Question 1Warm-upFoundation
An isotope has a half-life of 6 hours. How much of an 80 g sample is left after 12 hours?
12 hours is 2 half-lives.
Worked solution
- half-lives
- g
Answer: g
GCSE & IGCSE physics practice
Half-life questions and answers
The half-life of a radioactive isotope is the time it takes for the number of unstable nuclei in a sample (or its count rate or activity) to halve. After one half-life, half is left; after two, a quarter; after three, an eighth. The questions include reading half-life from data and allowing for background radiation.
8 questions · Foundation and Higher tier · Every answer is checked as you type it, with a full worked solution. Updated .
Where half-life comes up
| GCSE (AQA) | Physics and Combined Science, Foundation and Higher: explain half-life and find it from given information. Higher only: calculate the net decline, as a ratio, after a number of half-lives. |
|---|---|
| Cambridge IGCSE (0625) | Core: define half-life and use it in simple calculations (without background radiation). Supplement: calculate half-life from data or decay curves where background radiation hasn't been subtracted. |
The method
- Count how many half-lives have passed: time ÷ half-life.
- Halve the amount once for each half-life.
- To find the half-life, find the time for the count rate to fall to half.
- Background radiation: subtract it before halving, then add it back.
Half-life questions
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Warm-up
Question 2Warm-upFoundation
A sample's activity is 1600 Bq. Its half-life is 5 years. What is its activity after 15 years?
15 years = 3 half-lives.
Worked solution
- Bq
Answer: Bq
Exam-style
Question 3Exam-styleFoundation
A count rate falls from 800 to 100 counts per minute in 6 days. What is the half-life?
How many halvings take 800 to 100?
Worked solution
- : 3 half-lives
- days
Answer: days
Question 4Exam-styleFoundation
What fraction of a radioactive sample is left after 4 half-lives?
Halve four times.
Worked solution
Answer:
Question 5Exam-styleFoundation
A count rate falls from 640 to 160 counts per minute in 10 minutes. What is the half-life?
640 → 320 → 160.
Worked solution
- : 2 half-lives in 10 minutes
- Half-life minutes
Answer: minutes
Question 6Exam-styleFoundation
Readings of an isotope's activity: 1000 Bq at 0 h, 707 Bq at 2 h, 500 Bq at 4 h, 354 Bq at 6 h. What is its half-life?
When has it fallen to half of 1000?
Worked solution
- Half of 1000 Bq is 500 Bq, reached at 4 h.
- (Check: from 707 at 2 h it reaches about 354 at 6 h, also 4 h.)
Answer: hours
Challenge
Question 7ChallengeHigher
A source has an activity of 1200 Bq. Calculate the net decline in its activity after 3 half-lives.
Find what's left, then subtract from the start.
Worked solution
- After 3 half-lives: Bq
- Net decline Bq
Answer: Bq (a ratio of of the original)
Question 8ChallengeHigher
A measured count rate is 520 counts/min, including a background count of 20 counts/min. What will the measured count rate be after one half-life?
Only the source's count rate halves; the background stays the same.
Worked solution
- Source alone: counts/min
- After one half-life: counts/min from the source
- Measured: counts/min
Answer: counts/min
Common mistakes
- Dividing by the number of half-lives instead of halving repeatedly.
- Forgetting background radiation.
- Thinking the sample is gone after two half-lives.
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Sources
The questions are our own. The “where it comes up” notes are from each board's published specification, checked on 27 October 2026:
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