7.1 Basic Concepts and Formulae
381
Units
1 Curie (ci) = 3.7 × 10
10 disintegrations/s
1 Rutherford = 10
6 disintegrations/s
1 Becquerel (Bq) = 1 disintegration/s
Radiation dose
1 Rad = 100 ergs/g absorbed
Radioactive law
dN /dt = −N λ
(7.57)
N = N 0 e
−λ t
(7.58)
T 1/2 = 0.693τ
(7.59)
Activity = |dN /dt| = nλ
(7.60)
Successive decays
A→B→C
dN B /dt = λ A N A − λ B N B
(7.61)
N B =
λ A N
0
A
λ B − λ A
[exp(−λ A t) − exp(−λ B t)]
(7.62)
Transient equilibrium (λ A < λ B )
N B /N A = λ A /(λ B − λ A )
(7.63)
Secular equilibrium (λ A << λ B )
N B /N A = λ A /λ B
(7.64)
Alpha-decay (Gamow’s formula)
λ = (v/R) exp (−2π z Z/137β)
(7.65)
Geiger–Nuttal law
log λ = K log x + C
(7.66)
Beta-decay
λ =
G
2
|M if |
2 E
5
0
60π 3 (c) 6
(E 0 m e c
2 )
(7.67)