5.21):
.87,164,1142,1Q
m
m
1E
Li
H
=⋅=⋅+=
5.19. - c
5
10
,
.
1
1
.
,
.
Z
X
:
2
4
+
5
B
10
→
1
H
1
+
Z
X .
,
:
+=+
+=+
,A1104
,Z152
, Z = 6, = 13.
6
13
6
C
13
.
2
4
+
5
B
10
→
1
H
1
+
6
C
13
.
(5.20),
(
)
[
]
mmmm5,931EQ
CHB
−
−
+
⋅
=
∆
=
α
.
1. :
Q = ∆ = 931,5(4,00149 + 10,01294 – 1,00783 – 13,00335) = 3,03 .
5.20.
. -
.
.
, (5.20 )
2
c
m
Q
⋅∆=
,
∆m – ,
(m
p
+ m
Li
) (2m
α
).