What is radioactive activity and how is it measured?

Radioactive activity is the rate at which unstable nuclei in a sample undergo radioactive decay. It represents the number of nuclear disintegrations occurring per unit time. The SI unit of activity is the becquerel (Bq), defined as one decay per second. In clinical practice, activity is commonly expressed in megabecquerels (MBq) or gigabecquerels (GBq).

Radioactive activity is the rate of nuclear decay in a sample, measured in becquerels, and decreases exponentially over time.

Activity is proportional to the number of radioactive nuclei present and the probability that each will decay. Mathematically, activity (A) is defined as:

A = λ·N

Where λ is the decay constant and N is the number of radioactive nuclei.

As radioactive decay proceeds and the number of unstable nuclei decreases, activity falls exponentially over time.

Understanding the physics

Radioactive decay is governed by probability. Each unstable nucleus has a constant chance of decaying per unit time, described by the decay constant (). If a sample contains more radioactive nuclei, more decays occur per second and therefore activity is higher.

Because the number of nuclei decreases over time, activity also decreases exponentially:

A(t) = A₀e^−λt

A₀ is the initial activity.

Activity is not the same as the amount of substance in grams. Two samples with identical mass may have very different activities if they contain different isotopes or have different half-lives. Short half-life isotopes have larger decay constants and therefore higher activity for the same number of nuclei.

In clinical practice, activity is measured using a dose calibrator, which detects emitted radiation and converts the detected signal into an activity value based on calibration factors specific to each radionuclide.

It is important to distinguish activity from count rate. Activity refers to actual nuclear disintegrations occurring within the source, while count rate refers to the number of detected events recorded by an imaging system. Count rate depends on detector efficiency and geometry, whereas activity is an intrinsic property of the source.

Where this matters clinically

Administered activity determines image quality and radiation dose. Too little activity results in noisy images; too much increases patient and staff exposure. Accurate measurement of activity is essential for safe and effective nuclear medicine practice.