Answer to Question #10580 Submitted to "Ask the Experts"

I have measured the specific radioactivity levels in coal and fly ash samples using gamma spectrometry of ²³⁸U, ²²⁶Ra, ²³²Th, and ⁴⁰K. How do I convert these into gross alpha and gross beta activity? If I measure gross alpha and beta separately, how do I compare this with gamma spectrometry?

The experimental correlation between gross alpha activity or gross beta activity and radionuclide activity levels determined for these natural radioactive species by gamma spectrometry, while theoretically possible, is fraught with uncertainties and potential errors. There are a number of reasons for these difficulties.

The first question that arises relates to how you determined the activity concentrations of the natural chain parents ²³⁸U and ²³²Th by gamma spectrometry. Since these precursors emit no significant gamma radiation, I assume that you used some of their gamma-emitting progeny to make the activity determinations. In such cases, you would likely have assumed a secular equilibrium relationship between the progeny and the parent. Under this assumption, all of the progeny of the long-lived parent of the chain would have an activity equal to that of the parent, except for cases where branch decays are involved (e.g., ²¹²Bi), in which case the branching fractions must be applied. While such an assumption may be appropriate for the coal, it may not be valid for the fly ash since the combustion process may disturb the activity relationship among the parent and progeny. The ²²⁶Ra activity may be determined by counting its 186 keV gamma ray, but you may have to make corrections if ²³⁵U is in the sample because its 185 keV gamma ray may interfere with the analysis. The ⁴⁰K activity determination by gamma spectrometry should be acceptable.

If equilibrium does exist between progeny and the respective chain parent, or if you managed to adjust your analyses to account for disequilibrium, there remain other substantial problems in making correlations with gross alpha and beta activities. Theoretically, if all the progeny from ²³⁸U were in secular equilibrium with the uranium, there would be essentially eight alpha particles and six beta particles emitted per ²³⁸U decay (see the ²³⁸U decay chain). In order to have all of these alpha particles contribute to the observed count, it may be necessary to seal the sample in a fashion so as to prevent escape of ²²²Rn and still allow alpha radiation to reach the detector. Another complication is that the alpha particles range in energy from somewhat less than 4 MeV to almost 8 MeV, and for a sample of finite mass there will be differences in alpha particle detection efficiency among the alpha particles. If you prepared a standard that was similar in relative radionuclide composition to the samples of interest, you could make an empirical determination of the effective alpha counting efficiency so that the gross alpha count rate could be correlated with the ²³⁸U activity (and with the respective activities of any progeny if the equilibrium state is known). Similar considerations apply to gross beta particle counting of ²³⁸U progeny in a sample. The maximum beta particle energies from the various progeny range from about 0.1 MeV to more than 2 MeV, and the different progeny will exhibit different counting efficiencies.

Similar considerations apply to the alpha and beta radiations from the ²³²Th series. In this case, if equilibrium prevailed in the sample, one would expect the emission of six alpha particles and four beta particles per decay of the ²³²Th. Again, attenuation of the radiations will produce differences in counting efficiencies, and activity correlations with respective gross counting rates would be difficult unless a proper standard were available to establish effective gross alpha and beta counting efficiencies.

The ⁴⁰K, which decays by ß^- and ß⁺ decay, would add counts to the gross beta counts, but its contribution could not be easily ascertained without experimental work using standards to correlate the expected ⁴⁰K beta count rate with the gamma-determined ⁴⁰K activity.

In summary, gross alpha and gross beta counts are subject to significant uncertainties regarding their quantitative relationships to activities of radionuclides in the sample. These, together with possibly significant uncertainties concerning the degree of equilibrium between progeny and the parent radionuclide(s), make the kind of correlation that you appear to be seeking difficult to accomplish. If the state of equilibrium is known among the various progeny and the chain precursor(s), then it is a simple matter to calculate the expected activities of each of the progeny from the activity of the parent of the chain. Even in such an instance, however, it may be difficult to predict the theoretical alpha and beta gross count rates for a sample unless one had prepared a standard of similar characteristics as the sample and performed gross alpha and beta counting of the standard.

George Chabot, PhD, CHP