Answer to Question #8597 Submitted to "Ask the Experts"

In gamma spectroscopy, we can calculate the ²³⁸U using ²¹⁴Pb and ²¹⁴Bi. Can we estimate ²³²Th using ²¹²Pb and ²¹²Bi?

I am using an Ortec system and my analysis report sometimes gives a value of ²²⁸Ac which can be used for estimating ²³²Th assuming they are in equilibrium. Last report I printed has activity concentration for ²⁰⁸Tl, ²¹²Pb, ²¹²Bi, and ²²⁸Ra. Can any of this be used to estimate ²³²Th and, if yes, then how?

Usually I am using the following method to estimate ²³⁸U:

(²¹⁴Pb + ²¹⁴Bi)/2 +/- (SQRT((Error ²¹⁴Pb/2)^2+(Error ²¹⁴Bi/2)^2)

Is it okay to use this method?
 

It is possible to use the results for some of the progeny that you note to estimate the ²³²Th activity but not in all circumstances. As you know, the long-lived thorium decays initially to ²²⁸Ra, which has a 6.7 year half-life, the longest lived of all the radioactive progeny that follow. Thus, in a pure sample of ²³²Th, if no physical or chemical processes are ongoing that would disturb the ²³²Th-²²⁸Ra equilibrium, it would require about 35 years before the ²²⁸Ra achieved about the same activity as the ²³²Th. The ²²⁸Ra decay produces only an extremely low yield and low-energy gamma ray, which would not be reliable for making an estimate of ²³²Th. The decay product of ²²⁸Ra is ²²⁸Ac; the ²²⁸Ac has a 6.17 hour half-life so it grows into the ²²⁸Ra quite quickly and will achieve activity equilibrium with the ²²⁸Ra and the ²³²Th, both of which are solids under normal conditions. Therefore, assuming no processes have been ongoing that would disrupt the equilibrium, you should be able to use the ²²⁸Ac activity to determine the ²³²Th activity.

The progeny that follow ²²⁸Th in the decay chain would also achieve this equilibrium if none of the decay products were lost during the observation time. One of the progeny is ²²⁰Rn, a noble gas that might escape from the sample matrix under some circumstances. The ²²⁰Rn has only a 55-second half-life so its potential for escape before decaying to solid ²¹⁶Po is not as great as it would be if it had a longer half-life but, depending on the sample chemical and physical characteristics, some radon might escape if the sample is not sealed against such losses. Naturally, any loss of radon will negate the approach to equilibrium of the subsequent progeny, including the ²¹²Pb and ²¹²Bi that you mention, and the activities of these may not be equivalent to the activity of the ²³²Th. You can judge whether the lack of equilibrium is significant by comparing your activity estimations for the ²¹²Pb and ²¹²Bi with the activity of the ²²⁸Ac. They should be pretty much the same if the equilibrium has been maintained. If the equilibrium has prevailed, you may also use the ²⁰⁸Tl results to determine the ²³²Th activity. In this instance, however you must recall that the ²⁰⁸Tl is produced in a ²¹²Bi branching decay process so that its expected equilibrium activity would be only 36% of the ²³²Th activity.

If you find that the equilibrium has been maintained, you may also use the average of the activity estimations for the ²¹²Pb and ²¹²Bi as you have done when using the ²¹⁴Pb and ²¹⁴Bi. You will note, however, that the gamma ray yields from ²¹⁴Bi are rather low, the highest being about 7% for the 727 keV gamma rays and, depending on your counting statistics, this can lead to a poorer activity estimate for the bismuth compared to the lead. I am assuming you are using a germanium detector that allows suitable energy resolution to discern the species of interest. Depending on the detector characteristics, you could experience some contribution of the ²²⁴Ra 241 keV gamma rays to the 239 keV gamma ray region of the ²¹²Pb, although this should be fairly small.

Good luck in your continuing analyses.

George Chabot, PhD, CHP