What is half-life, and how is it used to work out how much of a source remains?
Half-life as the time for the activity to halve, calculating remaining activity, and uses such as dating and medicine.
A focused answer to the WJEC GCSE Science Double Award Unit 6 topic on half-life, covering half-life as the time for the activity to halve, calculating the remaining activity or amount, and uses such as radioactive dating and medicine.
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What this dot point is asking
WJEC Double Award Unit 6 wants you to explain half-life, calculate the remaining activity or amount, and describe uses of radioactive sources.
What half-life is
Because decay is random, we cannot say when one nucleus will decay, but with very large numbers of nuclei the activity halves predictably over each half-life.
How the activity falls
Calculating the remaining amount
To find the activity (or amount) after a time:
- Work out the number of half-lives: divide the total time by the half-life.
- Halve the starting activity that many times.
For example, after 3 half-lives, an activity of 800 counts/min becomes counts/min.
Uses of radioactive sources
The half-life decides what a source can be used for:
- Radioactive dating: carbon-14 (long half-life) is used to date once-living material; uranium isotopes date rocks.
- Medical tracers: a source with a short half-life is injected and followed with a detector, then decays away quickly so it does not stay in the body.
- Treating cancer: gamma sources are used to kill cancer cells.
A short half-life is safer inside the body (it decays away quickly); a long half-life lasts a long time, which suits dating but is a disposal problem for waste.
Reading a decay graph
Half-life can be found from a decay graph of activity (count rate) against time. To find it, pick a starting activity on the curve, find the time for it to fall to half that value, and read off the time taken - that is the half-life. You can check by repeating from a different starting point: the time to halve should be the same each time, because the half-life is constant. Being able to read the half-life off a graph, and to read the activity at a given time, is a common data-handling skill in this topic.
Why half-life matters for nuclear waste
The half-life is very important when dealing with radioactive waste from nuclear power. Waste with a long half-life stays dangerously radioactive for thousands of years, so it must be stored safely for a very long time, often deep underground. Waste with a short half-life becomes safe much more quickly. This is why the disposal of nuclear waste is a serious issue and a common discussion point: the long half-lives mean the waste must be isolated from people and the environment for an extremely long time.
Try this
Q1. What is the half-life of a radioactive source? [1 mark]
- Cue. The time for its activity (or number of undecayed nuclei) to halve.
Q2. After 2 half-lives, what fraction of the original activity remains? [1 mark]
- Cue. One quarter (a half of a half).
Exam-style practice questions
Practice questions written in the style of WJEC exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.
WJEC style3 marksThe activity of a source is 800 counts per minute. Its half-life is 2 hours. What will the activity be after 6 hours?Show worked answer →
A Unit 6 calculation. In 6 hours there are half-lives (1 mark). Halve the activity three times: (1 mark for working) counts per minute (1 mark). Markers reward finding the number of half-lives and halving the correct number of times. A common error is to subtract the half-life rather than halving the activity each time.
WJEC style3 marksDefine the half-life of a radioactive source and explain why the activity never quite reaches zero.Show worked answer →
A Unit 6 explain question. The half-life is the time taken for the activity (or number of undecayed nuclei) to halve (1); each half-life the activity falls to half its previous value (1); because you keep halving, the activity gets smaller and smaller but never quite reaches zero (1). Markers credit the definition (time to halve) and the idea of repeated halving never reaching zero. A common error is to define half-life as the time for the source to fully decay.
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