, , . - . , .
λ - .
t N , dN, dt N.
dN = -λNdt. (13.1)
(1)
N(t) = N0e-λt. (13.2)
N0 - t = 0.
C τ
. (13.3)
T1/2 - ,
T1/2 = ln2/λ=0.693/λ = τln2. (13.4)
A -
A(t) = λN(t). (13.5)
() ()
1 = 3.7*1010 /c, 1 = 1 /c.
1 2, 3,
(13.6)
N1(t) N2(t) - , λ1 λ2 - 1 2 . (6) N1(0) = N10; N2(0) = 0
, (13.7a)
. (13.7)
13. 1 |
2 .
λ2 < λ1 (), N1(t)λ1 + N2(t)λ2 .
λ2 >λ1 ()), 2.
λ2 >> λ1, (7) , A2 = λ2N2 A1 = λ1N1 . .
A1(t) = N10λ1 = N1(t)λ1 = A2(t) = N2(t)λ2. (13.8)
, ( ) .
. (13.9)
, , , .
, 1→2→...n,
dNi/dt = -λiNi +λi-1Ni-1. (13.10)
(10) N1(0) = N10; Ni(0) = 0
(13.11)
(13.12)
, , , i = m.
, - , . 1912 , : isos topos . .
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