Similar to double isotope dilution, substoichiometric analysis is applied to the quantitative analysis of a radioactive substance (m0) if it is present in such a small quantity that the specific activity before the dilution (a0) cannot be determined. The radioactivity of the standard and the unknown sample should be the same. A reagent is added to both the standard and the unknown solution in unequivalent quantities. This is why the method is called “substoichiometric analysis.” The prod­uct of the reaction (e. g., a complex compound) is separated (e. g., by extraction), and the activity of an aliquot is measured. As a result of the addition of the reagent in an unequivalent quantity, the activity of the product is inversely proportional to the concentration of the solution.

When several standard solutions with the same activity are used, a calibration curve is plotted (Figure 10.6). The concentration of the unknown sample is deter­mined using this calibration curve. This method is applied in RIA studies (as discussed in Section 12.3.1).

10.1.6.2 The Dynamic Isotope Dilution Method

The isotope dilution method can be applied in open-flowing systems (see Section 11.2.6). Let us assume a tank with volume V and flow rate w of a liquid passing through the tank. At t = 0, a radioactive indicator with a0 specific activity (or intensity) is added to the liquid. Assuming the mixing to be ideal, at t time, the specific activity (intensity), a, of the liquid leaving the tank is:

a = a0 e— (10.12)

For a series of tanks, the specific activity (intensity) of the liquid leaving the ith tank is:

(10.13)