Explain the concept of half-life and how this is related to the random…

The idea

Radioactive decay is random: you cannot predict which particular nucleus will decay next, or exactly when it will happen. Despite that randomness, a large sample shows a predictable statistical pattern. The half-life is the time taken for the number of undecayed nuclei in a sample to halve, or equivalently for the count rate from the sample to fall to half its starting value. Because individual decays are random, half-life is a statistical property of a large group of nuclei, not a timer attached to one nucleus. After one half-life half the nuclei remain, after two half-lives one quarter remain, and so on. A useful method is to halve the count rate repeatedly and add the half-life each time until you reach the measured value. When answering, connect the random nature of decay to why half-life describes a large sample rather than predicting a single nucleus.

What earns the marks

• Defines half-life as the time for the number of undecayed nuclei, or the count rate, to halve.
• Explains that radioactive decay is random, so a single nucleus's decay cannot be predicted.
• Connects half-life to the statistical behaviour of a large number of nuclei rather than one nucleus.
• Applies halving repeatedly, for example recognising that two half-lives leave one quarter of the original nuclei.

Common mistakes and how to put them right

• Claims half-life predicts exactly when one particular nucleus will decay.

  Put it right: Explain that decay is random and half-life applies to a large sample.

• Treats half-life as the time for all activity to stop.

  Put it right: State that activity halves each half-life and never reaches zero in this model.

• Halves the count rate only once when several half-lives have passed.

  Put it right: Apply the halving repeatedly for each half-life.

Exam tips

• Check whether the question asks about number of nuclei or count rate, because both halve over one half-life.
• Use a simple table of successive halvings to avoid arithmetic slips when several half-lives are involved.
• Link any explanation of randomness to the large-sample idea, since that is what makes half-life meaningful.