Specific Activity - Formulation

Formulation

First, radioactivity is expressed as the decay rate of a particular radionuclide with decay constant λ and the number of atoms N:

Next, mass of the radionuclide is given by

where m is mass number of the radionuclide and N_A is Avogadro constant.

Specific radioactivity S is defined as radioactivity per unit mass of the radionuclide:

In addition, decay constant λ is related to the half-life T_1/2 by the following equation:

Thus, specific radioactivity can also be described by

This equation is simplified by

When the unit of half-life converts a year

For example, specific radioactivity of radium 226 with a half-life of 1600 years is obtained by

This value derived from radium 226 was defined as unit of radioactivity known as Curie (Ci)