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Arndt, Michael F.; West, Lynn (Chemist) / A study of the factors affecting the gross alpha measurement and a radiochemical analysis of some groundwater samples from the state of Wisconsin exhibiting an elevated gross alpha activity
[DNR-176] (2004?)

1. Introduction,   pp. 3-14 PDF (5.7 MB)

Page 11

Rn-222 population increases until the Rn-222 decay rate equals the rate at which Rn-222 is
produced, which is equal to the decay rate of Ra-226. At this point, the population of Rn-222 has
stabilized. Now the stable population of Rn-222 atoms is producing Po-218 atoms at a constant
rate (the decay rate of Ra-226), and the Po-218 population will build until the decay rate of Po-
218 equals its rate of production (the decay rate of Ra-226). The process of building radionuclide
populations whose activities equal the activity of Ra-226 will keep occurring for each
radionuclide along the decay series, as long as the Ra-226 half-life is long compared to the half-
life of the radionuclide of interest, and as long as the half-life of the radionuclide is short
compared to the time scale of interest. Further down the decay series Pb-210 is encountered with
a 22 year half-life. On our time scale of interest (30 days), 22 years is a long time, and the Pb-
210 population will not have built to a large enough number and have stabilized such that the
decay rate ofPb-210 equals the decay rate of Ra-226. The next alpha-emitting radionuclide after
Po-214 is Po-210. If one uses the Bateman equations to determine the activity of Po-210
produced from Ra-226, one finds that it takes approximately 1440 days to produce 0.1 pCi of Po-
210 from 1 pCi of Ra-226. The low production of Po-210 from Ra-226 is due to the relatively
long half-life of Pb-210 (22 years). On a one-month time scale the Pb-210 population arising
from the decay of Ra-226 gives rise to a negligible Pb-210 activity. In effect, on a one-month
time scale the presence of Pb-2 10 in the decay chain acts as a "bottleneck" for the production of
Po-210 from Ra-226.
Actually, in Figure 3 it is seen that the activities of Rn-222, Po-218, and Po-214 are virtually the
same. This is because the half-lives of the progeny Po-218, Pb-214, Bi-214, and Po-214 are
much less than the half-life of Rn-222. Consequently, these progeny species come into secular
equilibrium with Rn-222 rather quickly on the time scale in Figure 3.
1.0 -
0.8  Pb-210
02                         Po-2 10
0     5    10    15    20   25    30
Time (days)
Figure 4. Pb-210 decay and Po-210 ingrowth.
As mentioned above the activity of Pb-210 was not determined in the samples. The amount of
Pb-210 present in the water samples is of interest because it decays into the alpha-emitting Po-
210. Figure 4 is a plot of the ingrowth of Bi-210 and Po-210 from 1 pCi of Pb-210 over a period
of 30 days. After 30 days, Bi-210 is in secular equilibrium with Pb-2 10, but the activity of Po-
210 produced is about 0.1 pCi. When one measures the activity of Po-210 in a sample, because
of its relatively short half-life (134 days), one decay corrects the Po-210 activity to obtain the Po-
210 activity in the sample at the time of collection. If 0.1 pCi is decay corrected backward 30

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