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S6 Physics: Radioactivity and Half-life – Practice Paper 2 (Intermediate, 10 Questions)
S6 Physics: Radioactivity and Half-life – Practice Paper 2 (Intermediate, 10 Questions)
Paper two applies half-life to activity, percentages and dating: unit conversion of time, the difference between decayed and undecayed fractions, carbon-14 dating, and the order in which two samples began to decay.
Quick answer Answers: 125 Bq, 50 g, 15 hours, 1/32, 87.5%, 22 hours, 11460 years, 4800 years, 12 days, and 1/8 which is 12.5%.
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 |
| Suggested time | 25 |
| Difficulty mix | Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1 |
| Chapter | Chapter: S6 Physics: Radioactivity and Half-life |
| Level | Intermediate |
02 Questions (10 items)
- FoundationA 1000 Bq sample passes through 3 half-lives. What is its activity then?
- FoundationAn 800 g radioactive sample passes through 4 half-lives. What mass remains?
- FoundationOnly 1/64 of a sample remains and the half-life is 2.5 hours. How many hours have passed?
- IntermediateA nuclide has a half-life of 30 minutes. What fraction is undecayed after 2.5 hours?
- IntermediateA sample has passed through 3 half-lives. What percentage has decayed?
- IntermediateThe activity of a sample falls from 8000 Bq to 500 Bq and the half-life is 5.5 hours. How many hours does this take?
- ChallengeCarbon-14 has a half-life of 5730 years. An ancient sample retains 25% of its original carbon-14. How old is it?
- ChallengeA nuclide has a half-life of 1600 years and 12.5% of a sample remains. How many years have passed?
- ChallengeSamples A and B of the same nuclide started with equal activity and the half-life is 4 days. A now reads 400 Bq and B reads 50 Bq. How many days earlier did B start decaying?
- Error redoA student argues that because activity halves each half-life, it must be one third after three half-lives. What is the correct fraction?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 1000 / 2 / 2 / 2 = 125 Bq. | Three half-lives means dividing by 8, not dividing by 3. |
| 2 | 800 / 16 = 50 g. | Four half-lives mean four halvings, that is dividing by two to the power four. |
| 3 | 1/64 = (1/2)^6, which is 6 half-lives, so 2.5 x 6 = 15 hours. | Sixty-four is two to the power six, so six half-lives have passed. |
| 4 | 2.5 hours = 150 minutes = 5 half-lives, so (1/2)^5 = 1/32 = 0.0312. | Convert the time into the same unit as the half-life before dividing. |
| 5 | (1/2)^3 = 1/8 is left, so the decayed fraction is 1 – 1/8 = 7/8 = 87.5%. | The question asks for the decayed part, not what remains; one eighth is only the remainder. |
| 6 | 8000 / 500 = 16 = 2^4, which is 4 half-lives, so 5.5 x 4 = 22 hours. | Find the drop factor 16 first, turn it into 4 half-lives, then multiply by the half-life. |
| 7 | 25% = 1/4 = (1/2)^2, which is 2 half-lives, so 5730 x 2 = 11460 years. | Turn the percentage into the fraction 1/4 to see that only two halvings have occurred. |
| 8 | 12.5% = 1/8 = (1/2)^3, which is 3 half-lives, so 1600 x 3 = 4800 years. | Twelve and a half per cent is one eighth, which means three halvings, not eight. |
| 9 | 400 / 50 = 8 = 2^3, so B has gone through 3 more half-lives; 4 x 3 = 12 days. | Lower activity means a longer decay time; a factor of 8 means three half-lives, not eight. |
| 10 | The correct value is (1/2)^3 = 1/8 = 0.125, that is 12.5%. Saying one third mistakes three halvings for three equal shares. | Repeated halving is multiplication by one half three times, not splitting the original into three parts. |
04 What to do after marking
- After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
- Repeat the same item two days later; move to the next paper only when both attempts are correct.
- Parents only need the answer and note columns; there is no need to explain every item.
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