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S6 Physics: Radioactivity and Half-life – Practice Paper 3 (Challenge, 10 Questions)
S6 Physics: Radioactivity and Half-life – Practice Paper 3 (Challenge, 10 Questions)
Paper three works with the decay constant and fractional half-lives: finding the decay constant from the half-life and back, treating a fractional number of half-lives with an exponent, rounding up for the shortest time, and sharing mass between parent and daughter.
Quick answer Answers: 0.0866 per day, 13.9 years, 10 half-lives, 0.3536, 200 minutes, 150 Bq, 60 g, 84 g, 1 to 4, and activity depending on both the decay constant and the number of nuclei.
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 | Challenge |
02 Questions (10 items)
- FoundationA nuclide has a half-life of 8 days. Find its decay constant in per day, to four decimal places.
- FoundationA nuclide has a decay constant of 0.05 per year. Find its half-life in years, to one decimal place.
- FoundationOnly 1/1024 of a sample remains. How many half-lives have passed?
- IntermediateA sample has passed through 1.5 half-lives. What fraction is undecayed, to four decimal places?
- IntermediateA nuclide has a half-life of 20 minutes. How many minutes at least are needed for the activity to fall to one thousandth?
- IntermediateA sample starts at 2400 Bq with a half-life of 12 hours. What is its activity after 48 hours?
- ChallengeNuclide A has a half-life of 5 days and decays into stable B. Starting from 80 g of pure A, what mass of B is present after 10 days, assuming all decay products stay in the sample?
- ChallengeStarting from 96 g of pure A with a half-life of 6 days decaying into stable B, what mass of B is present after 18 days?
- ChallengeX has a half-life of 8 years and Y has 24 years, with equal initial activity. What is the ratio of the activity of X to that of Y after 24 years?
- Error redoA student claims that a nuclide with a shorter half-life must always have lower activity. Is this correct?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | Decay constant = ln 2 / half-life = 0.693 / 8 = 0.0866 per day. | The decay constant is inversely proportional to the half-life: the longer the half-life, the smaller the constant. |
| 2 | Half-life = ln 2 / 0.05 = 0.693 / 0.05 = 13.9 years. | Rearranging the same relation lets you recover the half-life from the decay constant. |
| 3 | 1024 = 2^10, so 10 half-lives have passed. | Write the denominator as a power of two; the exponent is the number of half-lives. |
| 4 | (0.5)^1.5 = 0.3536, about 35.4%. | The number of half-lives can be fractional; use an exponent instead of adding partial halvings. |
| 5 | 2^n = 1000 gives n = 9.97, so round up to 10 half-lives; 20 x 10 = 200 minutes. | Round the number of half-lives up, because a partial half-life does not yet reach the target. |
| 6 | 48 / 12 = 4 half-lives, so 2400 / 16 = 150 Bq. | Four half-lives means dividing by 16, not by 4. |
| 7 | 10 / 5 = 2 half-lives, so 20 g of A is left and the mass of B is 80 – 20 = 60 g. | The mass lost by the parent becomes the mass of the daughter, so the two always add up to the original mass. |
| 8 | 18 / 6 = 3 half-lives, so 12 g of A remains and B accounts for 96 – 12 = 84 g. | Find the remaining parent mass first, then subtract it from the original to get the daughter mass. |
| 9 | X passes 3 half-lives and keeps 1/8, Y passes 1 half-life and keeps 1/2, so the ratio is (1/8) / (1/2) = 1 to 4. | Count the half-lives of each nuclide separately, then divide to get the ratio. |
| 10 | No. Activity equals the decay constant times the number of nuclei, so both factors matter; a short half-life with far more nuclei can give higher activity. | A short half-life only means each nucleus decays faster; without knowing the number of nuclei you cannot compare activities. |
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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