Introduction to Health Physics: Fourth Edition - Ruang Baca FMIPA UB

702 CHAPTER 13
and 230 Rn (thoron), which seep out of the ground from the ubiquitous uranium and
thorium series (the average concentration of uranium and thorium in the top 0.3 m
of soil is 1 ton and 3 tons, respectively, per square mile) and from their transformation
products. These transformation products attach themselves to airborne particles with
which they come in contact, thus contaminating the dust particles with radioactivity.
The limiting activity in the radon daughter chain is 214 Pb (RaB), a beta emitter whose
half-life is 26.8 minutes. In the thoron daughter chain, the limiting activity is 212 Pb
(ThB), a beta-emitting isotope with a half-life of 10.6 hours.
For routine monitoring of long-lived contaminants, allowance is made for these
activities by (1) counting the air sample several hours after collection, thereby allowing
the 26.8-minute activity to decay away, and (2) counting the air sample about
two ThB half-lives later. From these two measurements, the activity of the long-lived
contaminant can be calculated. The counting rate C1 of the first measurement is
due to the natural activity and the long-lived contaminant CLL:
C1 = Cn1 + CLL; (13.33)
when the second count is made, the natural activity has decayed to
Cn2 = Cn1 e −λt , (13.34)
where λ, the decay constant of ThB, is 0.0655 h −1 , and t is the time interval in hours
between the two counts. The second measurement, C2, includes the following:
C2 = Cn2 + CLL, (13.35)
C2 = Cn1 e −λt + CLL. (13.36)
Solving Eqs. (13.35) and (13.36) simultaneously for the long-lived activity gives
CLL = C2 − C1e −λt
1 − e −λt
. (13.37)
W EXAMPLE 13.10
In monitoring for airborne 90 Sr, a 10-m 3 air sample is taken with a membrane filter.
The first measurement, taken 4 hours after sampling, gives a net counting rate of
100 cpm. The second count, 20 hours later, gives a net counting rate of 50 cpm. If
the filter (after treatment to prevent electrostatic charge accumulation) was counted
in a windowless 2π gas-flow counter, what was the mean concentration of 90 Sr in
the air?
Solution
Substituting the respective values for C1 and C2 into Eq. (13.37) gives
CLL = 50 − 100e −0.065 h−1 ×20 h
1 − e −0.065 h−1 ×20 h
= 31.5 cpm