Answer to Question #1020 Submitted to "Ask the Experts"

Q

We have a sample containing uranium (and maybe some daughters) of unknown activity. How can we estimate the activity from the exposure rate (mR h^-1)?

A

I assume that the sample is at least two to three months old and, therefore, essentially restored to equilibrium with the ²³⁴Th and ²³⁴Pr grown back in. I also assume that the sample is small enough to be treated as a point source at 0.3 m (1 foot). Estimates calculated using a program called Microshield indicate that the dose rate at 0.3 m from a 1 gm sample of uranium is about 6.0×10^-5 mR h^-1 g^-1. Therefore, to determine the number of grams in your sample, divide the mR h^-1 measured at 0.3 m by 6.0×10^-5. If activity is required, then multiply the result by the specific activity of ²³⁸U (12,350 Bq g^-1) to give activity of ²³⁸U only (in becquerel). The total radioactivity, taking into account the ²³⁵U and all progeny is about four times this amount. Now, here's the problem: Obviously, for most reasonable samples, an mR h^-1 meter is not good enough. A MicroR meter is required. The best sensitivity, taking into account natural background, etc., that one can expect is about 3 microR h^-1 (maybe 1 or 2 with careful shielding and long sampling times). This gives a minimum detection level of about 0.003 mR h^-1 divided by 6.0×10^-5 or about 50 g of uranium. You can enhance the sensitivity somewhat by moving the meter closer to the source, which will result in a higher exposure rate and increasing the 6.0×10^-5 conversion factor by the ratio of the square of the distance (i.e., 0.3 m/distance in m squared). However, note that you must not move the detector so close to the source that it can no longer be considered a point source. The point source rule of thumb is that the rate meter should never be closer than 2.5 times the source diameter. Also be warned that uranium is extremely electron dense. For much larger samples the number 6.0×10^-5 mR h^-1 g^-1 will start to underestimate total ²³⁸U because of self shielding of gamma rays in the source. If this does not work for your sample, analysis using counting methods, preferably alpha spectroscopy or gamma spectroscopy, are recommended.

John Barnard, PhD