# Activity of a radioactive source

Glossary Definition for 16-19

## Description

Radioactivity is the random and spontaneous breakdown of unstable atomic nuclei involving the emission of alpha, beta or gamma radiation.

The activity of a radioactive sample is defined as the rate at which radioactive particles are emitted. Activity is usually represented by the symbol *A*.

## Discussion

Radioactivity is a random process; it is impossible to predict exactly when a particular nucleus will decay. However, the probability per unit time that a given nucleus will decay is constant.

For a number of nuclei, N, in a sample of a radioactive nuclide, the activity, A, is related to the decay constant λ, which is the probability of decay per nucleus per unit time. If, during time Δt, N changes by ΔN, where ΔN < 0, then the activity, A, is the rate of decay, i.e:

A = –ΔNΔt = λN

as long as Δt is small compared with the half-life of the nuclide.

Activity is measured by detecting the radioactive emissions from decay events and counting the number of such detections in a fixed time interval. For this to provide an accurate measurement, the time interval used must allow a sufficiently large number of decays to be detected, while being sufficiently small for the activity not to drop significantly between its start and end, i.e. it must be much less than the half-life of the sample.

A sample of a radioactive material may contain different nuclides, often resulting from previous decays. Furthermore, most radioactive nuclides decay by more than one process; for example, a nucleus of bismuth-212 may decay via either alpha or beta emission. The different processes will have different decay constants and hence different activities. In both cases, the total activity of the sample is the sum of the activities due to all the different decay processes.

## SI unit

becquerel, Bq

## Expressed in SI base units

s^{–1}

## Other commonly used unit/s

Ci (curie) (1 Ci = 3.7 × 10^{10} Bq), minutes^{–1}, hours^{–1}, years^{–1}

## Mathematical expressions

- The activity A of a source consisting of a particular radioactive nuclide at a particular time is A = –ΔNΔt = λN
- In calculus notation A = –dNdt = λN

where λ is the decay constant of the nuclide and N is the number of radioactive nuclei at that time.