6.4 - Radioactivity Definitions

Some of this information is from the Rad Onc Blog

### Activity ( $A$)

Activity is the rate of decay of a radioactive material. Activity (A) is related to the number of radioactive atoms N and the decay constant $\lambda$.

(1)
\begin{align} A = - \lambda N \end{align}

The special unit for activity is the Becqurel (Bq), defined as 1 disintegration per second (dps).

### Apparent Activity ( $A_{app}$ )

The apparent activity is the activity of an unshielded source that would give the same exposure rate at a distance of 1 m, compared with the current filtered source. It is found by dividing the exposure rate of the source at 1 m by the exposure rate of an unfiltered source at 1 m.

### Specific Activity

The specific activity is the activity per gram of a radioactive material. It is used when comparing different radioactive isotopes and for determining half life. Its units are Bq/g.

### Air Kerma Rate Constant ( $\Gamma_{AKR}$ )

The Air Kerma Rate Constant is unique for each radionuclide, and is the relationship of kerma at a distance to the activity of the source per hour. It allows calculation of the reference air kerma rate, a useful specification of brachytherapy sources.
The units of the $\Gamma_{AKR}$ are:

(2)
\begin{align} \frac{(\mu\ Gy.m^2)}{GBq.h} \end{align}

### Reference Air Kerma Rate ( $\dot{K}_{air}.(d_{ref})_{air}$ )

The Reference Air Kerma Rate is the Air Kerma Rate arising from a brachytherapy source at a distance of 1 m. It allows useful comparison of different sources to determine their activity.

It is equal to:

(3)
\begin{align} \dot{K}_{air}.(d_{ref})_{air} = \frac{A_{app}.\Gamma_{AKR}}{d^2_{ref}}Gy/hr \end{align}

ie: The apparent activity, multiplied by the air kerma rate constant for the source in question, divided by the reference distance squared (in this case 1 m therefore 1).