Radioactive decay is random: for one unstable nucleus there is no way to predict when it will decay. Every nucleus has the same fixed chance of decaying in each time interval, and that chance does not change as time passes. A half-life describes a large group, not a single atom.
This idea connects interpreting random count-rate data with the calculations in half-life and background.
What does a half-life actually say?
Suppose a half-life is 10 minutes. For one nucleus, this means there is a 50% chance it decays within 10 minutes. It does not mean it will decay at 10 minutes, or even that it will decay at all in that time.
For a very large sample, the chances average out. About half of the nuclei decay in each 10 minutes, so calculations with half-life work well for groups.
How do I explain it in an answer, step by step?
- Say what is random: which nucleus decays, and when, cannot be predicted.
- Give the chance idea: each nucleus has the same chance of decaying in a given time.
- Say what is predictable: with many nuclei, about half decay in one half-life.
- Link to evidence: count-rate readings vary from one interval to the next, even with nothing changed.
Worked example
(Invented data.) A detector counts a long-lived source for 1 minute, five times in a row: 52, 47, 58, 49 and 55 counts.
Mean count: 52 + 47 + 58 + 49 + 55 = 261, and 261 ÷ 5 = 52.2 counts per minute.
What the variation shows: the readings are not identical, yet they cluster around 52. Nothing about the source changed between counts. That scatter is what random decay looks like.
Now a model: a sample has 400 nuclei and a half-life of 5 minutes. The prediction for the group is about 200 nuclei left after 5 min and about 100 after 10 min.
A real run might give 196 or 207. The model does not say which nuclei decayed.
The mistake to watch for
Mistaken answer: “The nucleus has lasted two half-lives, so it is overdue and will decay next.”
The student treated decay like a countdown timer.
There is no timer. A nucleus that has survived two half-lives still has a 50% chance of decaying in the next half-life, exactly the same as a new one. It does not age or remember its history.
A second mistaken idea is that a tiny sample of 4 nuclei must have exactly 2 left after one half-life. With so few, the actual number could easily be 1, 3 or even 4. The half-life prediction improves as the sample gets larger.
Check yourself
1. Why do repeated counts from the same source over equal times give different numbers?
Show answer
Decay is random, so the number of nuclei that decay in each interval varies slightly around an average. The source and detector have not changed. Background radiation also varies randomly.
2. A nucleus has a half-life of 4 hours and has not decayed after 12 hours. What is the chance it decays in the next 4 hours?
Show answer
50%. It has no memory of the 12 hours that have passed, so the chance is the same as for any nucleus over one half-life.
3. A student says, “The half-life tells me exactly when this nucleus will decay.” Give a correct statement.
Show answer
The half-life tells you the time for half of a large number of nuclei to decay, or for the count rate to halve. It cannot tell you when one nucleus will decay, because decay is random.
Where this leads next
The next lesson shows how to separate a half-life calculation from a statement about personal risk: distinguishing a model calculation from personal radiation-risk advice.
If writing precise scientific explanations is hard, our teachers can help in online one-to-one Physics tuition. The graph-model and residual explorer lets you see how real scatter sits around a smooth model curve.