IGCSE Physics Half-Life Notes
Half-life is the time for half the radioactive nuclei to decay. Learn to read decay curves and halve activity step by step.
Key concepts
- Half-life
- The average time taken for half the unstable nuclei in a sample to decay, or for the activity to halve.
- Activity
- The number of decays per second, measured in becquerels (Bq); it falls over time.
- Decay curve
- A graph of activity against time that halves every half-life, forming an exponential shape.
- After each half-life the activity (or number of undecayed nuclei) halves.
- After n half-lives, the remaining fraction is (½)ⁿ.
- Half-life is constant for a given isotope and unaffected by temperature or chemistry.
Key formulas
Fraction remaining
remaining = (½)ⁿ
n = number of half-lives elapsed.
Worked example
An isotope has a half-life of 5 years and an activity of 800 Bq. What is the activity after 15 years?
- 1Find the number of half-lives: 15 ÷ 5 = 3.
- 2Halve once: 800 → 400 Bq.
- 3Halve twice: 400 → 200 Bq.
- 4Halve a third time: 200 → 100 Bq.
Answer: 100 Bq
Common mistakes
✗ Dividing the activity by the number of half-lives.
✓ Halve the activity once per half-life — do not divide by n.
✗ Misreading the decay curve axes.
✓ Read activity from the y-axis and time from the x-axis carefully.
✗ Thinking half-life changes with conditions.
✓ Half-life is fixed for an isotope, whatever the temperature or state.
Quick check
Try these, then reveal the answers.
Define half-life.Reveal answer
The time for half the radioactive nuclei (or the activity) to decay.
A sample of 1600 Bq has a half-life of 2 days. What is the activity after 6 days?Reveal answer
200 Bq (three half-lives).
What fraction remains after 4 half-lives?Reveal answer
1/16.
Exam tips
- Count how many half-lives fit into the total time first.
- Halve the quantity step by step rather than dividing at once.
- Use the decay curve to read off half-life if a graph is given.
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Frequently asked questions
Does half-life depend on temperature?+
No — half-life is a fixed property of an isotope and is unaffected by temperature, pressure or chemical state.
How do I find the fraction remaining after several half-lives?+
Raise a half to the power of the number of half-lives, (½)ⁿ.
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