1. v, T mc2?
.
T = mc2,
,
v = c 0.87 c.
2. T = 0.5 , , ?
N(t), t,
N(t) = N(0) exp(-t/ ), | 2.1 |
- , N(0) - . 2.2 10- 6 .
N(t) = N(0)/2 = N(0) exp(-t/ ), | 2.2 |
exp(- t/ ) = 1/2, t = ln2.
2.3 |
t0 - , .
2.4 |
T p
2.5 |
2.6 |
m - , v - . (2.5) (2.6)
2.7 |
mc2 106 .
l = v t | 2.8 |
(2.8) (2.4) (2.7),
3. 10B 0.72 - T1/2 = 6.7 10-10 . E -.
- .
4. T = 10 .
(Tp << mpc2).
,
, c = 197 ,
(Te >> mec2).
5. , = 10- 9 . t L = 10 ?
:
/ | .. |
,
.
: |
: |
: |
6. = 3 10-11. p .
1. - T = 6.5 197Au. : 1) b -, = 900; 2) rmin - ; 3) (T') 4) (E') - .
1) , ,
Z 1 - , Z 2 - .
2)
.
r = rmin = 0. :
b,
|
|
3)
, ,
4)
T' = T - E' = 6.5 - 5.4 = 1.1 .
2. T = 2 197Au. = 60. , 27Al?
,
Z1 - , Z2 - .
, 197Au 27Al :
37 , .
3. a - T = 5 208Pb 900.
4. l = 1 -
j = 105 /2 . - T = 5 . - , = 170 ? S = 1 2.
, , n - , - .
- , l - , A - NA - .
5. d /d 197Au 15, , d = 7 /2 Q = 1 S = 0.5 2, l = 30 , N = 1.97 105 . .
a + A B + b
,
n - , N - a, - , b, d , . .
= N/ , = S/l2, N = Q/ep, n = d NA/A, ep - , NA - A - 197Au.
= 2.65 103 /.
T = 3 :
.
6. T = 750 40Ca min = 18. 40Ca.
min R
, ,
7. R A (A > 10) R r0A1/3.
r0 1.23 10-13 = 1.23 .
27Al, 90Zr, 238U.
|
|
27Al R = 1.23 x 271/3 = 3.7 .
90Zr R = 1.23 x 901/3 = 5.5 .
238U R = 1.23 x 2381/3 = 7.6 .
8. .
mN 1 ... = 1.66 10-24 . ,
A.
9. mn = 939.6 mp = 938.3 . 2H , E(2,1) =2.2 .
M(A,Z) = Zmp + (AZ)mn E(A,Z), Z A - .
M(2,1) = 1 x 938.3 + 1 x 939.6 2.2 = 1875.7 .
10. 16O m(A,Z) = 15.9949 ... 16O.
(A,Z) = E(A,Z)/A,
E(A,Z) - , A - .
E(A,Z) = [Zmp + (A-Z)mn - m(A,Z)]c2 = [Zmp + (A-Z)mn - m(A,Z) - Zme]c2
1...= 931.49 , 16O
= 7.5 /.
11. ...: 16O - 15.9949, 15O - 15.0030, 15N - 15.0001. 16O?
n(A,Z) = mn +m(A-1,Z) - m(A,Z),
p(A,Z) = mp +m(A-1,Z-1) - m(A,Z).
.
16O
n = 939.6 + (15.0030 ... - 15.9949 ...)931.5 = 15.6 ,
p = 938.3 + (15.0001 ... - 15.9949 ...)931.5 = 15.6 .
12. - 38Ca, 40Ca, 48Ca.
(A, Z)
n(A,Z) = [mn + m(A-1,Z) - m(A,Z)]c2.
m(A,Z)c2 = [Zmp + (A-Z)mn]c2 - E(A,Z).
n(A,Z) = [mn + Zmp + (A-1-Z)mn]c2 - E(A-1,Z) - [Zmp + (A-Z)mn]c2 + = E(A,Z) - E(A-1,Z).
a1 = 15.78 , a2 = 17.8 , a3 = 0.71 , a4 = 94.8 , a5 = 0 A, a5 = +34 - a5 = - 34 - .
(A,Z) :
38Ca
40Ca
48Ca
(A -1, Z) :
37Ca
39Ca
47Ca
.
:
38Ca n(38,20) = 317.9 - 299.5 = 18.4 ,
40Ca n(40,20) = 346.3 - 330.6 = 15.7 ,
48Ca n(48,20) = 418.4 - 410.3 = 8.1 .
13. , , 23Na, 23Mg. E(23Na) = 186.56 , E(23Mg) = 181.72 .
R
23Na Z, 23Mg Z + 1. 23Na 23Mg
R = 1.23 A1/3 R(23Mg) = R(23Na) 1.23 x 231/3 =3.5 .
14. 27Si +- "" 27Al. 3.48 . .
R - , e - Z - , 27Al,
+-
= E 1.80 .
1. . |l,s,j>n = |1,1/2,3/2>, |l,s,j>p = |1,1/2,3/2>. j?
. |l,s,j>1 = |1,1/2,3/2> |l,s,j>2 = |1,1/2,3/2>. j?
|
|
, | j1 j2 | < j < j1 + j2, j = 0, 1, 2, 3.
j = 1, 3 , .. l, s, j, jz, . j = 0, 2.
. j j1 = j2 = 3/2 Z, jz = (j1)z + (j2)z.
-3/2 | -1/2 | 1/2 | 3/2 | |
-3/2 | -3 | -2 | -1 | |
-1/2 | -2 | -1 | ||
1/2 | -1 | |||
3/2 |
, n, l, j, jz. jz = (j1)z + (j2)z, . , , (j1)z (j2)z, . jz, . ,
-3/2 | -1/2 | 1/2 | 3/2 | |
-3/2 | -2 | -1 | ||
-1/2 | ||||
1/2 | ||||
3/2 |
jz = -2, -1, 0, 1, 2 j = 2. jz = 0 j = 0. , j = 0 2.
2. =0.86 N - j = 1 L = 0 (S1-), j = 1 L = 2 (D1-) .