.
N = e /2mpc, |
mp - .
, - , - , . gl gs .
gl | +1 | |
gs | +5.586 | -3.826 |
j = 1 S1 D1 L = 0 L = 2. L = 0 , L = 2 . l = L/2 = 1 (. ).
L = 0 (ln = lp = 0): = N(1 0 + 0 0 + 5.586 1/2 - 3.862 1/2) = 0,88 mN . | |
L = 2 (ln = lp = 1): = N(1 1 + 0 1 5.586 1/2 + 3.862 1/2) = 0,12 N. |
L = 2 X. X 0,12 N + (1 X) 0,88 N = 0,86 N. X = 0.026. L = 2 2,6%.
3. , Q0 175Lu +5.9 2. ? ?
, Ze Q0 = 2Z(b2 - a2)/5, b - , Z, a a - X Y.
, |
= (b + a)/2 - .
. |
, R = r0A1/3. Q0 > 0, b > a, Z.
4. 85Rb Q = 0.7 . Q0, 85Rb J = 5/2.
Q Q0
J - .
5. I 10C, 11C, 12C, 13C, 14C.
I I = | Iz |. Iz , Z N ,
. |
I = |Z - N|/2.
:
10C - I = (6 4)/2 = 1,
11C - I = (6 5)/2 = 1/2,
12C - I = (6 6)/2 = 0,
13C - I = (7 6)/2 = 1/2,
14C - I = (8 6)/2 = 1.
6. 1s, 2s 3s 90Zr .
l = 0 :
, |
n - , m - R - ( ). 1s, 2s 3s
= 3 x 7.3 = 22
5 x 7.3 = 36.5
|
|
l = 0
En = (2n + 3/2), = 41 A1/3 = 41 x 901/3 = 9.1 90Zr.
= = 2 = 18.2 .
7. J P - 15O, 16O, 17O, 18O.
16O 18O -, JP = 0+. 15O " " ( - 16O) 1p1/2. J " " J = 1/2, l P = (-1)l = (-1)1 = -1, JP = 1/2-. 17O 1d5/2 - 16O. 17O JP = 5/2+.
8. , 180Hf " ".
-
,
J - , J = 0, 2, 4, , I - . :
E2: E4: E6: E8 = J2(J2 + 1): J4(J4 + 1): J6(J6 + 1): J8(J8 + 1) = = 2(2 + 1): 4 (4 + 1): 6(6 + 1): 8 (8 + 1) = 3: 10: 21: 36.
:
E2: E4: E6: E8 = 93: 307: 637:1079 = 93/31: 307/31: 637/31: 1079/31 = 3: 9.90: 20.55: 34.81.
, J = 1, 3, 5, , " " .
9. 106Pd. 2+.
, JP = 0+. JP = 2+. N: EN = (N + 5/2) , - . JP = 2+, () N = 1, N = 2.
E0 = 5/2 , E1 = 7/2 , E2 = 9/2 .
2+ -
E2 - E0 = (9/2 - 5/2) = 2 =1.127 .
() 2+-
E1 - E0 = (7/2 - 5/2) = = 0.564 .
- :
- JP = 2+.
- , JP = 0+, 2+, 4+, 2+.
1. 32P 2 . ?
:
,
N0 - t = 0, N(t) - , t, - ( ). N - ( ) , , 1 = 3.7 1010 /. T1/2 - (, ) 32P 14.5 . T1/2 T1/2 = ln 2/ .
m
|
|
NA - , A - .
= 7.1 10-12 .
2. 131I ? 131I 193 .
N(t) = N0 , ( 24 ) .
.
, T1/2- 131I , T1/2 = ln2/ = 0.693/ .
.
3. W, 1 210Po , , E = 5.4 .
e = 2.718 . D = 1 - 1/2.718 = 0.632 . N m N = mNA/A, NA - , A - . , , 210Po
.
4. , , 40Ar 40K e-. 300 40Ar 40K.
40K
,
N0 - 40K , t - . T1/2 - 40K, 1.277 109 . 40K e- 10.67% ,
.
:
,
5. - 226Ra 222Rn. 1 ? 226Ra T1/2(Ra) = 1600 , 222Rn - T1/2(Rn) = 3.82 .
1N1 = 2N2,
NRn = NRa Ra/ Rn = NRaT1/2(Rn)/T1/2(Ra).
226Ra
NRa = m NA/A,
m A- 226Ra, NA - .
V = VMNRn/NA,
VM - (22.4 /).
6. 31P(n,p)31Si, , 31P d = 1 /2 J = 2 1010 -1 -2 t = 4 - I, t = 1 , I(t) = 3.9 106 /. T1/2(31Si) = 157.3 .
31Si, 1
,
n - , NA - , A- 31Si. 1 N(t), = ln 2/T1/2 = 60 0.693/157.3 = 0.264 -1 - 31Si.
,
N(0) = 0. , t 31Si
.
t 31Si
2 10-26 2 = 20 .
7. - , - 212Bi 208Tl 0,49 0,61 . E .(A,Z) 212Bi - 1654.32 , 208Tl - 1632.23 - - 28.30 .
a - Q0
Q0 = (M(A,Z) - M(A- 4,Z- 2) - M(a))2 = E(A- 4,Z- 2) + E(a) - E(A,Z),
|
|
M(A,Z) - , M(A - 4, Z - 2) - , M(a) - - E(A,Z), E.(A- 4,Z- 2), E(a) . , , -
Q = Q0 + Ei - Ef,
Ei Ef - .
a -
(0.49 ) 208Tl
= (1632.23 + 28.30 - 1654.32 - 0.49) 208 .../212 ... = 5.61 .
(0.61 ) -
= (1632.23 + 28.30 - 1654.32 - 0.61) 208 .../212 ... = 5.49 .
8. l, - :
A B + b
A = B + b + , |
A, B, b - A, B b , - b.
PA = PBPb(-1)l |
PA, PB, Pb - A, B b . - 0, . -
i = f + |Ji - Jf| < l < Ji + Jf, |
i, f - .
Pi = Pf(-1)l, |
Pi, Pf - .
) 0 < l < 5, l = 0, 2, 4;
) 2 < l < 3, l = 2;
) 0 < l < 5, l = 0, 2, 4;
) 1 < l < 4, l = 1, 3.
9. , ,
+ - 27Si.
+ -
Q = M.(A, Z) - M.(A, Z - 1) - 2 me,
M.(A, Z) - M.(A, Z - 1) - - ( ). 27Si 25137.961 , 27Al - 25133.150 .
Tmax = Q = 25137.961 - 25133.150 - 2 0.511 = 3.789 .
10. 7Li, e- 7Be. - E(7Be) = 37.6 , E(7Li) = 39.3 .
7Be + e- 7Li + e. e -
Qe = E(A, Z-1) E(A, Z) (mn mp)c2 + mec2 = E(A, Z-1) E(A, Z) 0.78 ,