7.1 Basic Concepts and Formulae 381
Units
1 Curie (ci)= 3. 7 × 1010 disintegrations/s
1 Rutherford= 106 disintegrations/s
1 Becquerel (Bq)=1 disintegration/s
Radiation dose
1Rad=100 ergs/g absorbed
Radioactive law
dN/dt=−Nλ (7.57)
N=N 0 e−λt (7.58)
T 1 / 2 = 0. 693 τ (7.59)
Activity=|dN/dt|=nλ (7.60)Successive decays
A→B→C
dNB/dt=λANA−λBNB (7.61)NB=λAN^0 A
λB−λA[exp(−λAt)−exp(−λBt)] (7.62)Transient equilibrium (λA<λB)
NB/NA=λA/(λB−λA) (7.63)Secular equilibrium (λA<< λB)
NB/NA=λA/λB (7.64)Alpha-decay(Gamow’s formula)
λ=(v/R)exp(− 2 πzZ/ 137 β) (7.65)Geiger–Nuttal law
logλ=Klogx+C (7.66)Beta-decay
λ=G^2 |Mif|^2 E 05
60 π^3 (c)^6 (E 0 mec^2 ) (7.67)