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Radioactive half-life — Physics, 14–17 years

Half-life describes the steady pattern in which an unstable sample loses half of its remaining activity.

The idea

Radioactive atoms change randomly, so we cannot predict which single atom will decay next. For a large sample, however, the activity follows a reliable pattern: after one half-life, half the original unstable nuclei remain; after two, one quarter remains. The half-life is the time for each halving.

Why it matters

Scientists needed a way to describe decay when individual events cannot be predicted. Counting decays in many atoms revealed a stable statistical pattern, so half-life became a useful clock and comparison. It lets us estimate how much material remains without knowing the history of every atom.

Worked example

A sample begins with 80 g of a radioactive substance and has a half-life of 6 days. After 6 days, 40 g remain. After 12 days, half of 40 g remains: 20 g. After 18 days, half of 20 g remains: 10 g. Each step halves the amount still present.

The common trap

A common mistake is to think that one half-life removes half of the original sample every time. The wording feels natural, but each half-life removes half of what is left, not half of the beginning amount. That is why the sequence is 100, 50, 25, 12.5 rather than 100, 50, 0.

Where it appears

Half-life is used in medical imaging, where a short-lived tracer can show how an organ works while its activity fades. It is also used to date some rocks and archaeological remains, and to plan safe storage of radioactive waste. The method needs a suitable isotope and careful measurements.

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