Data on the activity of a radioactive sample are collected over time.
| Time / hours |
Activity / Bq |
| 0 |
800 |
| 2 |
560 |
| 4 |
400 |
| 6 |
280 |
| 8 |
200 |
| 10 |
140 |
(a) (i) Define *half-life*. [1]
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(ii) Estimate the half-life of the sample from the data. [2]
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(b) Calculate the decay constant *λ* for this sample. [2]
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(c) Another sample of a different radioactive nuclide has the same initial activity but a shorter half-life. Sketch, on the axes below, the variation of activity with time for this second sample. The original data curve is shown as a dashed line for reference. [2]
[VISUALIZATION: A graph grid with Time / hours on the x-axis (0 to 10) and Activity / Bq on the y-axis (0 to 800). The original data points/curve from the table are shown as a dashed line.]
Question
(i) Define *half-life*. [1]
Hint
Hint
Hint
Think about how the amount or activity of a radioactive substance changes over time.
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Answer
Answer
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Explanation
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Complete Answer
The time taken for the activity (or number of undecayed nuclei) of a radioactive sample to decrease by half / fall to 50% of its initial value.
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Question
(ii) Estimate the half-life of the sample from the data. [2]
Hint
Hint
Hint
Look at the initial activity in the table. Find half of this value. Then find the time corresponding to this halved activity in the table.
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Answer
Answer
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Explanation
Explanation
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Question
(b) Calculate the decay constant *λ* for this sample. [2]
Hint
Hint
Hint
Use the formula that relates the decay constant (λ) to the half-life (T_1/2). You found T_1/2 in part (a)(ii).
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Answer
Answer
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Explanation
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Complete Answer
\(\lambda \approx 0.17 \text{ hour}^{-1}\) (or \(4.8 \times 10^{-5} \text{ s}^{-1}\))
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Question
(c) Another sample of a different radioactive nuclide has the same initial activity but a shorter half-life. Sketch, on the axes below, the variation of activity with time for this second sample. The original data curve is shown as a dashed line for reference. [2]
[VISUALIZATION: A graph grid with Time / hours on the x-axis (0 to 10) and Activity / Bq on the y-axis (0 to 800). The original data points/curve from the table are shown as a dashed line.]
Hint
Hint
Hint
The new sample starts with the same activity (800 Bq). A shorter half-life means it decays faster than the original sample. Draw a curve that reflects this.
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Answer
Answer
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Mark Scheme
Mark Scheme
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Explanation
Explanation
Complete Answer
Sketch shows a curve starting at (0, 800 Bq), decaying exponentially, and consistently below the original dashed curve.
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Mark Scheme
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Answer Explanation
Answer Explanation
