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.

AQA 8463AQA 8464 GCSE PhysicsCombined Science: Trilogy FoundationHigher

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The 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:

  • Use half-life with data.
  • Apply the atomic structure model, evidence or method to an unfamiliar exam context.
  • Recognise and correct this wrong turn: Subtracting the half-life instead of halving activity.

Before you revise

Diagnostic question

Choose an answer from memory. Your result tells you what to watch for in the guide.

Which statement correctly summarises half-life and radioactive decay?

Core revision guide

Learn the model, then use it

Half-Life and Radioactive Decay questions become manageable when the central model, evidence and exam method are kept together. Read the explanation, test the misconception and then apply the idea without looking back.

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.

Build the physics 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.

The relationship for this guide

Activity after half-lives: remaining activity = initial activity × (½)ⁿ (Bq or counts/s). Choose each relationship from the physical change described, convert quantities into compatible units and keep the unit beside the final answer.

An activity-time curve passes through 800, 400, 200 and 100 becquerels at six-day intervals.
Equal 6-day intervals halve the activity; background count must be considered when using measured count rate.Open the full-size exam diagram
Activity after half-livesremaining activity = initial activity × (½)ⁿBq or counts/s

Misconception clinic

Replace the tempting answer

Read each belief, say what is wrong with it, then compare your correction.

Tempting idea: Subtracting the half-life instead of halving activity.

Use instead: 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.

Tempting idea: Using raw counts without background correction.

Use instead: 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.

Tempting idea: Saying random means no pattern for a large sample.

Use instead: Count the number of half-lives, halve sequentially or read the graph, and include units and background correction in practical answers.

Retrieval practice

Quick checks

1. Which exam method is most reliable for half-life and radioactive decay?

2. Which statement correctly applies half-life and radioactive decay to a question?

3. A pupil writes: “Subtracting the half-life instead of halving activity.” Which replacement is accurate?

Explore the relationship

Half-life data model

Choose a starting activity and number of half-lives, then calculate A = A₀ × (½)ⁿ.

What to notice: use the readout to describe how one variable changes when the other is controlled.

Worked examples

See the method being built

These examples expose the difference between a secure use half-life with data method and the common error “Subtracting the half-life instead of halving activity.”.

Example 1 · Repeated halving

A source has activity 640 Bq and half-life 3 h. Find activity after 9 h.

  1. 9 h is three half-lives.
  2. Halve three times: 640 → 320 → 160 → 80.
  3. 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.

  1. State the raw count.
  2. Subtract background.
  3. 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.

  1. Describe one nucleus.
  2. Describe a large sample.
  3. Link to probability.
Show the answer

Each nucleus decays unpredictably, but many nuclei have a stable average probability, giving a predictable halving pattern.

Exam precision

Exam technique: Use half-life with data

Do this: Count the number of half-lives, halve sequentially or read the graph, and include units and background correction in practical answers.

Independent practice

Exam-style questions

Write an answer before opening the marking guidance. Then edit the exact phrase or step that would gain the next mark.

1. Define half-life.

[2 marks]
Show marking guidance and model answer

Marking guidance: 2 marks are available for relevant, linked physics points that match the model answer.

Model answer: 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 marking guidance and model answer

Marking guidance: 2 marks are available for relevant, linked physics points that match the model answer.

Model answer: Two.

3. A 5-day half-life source starts at 800 Bq. Find activity after 10 days.

[3 marks]
Show marking guidance and model answer

Marking guidance: Award one mark for the correct relationship, one for a valid substitution and one for the final answer with its unit.

Model answer: 800 → 400 → 200 Bq.

4. Explain why background radiation is subtracted.

[3 marks]
Show marking guidance and model answer

Marking guidance: Award up to 3 marks for distinct physics points joined into a clear cause-and-effect chain.

Model answer: 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 marking guidance and model answer

Marking guidance: Award one mark for the precise statement shown in the model answer.

Model answer: You cannot predict which individual nucleus will decay or exactly when.

6. Describe a decay graph for a radioactive source.

[2 marks]
Show marking guidance and model answer

Marking guidance: 2 marks are available for relevant, linked physics points that match the model answer.

Model answer: It curves downwards, falling by equal fractions in equal half-life intervals and approaching background.

Questions pupils ask

Half-Life and Radioactive Decay FAQs

What is the main idea in 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.

What mistake should I avoid in Half-Life and Radioactive Decay?

Subtracting the half-life instead of halving activity. 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.

Useful next steps

Connect this guide to your next task

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