Edexcel IGCSE Physics · Spec 7.12-7.13
Half-Life Calculations
Covers distinguish activity from detector count rate, Correct measurements for background radiation and Solve repeated-halving and graph problems.
Physics revision video
Half-Life Calculations
Prefer to watch on YouTube? Open this video on YouTube.
Explained
Half-life, and the three things that get confused
Radioactive decay is random. You cannot say when any particular nucleus will decay, only how a large number of them behave on average. Half-life is how that average behaviour is described: the time taken for half the radioactive nuclei in a sample to decay, or equivalently for the activity to halve.
Activity and count rate are not the same
Activity is the number of nuclear decays per second in the source, measured in becquerels, where one becquerel is one decay per second.
A count rate is what a detector reads, in counts per second or counts per minute. It is always lower than the activity, because radiation is emitted in every direction and the detector only intercepts a fraction of it.
For half-life calculations this does not matter, because both halve over the same time. For a question asking what a reading represents, it matters a great deal.
Background radiation
A detector always registers something, even with no source present. That is background radiation, from rocks such as granite, from cosmic rays, from food and drink, and from medical sources.
Before using any reading, subtract the background count. A detector reading 340 counts per minute with a background of 40 means the source is producing 300. Halve 300 to get 150, then add the background back to get 190 as the reading after one half-life. Skipping the subtraction makes every subsequent halving wrong.
Doing the calculation
Most questions are repeated halving. Write out the sequence rather than trying to do it in your head: 800, 400, 200, 100 is three half-lives, so if the half-life is 5 years the time is 15 years.
To go the other way, count how many halvings took place and divide the total time by that number. From a graph, find the starting activity, halve it, read across to the curve and down to the time axis. Doing it a second time from a different starting point is a good check, because for a genuine half-life you should get the same answer.
What examiners say about this topic
A principal examiner report for Edexcel International GCSE Physics says that definitions of half-life were usually sufficient for both marks, but that weaker candidates gave imprecise descriptions of what is being halved. It advises candidates to keep their definitions simple, describing the time for the activity to halve as the most straightforward correct response.
The same report notes that weaker candidates sometimes misread the scale on the time axis, and that where a question asked candidates to use data from a graph, those who made no quantitative reference scored nothing at all.
Another report shows the value of working. A candidate who reached an incorrect final answer still gained a mark because the working clearly showed the idea that the time period represented two half-lives. Where no working was shown and the answer was wrong, no marks were available.
Why the graph never reaches zero
Each half-life removes half of what remains, so there is always something left. The curve falls steeply at first and then flattens, approaching the axis without touching it. This shape is called exponential decay, and recognising it is often the first mark in a graph question.
It is also why disposing of radioactive waste is difficult. A substance with a half-life of thousands of years is still active thousands of years later, and nothing you do to it changes the rate.
Spec 7.12-7.13
What you need to know
- Distinguish activity from detector count rate
- Correct measurements for background radiation
- Solve repeated-halving and graph problems
Active recall
Quick check
Answer each question before opening the answer.
What does one becquerel mean?
One nuclear decay per second
How is corrected count rate calculated?
Measured count rate minus background count rate
What fraction remains after three half-lives?
One eighth
Physics revision app
Take this topic further in the app
275 guided topics with questions marked as you answer them, section checkpoints and timed practice papers. Fifteen topics are free to try, with no card needed.