# 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, for which the SI unit is the becquerel, equal to one reciprocal second. The becquerel is defined as the number of radioactive transformations per second that occur in a particular radionuclide. The older, non-SI unit of activity is the curie, which is transformations per second.

Since the probability of radioactive decay for a given radionuclide is a fixed physical quantity, 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.

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 allowing the definition of specific activity in Ci/g. The amount of specific activity should not be confused with level of exposure to ionizing radiation and thus the exposure or absorbed dose. The absorbed dose is the quantity important in assessing the effects of ionizing radiation on humans.

## Formulation

### Relationship between ''λ'' and T_{1/2}

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

*N*:

The integral solution is described by exponential decay:

where

*N*

_{0}is the initial quantity of atoms at time

*t*= 0.

Half-life

**T**is defined as the length of time for half of a given quantity of radioactive atoms to undergo radioactive decay:

_{1/2}Taking the natural logarithm of both sides, the half-life is given by

Conversely, the decay constant

*λ*can be derived from the half-life

*T*

_{1/2}as

### Calculation of specific activity

The mass of the radionuclide is given bywhere

*M*is molar mass of the radionuclide, and

*N*

_{A}is the Avogadro constant. Practically, the mass number

*A*of the radionuclide is within a fraction of 1% of the molar mass expressed in g/mol and can be used as an approximation.

Specific radioactivity

*a*is defined as radioactivity per unit mass of the radionuclide:

Thus, specific radioactivity can also be described by

This equation is simplified to

When the unit of half-life is in years instead of seconds:

#### Example: specific activity of Ra-226

For example, specific radioactivity of radium-226 with a half-life of 1600 years is obtained asThis value derived from radium-226 was defined as unit of radioactivity known as the curie.

### Calculation of half-life from specific activity

Experimentally measured specific activity can be used to calculate the half-life of a radionuclide.Where decay constant

*λ*is related to specific radioactivity

*a*by the following equation:

Therefore, the half-life can also be described by