Radioactive activity and the becquerel

Radioactive activity tells you how many nuclear transformations occur per unit time. The SI unit is the becquerel: 1 Bq = 1 transformation per second. Activity is a property of the source; it is not the same quantity as detected count rate, absorbed dose or biological effect.

Activity is a decay rate

If N unstable nuclei are present and each has decay constant λ, the expected activity is A = λN. As the parent population decays, activity falls with the same exponential factor as N.

Activity calculator

Number of nuclei N decay constant λ (s⁻¹)

For one radionuclide, doubling N doubles the expected activity. The slope is the decay constant λ.

Becquerel is not a measure of energy

Two sources can have the same activity but emit radiation with very different particle or photon energies. Conversely, a low-activity source may remain detectable for a long time if its half-life is long. A becquerel counts transformations per second; it does not say how much energy each transformation releases.

Measured counts are not automatically equal to becquerels. Geometry, absorption, detector efficiency and background affect the count rate.

Why count rate and activity differ

A detector usually records only part of the radiation emitted by a source. Some radiation travels in other directions, some is absorbed before reaching the detector, and the detector itself may not register every interaction. Background counts add another contribution. Converting count rate into source activity therefore requires a calibrated measurement model.

Activity, half-life and amount are linked

Because λ = ln 2 / T½, a given number of nuclei has higher activity when its half-life is shorter. But comparing equal masses of different radionuclides also requires converting mass into number of nuclei. This is why activity cannot be inferred from mass alone without knowing the nuclide.

Worked examples

1. Convert transformations to becquerels

Solution

A source undergoes 2,400 transformations in 60 s. Its average activity is 2,400/60 = 40 Bq.

2. Use A = λN

Solution

For N = 5.0 × 10⁸ nuclei and λ = 2.0 × 10⁻⁴ s⁻¹, A = λN = 1.0 × 10⁵ Bq.

3. Separate activity from counts

Solution

A 10 kBq source does not guarantee a detector will show 10,000 counts/s. The measured rate can be lower because of solid angle, absorption and detector efficiency, and it can include background.