Physics and Engineering of Radiation Detection

24 Chapter 1. Properties and Sources of Radiation

Interestingly enough, this is exactly the mean life of protactanium-233 and

it shows that after about one mean life of the daughter its activity becomes

approximately equal to that of the parent.

E.2 Transient Equilibrium

The parent and daughter nuclides can also exist in a transient state of equilibrium in
which their activities are not equal but differ by a constant fraction. This happens
when the half life of the parent is only slightly higher than that of the daughter, i.e.

T 1 P/ 2 >T 1 D/ 2 or λdP<λdD.

The approximate activity 1.3.33 derived earlier is valid in this situation as well.

AP

AD

 1 −

λdP

λdD

However now we can not neglect the second term on the right side as we did in the
case of secular equilibrium. In this case the equation depicts that the ratio of parent
to daughter activity is a constant determined by the ratio of parent to daughter
decay constant. Figure 1.3.5 shows the typical behavior of such a material. A
common example of transient equilibrium decay is the decay ofPb^21200 intoBi^21200.

E.3 No Equilibrium

If the half life of parent is less than the half life of daughter, i.e.

T 1 P/ 2 <T 1 D/ 2 orλdP>λdD,

then the activity due to parent nuclide will diminish quickly as it decays into the
daughter. Consequently the net activity will be solely determined by the activity of
the daughter. Figure 1.3.7 depicts this behavior graphically.

1.3.F BranchingRatio

In the preceding sections we did not make any assumption with regard to whether
there was a single mode or multiple modes of decay of the nuclides. In fact the
majority of the nuclides actually decay through a number of modes simultaneously
with different decay constants. Branching ratio is a term that is used to characterize
the probability of decay through a mode with respect to all other modes. For example
if a nuclide decays throughαandγmodes with branching ratios of 0.8 and 0.2, it
would imply thatα-particle is emitted in 80% of decays while photons are emitted
in 20% of decays. The total decay constantλd,tof such a nuclide havingNdecay
modes is obtained by simply adding the individual decay constants.

λd,t=

∑n

i=1

λd,i (1.3.34)

Hereλd,irepresents the decay constant of theith mode for a material that decays
through a total ofnmodes. The total decay constant can be used to determine the