Equation of Isotope Dilution Analysis:

Equilibration the desired constituent is separated, weighed and its activity is measured.

Sp. activity of tracer (SA) + Analyte Mixture = Sp. Activity of isolated part

Here, specific activity is defined as SA = Activity / Mass in mg = A counts per min (R) / m.

In general, the separation is performed by chemical separation methods as mentioned already. Of all, solvent extraction is the most widely used separation method because of its simplicity and ease in handling.

Let us consider a complex sample of m g containing m1 g of the component of interest. A radiotracer with total activity of A counts per min having a mass of m* is added to the anal yte so that its specific activity becomes SA₁ = A/ m*. After chemical separation, if m₁ g component containing both the active and inactive components is isolated and its activity is measured as A₁ counts per min. Its specific activity will be SA₂ = A₁ /m₁ and will remain constant regardless of how much of the pure component is isolated. Following balance sheet can be formulated.

Before mixing                              After mixing (before purification)

Amounts                    m₁ (inactive) + m* (active)        m₁   +   m₂ (mixture)

Sp. Activity               SA₁                                                SA₂

After purification, only a fraction (not quantitative) is isolated. Since specific activity of the component of interest will remain same before and after purification, this is as follows

m*  SA₁           =         (m₁   + m* ) SA₂

On solving this equation for the analyte of interest m₁ then we get

m₁       =         m* (SA₁/ SA₂ - 1)

Therefore, percentage amount of the component of interest in m g sample may be calculated.

Percentage of unknown   = 100× m */ m(SA₁/ SA₂ - 1)