Activity and Half-Life

Although we cannot predict when any individual nucleus will decay, the mathematics of large numbers gives us powerful tools for describing radioactive decay quantitatively. The key concepts are activity, decay constant, and half-life — and they are all connected by elegant exponential relationships.

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Activity

The activity of a radioactive source is the number of nuclei that decay per unit time. It is measured in becquerels (Bq), where 1 Bq = 1 decay per second.

Activity depends on two things: how many undecayed nuclei are present, and how quickly each one is likely to decay. This gives us the fundamental equation:

A = λN

where:

• A = activity (Bq)
• λ = decay constant (s⁻¹)
• N = number of undecayed nuclei remaining

As nuclei decay, N decreases, so activity decreases over time. A source does not have a constant activity — it weakens as the radioactive atoms are used up.

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The Decay Constant

The decay constant λ (lambda) represents the probability that any given nucleus will decay per unit time. It is a fixed property of a particular isotope and does not change with external conditions.