The specific activity of a radioisotope is a measure of how highly radioactive it is. Specifically, it is the ratio of disintegrations per second in a given quantity of that isotope to its mass. It is inversely proportional to the half life. The equation is:

SA = (ln 2 * 6.02 * 1023) / (t1/2 * A)

where 6.023 * 1023 is Avogadro's Number, t1/2 is the half-life, and A is the atomic mass.

The specific activity is useful for a number of reasons. For one thing, directly measuring the half-life of extremely long-lived isotopes (which can be tens of thousands of years or more) is very difficult, because of the small number of disintegrations in any reasonable period of time. However, the specific activity can be measured instead, and the half-life determined from it. Also, quantities of radioactive materials are nearly always described in Curies (or microcuries), and the specific activity allows one to determine the mass of such quantities (or, conversely, the number of Curies in a given mass).

For example, fluorine-18, a frequently used tracer in positron emission tomography, has a half-life of 6586.2 seconds (110 minutes) and an atomic mass of 18, has a specific activity of 3.52 * 1018 Becquerels per gram, or 9.51 * 107 Curies per gram (Ci/g).

This means that 1 Ci of fluorine-18, which is a fairly reasonable dose for PET studies, is about 0.01 micrograms!

Reference figures taken from Radiochemistry and Nuclear Methods of Analysis; Ehmann, Vance; 1991.