Answer to Question #4609 Submitted to "Ask the Experts"

If a raw water sample has 20 pCi/L of ²²⁶Ra, how can this value be converted to units of eq/L of ²²⁶Ra?

I assume that your notation of eq/L represents gram-equivalents per liter. On that basis, we can make the conversion fairly simply by first determining the number of atoms of ²²⁶Ra present in 20 pCi (call this number N_a). This number can then be converted to gram-atomic-weights of ²²⁶Ra, GA, by dividing by Avogadro’s number, and finally the conversion to gram-equivalents, G-Eq, is made by multiplying the number of gram-atomic-weights by 2, since radium will exist as a divalent cation in water solution. In the conversion to number of atoms we must recognize that the amount of activity is represented by the product of the number of radioactive atoms present and the radioactive decay constant for the radionuclide of interest. The decay constant is given by the natural logarithm of 2 divided by the half-life of the radionuclide; for ²²⁶Ra the half-life is 1,600 years. The conversion is then as follows (the unit dpm refers to atoms disintegrating per minute):

N_a = (20 pCi)(2.22 dpm/pCi)/[(ln2)/(1600 y)(365d/y)(24 h/d)(60 min/h)] = 5.387 x 10¹⁰ atoms, and

GA = 5.387 x 10¹⁰ atoms/6.023 x 10²³ atoms/gram-atomic-weight = 8.944 x 10^-14 gram-atomic-weights, and

G-Eq =(8.944 x 10^-14 gram-atomic-weights)(2 gram-equivalents/gram-atomic-weight) = 1.789 x 10^-13 gram-equivalents.

Hence the ²²⁶Ra concentration could be written as 1.79 x 10^-13 eq/L, or 1.79 x 10^-13 N, where N stands for normal.

George Chabot, PhD, CHP