This set covers the whole topic: subtracting background, reading half-life from a graph, successive halving, randomness and model versus risk advice. All data are invented for practice.
Work through the questions in order, from easier to harder. Write the units every time, then open the answer.
The mistake log and retest queue is a good place to record what you got wrong. This set belongs to half-life and background.
Questions
Q1. With no source present, a detector records 48 counts in 12 minutes. What is the background count rate?
Show answer
Rate = counts ÷ time = 48 ÷ 12 = 4 counts/min.
Q2. With a source near it, the same detector records 372 counts in 3 minutes. The background rate is 4 counts/min. What is the corrected count rate from the source?
Show answer
Background in 3 min = 4 × 3 = 12 counts. Corrected total = 372 − 12 = 360 counts. Corrected rate = 360 ÷ 3 = 120 counts/min.
Q3. State what is meant by the half-life of a radioactive isotope.
Show answer
The half-life is the time taken for the count rate (or the number of undecayed nuclei) of a sample to fall to half of its starting value. It is also the time for half the nuclei present to decay.
Q4. A sample has 80 g of an isotope with a half-life of 5 hours. How much remains after 15 hours?
Show answer
15 ÷ 5 = 3 half-lives. 80 → 40 → 20 → 10. 10 g remains.
Q5. The corrected count rate from a source is recorded in a table.
| Time (h) | 0 | 2 | 4 | 6 |
|---|---|---|---|---|
| Corrected rate (counts/min) | 640 | 320 | 160 | 80 |
(a) Find the half-life. (b) Predict the corrected rate at 10 h.
Show answer
(a) 640 halves to 320 in 2 h, then to 160 in a further 2 h, so the half-life is 2 h.
(b) 10 ÷ 2 = 5 half-lives. 640 → 320 → 160 → 80 → 40 → 20. The rate is 20 counts/min.
Q6. The background is 10 counts/min. A detector records a source at 0, 5 and 10 minutes with measured rates 130, 70 and 40 counts/min. (a) Find the corrected rates and the half-life. (b) What measured rate would the detector show at 20 minutes?
Show answer
(a) Corrected: 120, 60, 30 counts/min. Each is half the last, with 5 min between, so the half-life is 5 min.
(b) 20 min is 4 half-lives: 120 → 60 → 30 → 15 → 7.5 counts/min. Add the background back: 7.5 + 10 = 17.5 counts/min.
Q7. An isotope has a half-life of 12 days. What fraction of it is left after 36 days, and what percentage has decayed?
Show answer
36 ÷ 12 = 3 half-lives. Fraction left = (½)³ = 1/8 (12.5%). Decayed = 7/8 = 87.5%.
Q8. A corrected count rate falls from 2400 counts/min to 75 counts/min in 35 minutes. What is the half-life?
Show answer
2400 → 1200 → 600 → 300 → 150 → 75 is 5 halvings. Half-life = 35 ÷ 5 = 7 min.
Q9. A student says: “The half-life is 10 minutes, so this atom will decay at exactly 10 minutes, and after 20 minutes all the atoms will be gone.” Give two corrections.
Show answer
First, decay is random, so the half-life cannot say when one atom decays. Each atom has a 50% chance of decaying in 10 minutes. Second, after 20 minutes (two half-lives) one quarter of the nuclei remain, not none.
Q10. A source is counted for 60 s five times, giving 204, 197, 215, 190 and 209 counts. (a) Find the mean. (b) A classmate says the counter must be faulty because the numbers differ. Respond.
Show answer
(a) 204 + 197 + 215 + 190 + 209 = 1015, and 1015 ÷ 5 = 203 counts per 60 s.
(b) Decay is random, so counts in equal intervals vary around an average, even with nothing changed. The variation is expected and does not show a fault.
Q11. A source has an activity of 640 kBq and a half-life of 2 days. (a) Find the activity after 10 days. (b) A student says, “So it is safe after 10 days.” Evaluate that statement.
Show answer
(a) 10 ÷ 2 = 5 half-lives. 640 → 320 → 160 → 80 → 40 → 20. The activity is 20 kBq.
(b) The calculation shows the activity falls to 1/32 in this model. It does not show dose or safety, which depend on the radiation type, time, distance and shielding. A qualified person should judge safety.
If you got these wrong
| Where the error was | What it usually means | Go to |
|---|---|---|
| Q1, Q2, Q6(a) | Background found or subtracted over the wrong time | Subtract background from supplied counts |
| Q3, Q5(a), Q6(a) | Half-life read from the wrong axis or as a value, not a time | Determine half-life from a decay graph |
| Q4, Q5(b), Q6(b), Q7, Q8, Q11(a) | Halvings counted or repeated incorrectly | Apply successive halving to a stated interval |
| Q9, Q10 | Treating decay as a timer or ignoring randomness | Explain why one atom has no predictable decay time |
| Q11(b), Q9 (second part) | Turning a calculation into a safety statement | Distinguish a model calculation from personal radiation-risk advice |
Keep the question numbers you missed, redo them a few days later with changed numbers, and log the pattern. If the same type returns, our teachers can work on it with you in online one-to-one Physics tuition.