Radioactive decay is random because the exact moment at which an individual unstable nucleus decays cannot be predicted. It is spontaneous because the decay occurs without an external trigger. This is required for both SL and HL in IB Physics E.3.
An unstable nucleus has a combination of protons and neutrons that allows it to change into a more stable, lower-energy state. The change may involve alpha, beta or gamma decay. The energy released comes from a reduction in the nucleus's mass-energy, so spontaneous decay does not mean that energy appears from nowhere.
Quantum physics does not assign an exact decay time to each nucleus. Instead, it gives a probability that a nucleus will decay during a particular time interval. Two identical nuclei can therefore decay at completely different times even though they have the same nuclear structure.
| Property | Meaning |
|---|---|
| Random | The decay time of one nucleus cannot be predicted, and previous survival does not determine when it will decay. |
| Spontaneous | No collision, heating or other external stimulus is required to initiate the decay. |
| Statistically predictable | A large collection of nuclei follows a regular decay pattern, allowing its half-life to be measured. |
This explains why a large sample behaves predictably even though individual events do not. After one half-life, approximately half the original unstable nuclei remain; after two half-lives, approximately one quarter remain. The exact nuclei that decay cannot be identified beforehand.
At HL, this is expressed using the decay constant: each undecayed nucleus has the same probability per unit time of decaying. This produces the exponential decay law.
A common misconception is that “random” means “without physical laws.” It does not: individual events are unpredictable, but the statistical behaviour of a large sample is highly predictable.
Exam technique: For an Explain question, state both ideas separately: no exact individual decay time can be predicted, and no external trigger is needed. Then link randomness to predictable half-life behaviour in a large sample.
