Specific activity

Specific activity is the activity per quantity of a radionuclide and is a physical property of that radionuclide.

Activity is a quantity related to radioactivity. The SI unit of activity is the becquerel (Bq), equal to one reciprocal second. The becquerel is how many radioactive transformations per second occur in a radioactive isotope. Its related and more common unit is the Curie (abbreviated Ci) which is 3.7 x 10¹⁰ transformations per second.

Since the probability of radioactive decay for a given radionuclide is a fixed physical quantity (with some slight exceptions, see Changing decay rates), the number of decays that occur in a given time of a specific number of atoms of that radionuclide is also a fixed physical quantity (if there are large enough numbers of atoms to ignore statistical fluctuations).

Thus, specific activity is defined as the activity per quantity of atoms of a particular radionuclide. It is usually given in units of Bq/g, but another commonly used unit of activity is the curie (Ci) allowing the definition of specific activity in Ci/g.

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

Mass of the radionuclide is given by

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

Specific radioactivity a 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).

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