Use half-life with data
Half-life describes a repeated halving of activity or count rate. Correct for background radiation where needed, plot a decay curve and distinguish random individual decay from the predictable pattern of a large sample.
GCSE Physics resources
AQA GCSE Atomic structure
Half-Life and Radioactive Decay
Half-life describes a repeated halving of activity or count rate. Correct for background radiation where needed, plot a decay curve and distinguish random individual decay from the predictable pattern of a large sample.
Start here
The quick revision snapshot
Half-life describes a repeated halving of activity or count rate. Correct for background radiation where needed, plot a decay curve and distinguish random individual decay from the predictable pattern of a large sample.
By the end, you should be able to…
- Explain use half-life with data using precise physics language.
- Apply the relevant equations, diagrams or practical method to an exam-style situation.
- Use the mini quizzes and practice answers to identify and correct a misconception.
Core learning content
Learn the idea before you practise it
Start with this short teaching sequence for Half-Life and Radioactive Decay. Read the model, use the visual, then test your recall before moving into examples and exam practice.
Build the picture
Each unstable nucleus decays at a random time, so a small sample gives irregular results. In a large sample the number of undecayed nuclei falls by about half in each half-life. Always subtract background count before using an activity or count-rate graph.
Use the right relationship
Choose a relationship because of the physical change in the question, not because it is familiar. Activity after half-lives: remaining activity = initial activity × (½)ⁿ (Bq or counts/s). Mass number: A = protons + neutrons (no unit). Atomic number: Z = number of protons (no unit). Keep the unit next to each value while you substitute.
What a strong answer does
Count the number of half-lives, halve sequentially or read the graph, and include units and background correction in practical answers. Before writing, underline the command word and identify the information that matters. Keep a calculation as equation, substitution and answer with unit; keep an explanation as a linked chain using because, so or therefore. Finish by checking that the final sentence answers the exact context in the question and that the number, direction or conclusion agrees with the evidence given.
Retrieval practice
Quick checks
Answer without looking back first. The feedback explains the model, so a wrong answer still helps you learn.
Mini quiz 1
Check the core idea
Mini quiz 2
Apply the model
Mini quiz 3
Use exam precision
Try it
Half-life data model
How does repeated halving create a predictable pattern from random decay?
What to notice: the readout and written explanation remain available if you do not use the controls.
Worked examples
See the method being built
Cover the answer, attempt the method and then compare your physics language as well as the number.
Example 1 · Repeated halving
A source has activity 640 Bq and half-life 3 h. Find activity after 9 h.
- 9 h is three half-lives.
- Halve three times: 640 → 320 → 160 → 80.
- Give Bq.
Show the answer
Activity = 80 Bq.
Example 2 · Background correction
A detector measures 90 counts/min near a source; background is 12 counts/min. Find corrected count.
- State the raw count.
- Subtract background.
- Use corrected value in comparisons.
Show the answer
Corrected count rate = 90 − 12 = 78 counts/min.
Example 3 · Random decay
Explain how radioactive decay can be random but a half-life predictable.
- Describe one nucleus.
- Describe a large sample.
- Link to probability.
Show the answer
Each nucleus decays unpredictably, but many nuclei have a stable average probability, giving a predictable halving pattern.
Misconception clinic
Common wrong turns
Each of these is tempting because it sounds almost right. Replace it with the precise physics before you meet it in a question.
- Subtracting the half-life instead of halving activity.
- Using raw counts without background correction.
- Saying random means no pattern for a large sample.
Independent practice
Exam-style questions
Use the working space first. Reveal the guidance only after you have committed to an answer, then improve the exact part that would gain the next mark.
1. Define half-life.
[2 marks]Show answer and marking guidance
The time for activity or count rate to fall to half its initial value.
2. A source falls from 400 Bq to 100 Bq. How many half-lives have passed?
[2 marks]Show answer and marking guidance
Two.
3. A 5-day half-life source starts at 800 Bq. Find activity after 10 days.
[2 marks]Show answer and marking guidance
800 → 400 → 200 Bq.
4. Explain why background radiation is subtracted.
[3 marks]Show answer and marking guidance
It is not produced by the source and would otherwise make source count appear too large.
5. State what “random” means for radioactive decay.
[1 mark]Show answer and marking guidance
You cannot predict which individual nucleus will decay or exactly when.
6. Describe a decay graph for a radioactive source.
[2 marks]Show answer and marking guidance
It curves downwards, falling by equal fractions in equal half-life intervals and approaching background.
Questions pupils ask
GCSE Physics FAQs
What is the key idea in Half-Life and Radioactive Decay?
Atomic-structure questions combine a model of the atom, radiation properties and careful use of nuclear notation. Always distinguish irradiation from contamination.
How should I practise Half-Life and Radioactive Decay?
Read the snapshot, attempt the worked examples without looking, complete the mini quizzes and then use the practice questions to check your wording and method.
Next step
Keep your revision moving
Physics sticks when you move between explanation, retrieval and application.