Radioactive decay is random.

The idea

Random decay means you cannot predict when any particular unstable nucleus will decay, nor which nucleus in a sample will decay next. Each nucleus has a fixed probability of decaying in a given time, but the actual moment is a matter of chance. This is why a single count-rate reading is unreliable: the count over the next minute might be higher or lower than the last. However, because a sample contains enormous numbers of nuclei, the overall pattern is predictable. The activity falls by half in each half-life, giving a smooth decay curve.

For example: A source with a half-life of 5 days and an initial count rate of 800 counts per minute would be expected to give about 400 counts per minute after 5 days and about 200 counts per minute after 10 days, even though no one can say when an individual nucleus will decay.

What earns the marks

• Defines random decay as being unable to predict which nucleus decays next or exactly when a given nucleus will decay.
• Explains that each nucleus has a constant probability of decaying per unit time, but the timing of any individual decay is chance.
• Uses the large number of nuclei in a sample to explain why the overall activity follows a predictable half-life pattern.
• Applies half-life reasoning to calculate expected count rate or activity after one or more half-lives, for example halving 800 counts per minute to 400 then 200.
• Distinguishes random decay from a regular or clockwork process, noting that a single short count may not match the expected average.

Common mistakes and how to put them right

• Saying that a nucleus 'gets old' and decays after a set time.

  Put it right by stating that decay is not scheduled and the nucleus has the same chance of decaying at any moment.

• Treating a single count-rate measurement as proof that half-life has changed.

  Put it right by explaining that random variation makes individual readings unreliable and repeated readings or longer counts are needed.

• Confusing half-life with the time for all nuclei to decay.

  Put it right by stressing that half-life is the time for half the unstable nuclei to decay, or for the count rate to halve.

Exam tips

• Use the phrase 'cannot predict' when defining random decay, and add that the overall behaviour of a large sample is predictable.
• For half-life calculations, count how many half-lives have passed, then halve the starting value that many times, showing each step.
• When interpreting a graph, read the half-life from the curve by finding the time for the count rate to fall to half its initial value, not by joining points with a ruler.