Secular Equilibrium
When ld>>lp, that is, when the parent half-life is much longer than that of
the daughter nuclide, in Eq. (3.16), we can neglect lpcompared to ld. Then
Eq. (3.16) becomes
(Ad)t=(Ap)t (3.19)
Equation (3.19) is called the secular equilibrium. This equilibrium holds
when the half-life of the parent is much longer than that of the daughter
nuclide by more than a factor of 100 or so. In secular equilibrium, both
parent and daughter activities are equal, and both decay with the half-life
of the parent nuclide. A semilogarithmic plot of activity versus time repre-
senting secular equilibrium is shown in Figure 3.6. Typical examples of secu-
lar equilibrium are^113 Sn (t1/2=117 days) decaying to 113mIn (t1/2=100 min),
and^68 Ge (t1/2=280 days) decaying to^68 Ga (t1/2=68 min).
Questions
- Calculate (a) the total number of atoms and (b) the total mass of^131 I
present in a 30-mCi (1.11-GBq)^131 I sample (t1/2=8.0 days). - Calculate (a) the disintegration rate per minute and (b) the activity in
curies and becquerels present in 1 mg of^201 Tl (t1/2=73 hr).
32 3. Kinetics of Radioactive Decay
Fig. 3.6. Plot of activity versus time illustrating secular equilibrium. In equilibrium,
the daughter activity becomes equal to that of the parent.