Answer to Question #9606 Submitted to "Ask the Experts"

I have a database of radionuclide concentrations (in Bq kg^-1) of ²³⁸U, ²³²Th, and ⁴⁰K for different soil types. I want to model the radon flux from different soil types, and I want the ²²⁶Ra distribution for different soil types. Can I assume that ²²⁶Ra is in secular equilibrium with its parent, and can I use the radionuclide concentration of ²³⁸U as the value for radium?

I also have a database with terrestrial gamma dose rate (nSv h^-1) values recorded at different stations for the same soil types. How can I relate the radionuclide concentration values (Bq kg^-1) of the three radionuclides with the terrestrial gamma dose rate (nSv h^-1) values recorded for the same soil types?

The degree of equilibrium between radium and uranium may vary depending on the geological conditions and history of the soil being considered, as well as on other possible physical and chemical factors that could alter equilibrium. Because of the relatively long half-lives of precursors ²³⁴U (2.47 x 10⁵ years) and ²³⁰Th (8.0 x 10⁴ years), it would take more than a million years for the ²²⁶Ra to achieve equilibrium with the ²³⁸U. If you are reasonably confident that the material you are concerned with has been stable for a long period you may assume equilibrium between the radium and uranium. If you have no information to the contrary, this assumption may be used. In such a case, if the equilibrium has been disturbed, the assumption that the ²³⁸U activity concentration is an indirect measure of the ²²⁶Ra activity concentration will be conservative. More often, analysts want to use a reverse analytical process in which the ²²⁶Ra concentration is used to estimate the ²³⁸U concentration, and for such analyses a disruption in equilibrium could lead to an underestimate of the uranium concentration.

Regarding your second question, there has been work done to correlate external dose rates to an individual standing on the earth with soil radionuclide concentrations, taking into account the thickness of the contaminated soil layer, for a large number of radionuclides. Among the most used of these, at least in the United States, is a compilation available in the Environmental Protection Agency (EPA) document Federal Guidance Report 12, External Exposure to Radionuclides in Air, Water, and Soil. For a given radionuclide, this lists the effective dose rate to an individual per unit concentration of the radionuclide in soil (units of Sv per Bq s m^-3). Calculations have been done for cases in which the radionuclide is assumed to be present (1) as a surface contaminant distributed evenly over a large area, (2) as a contaminant present uniformly throughout the first 1 cm of soil, (3) as a contaminant present uniformly throughout the first 5 cm of soil, (4) as a contaminant present uniformly throughout the first 15 cm of soil, and (5) as a contaminant present uniformly throughout an infinite thickness of soil. Results are given in Tables III.3 through III.7 of the EPA document. I assume you would probably be using the data for infinite thickness if you are dealing with soil that has not been contaminated with the radionuclides of interest by man's activities. Since the effective doses are given for individual radionuclides, you would have to sum all the individual results for all the uranium progeny to get the expected total effective dose rate per unit uranium concentration. You would have to do similarly for the ²³²Th progeny. The ⁴⁰K would be straightforward since it decays to a stable species.

Naturally, you have to know the relative amounts of the uranium, thorium, and potassium in the soil in order to determine absolute concentrations from measured dose rates. If you already know the absolute concentrations of the radionuclides, then it is a simple matter to estimate the expected effective dose rates by multiplying the concentration of each respective radionuclide by the respective dose conversion factor from the EPA report. I should note here that the EPA document assumed a soil density of 1.6 x 10³ kg m^-3, and you may need this to convert your mass concentrations to volume based concentrations. The EPA effective dose results are based on use of the tissue weighting factors that had been recommended in International Commission on Radiological Protection (ICRP) Publication 26.

The same results, with some enhancements, that are available in the cited EPA document are also available in a download from the Nuclear Regulatory Commission (NRC) website. The software is referred to as the Radiological Toolbox. The software contains a wealth of information of interest to health physicists and others concerned with ionizing radiation and runs on Windows XP (as well as some earlier versions of Windows). If you run it in Windows Vista (and probably Windows 7) all of the functions will not work, although the portion you would be interested in does run (at least on Vista). Once you've loaded the software, to access the information of interest, click on "Dose Coefficients" on the left and then click "Public External Coefficients (FGR 12)" near the bottom. You can select a radionuclide of interest from the drop-down list in the "Nuclide" box, and click the appropriate radio button in the "Select exposure mode" box (probably "Infinite Soil" for your case). One advantage of using this software is that if there are radionuclides related through serial decay, you can select the parent nuclide then click the box "Include all daughters?," click "Display," and the effective dose rate per unit concentration will be listed (as well as individual organ doses) for each of the progeny as well as for the parent. These assume equilibrium conditions so if there is any variation from equilibrium of the progeny with the parent of the chain, the results may require modification (if you have sufficient information about the extent of disequilibrium). You will notice that there are also results for effective dose based on recommendations of tissue weighting factors from ICRP Publication 60; these can be useful if you prefer the more recent ICRP recommendations.

You should keep in mind that the results from the above sources represent effective dose rates per unit concentration, which take into account the distribution of dose among the major organs/tissues of the body with organ doses weighted by appropriate tissue weighting factors. The measured values you refer to may not be effective dose rates. For example, they might be dose equivalent rates at the instrument location. Depending on how much accuracy you require you may have to make some adjustments to the readings to better approximate effective dose rates.

There is considerably more that we could discuss relative to the conversions among dosimetric and operational quantities and the analytical methods that could be used to calculate dose rates at fixed points above the contaminated soils, but such discussion is beyond the scope of my intent.

George Chabot, PhD, CHP