Radioactivity: (a) radioactive decay; spontaneous and random nature of decay

The idea

Radioactive decay is the process by which an unstable nucleus emits radiation to become more stable. It is spontaneous: the decay is not triggered by external factors such as temperature, pressure or chemical state, and cannot be predicted or controlled. It is random: for any given nucleus, we cannot know when it will decay, and in a sample, different nuclei decay at different times. The decay of one nucleus is independent of others. These properties are fundamental to understanding phenomena like exponential decay and half-life. For example, a single carbon-14 nucleus might decay in the next second or in thousands of years; we can only assign a probability. The rate of decay is proportional to the number of undecayed nuclei, leading to N = N₀e^(−λt).

What earns the marks

• Spontaneous: decay is not affected by external conditions such as temperature, pressure or chemical environment.
• Random: for an individual nucleus, the exact time of decay is unpredictable; each nucleus has a fixed probability of decay per unit time.
• Decay is a nuclear process; it involves changes in the nucleus, often emitting alpha, beta or gamma radiation.
• The rate of decay is proportional to the number of undecayed nuclei, N, giving the exponential decay law N = N₀e^(−λt).
• Half-life is the average time for half the nuclei in a sample to decay, and it is constant for a given isotope.

Common mistakes and how to put them right

• Misunderstanding: thinking that decay can be sped up by heating or chemical reactions.

  Put it right: Decay is spontaneous and unaffected by external conditions.

• Misunderstanding: believing that after one half-life all nuclei have decayed.

  Put it right: After one half-life, half of the original nuclei remain undecayed; decay continues exponentially.

• Misunderstanding: assuming that the decay of one nucleus affects the timing of another.

  Put it right: Decays are independent events; the decay of one nucleus does not influence others.

• Misunderstanding: confusing random with unpredictable in the sense of having no pattern.

  Put it right: While individual decays are random, large samples show statistical patterns such as exponential decay.

Exam tips

• Remember that 'spontaneous' means the decay is not caused by external factors, and 'random' means we cannot predict which nucleus decays next or when.
• In calculations, use the exponential decay equation N = N₀e^(−λt) and ensure you can rearrange it for λ or t.
• When explaining half-life, emphasise that it is an average time and that after each half-life the number of undecayed nuclei halves.