Answer to Question #6703 Submitted to "Ask the Experts"

Thank you for your question pertaining to the calculation of the percent enrichment of uranium (U). The calculation is performed by converting the activity concentration for ²³⁸U, ²³⁵U, and ²³⁴U to mass concentrations (e.g., g U/g soil) and then dividing the mass of  ²³⁵U by the total uranium mass. An example calculation is provided for clarity. Uranium half-life values obtained from the National Nuclear Data Center are ²³⁸U (4.468 x 10⁹ y), ²³⁵U (7.04 x 10⁸ y), and ²³⁴U (2.455 x 10⁵ y).

Assume that alpha spectrometry was used to analyze a soil sample containing enriched uranium and the following results were obtained: ²³⁸U (3.61 pCi/g), ²³⁵U (1.14 pCi/g), and ²³⁴U (23.87 pCi/g). The first step is to convert ²³⁸U activity concentration to mass concentration. Specifically, the activity concentration is divided by the decay constant (ln 2/half-life), and multiplied by [(238 g/mol)/(6.02 x 10²³ atoms/mol)]. Applying various time conversion factors and noting 1 pCi = 2.22 dpm, the ²³⁸U mass concentration is 1.073 x 10^-5 g ²³⁸U/g soil. Similar calculations are performed for ²³⁵U and ²³⁴U, resulting in 5.226 x 10^-7 g ²³⁵U/g soil and 3.834 x 10^-9 g ²³⁴U/g soil.

Finally, the percent ²³⁵U enrichment is calculated by dividing the ²³⁵U mass by the total U mass: (5.226 x 10^-7)/[(1.073 x 10^-5)+(5.226 x 10^-7)+(3.834 x 10^-9)] = 4.64 x 10^-2 (or 4.64%).

Eric W. Abelquist, PhD, CHP