IGCSE · 5 · extended response
A half-life hidden by background counts
Nuclear physics · Original GioPhysics question with a detailed, mark-by-mark answer guide.
- Demand
- discriminating
- Marks
- 6
- Topics
- 1
- Answer
- Complete
Raw detector counts
Supplied question data. Read the labelled axes and use the observations to test the physical model.
Vertical axis (y): Counts per window
Horizontal axis (x): Time / min
Read the exact data as a table
| Time / min | Counts per window |
|---|---|
| 0 | 360 |
| 5 | 200 |
| 10 | 120 |
| 15 | 80 |
| 20 | 60 |
These are the supplied values, not a worked answer. No fitted trend is drawn.
Optional enrichment: this challenge may extend beyond the usual syllabus depth and assumes confidence with algebra and graph interpretation. A detector counts the same sealed radioactive source in consecutive equal-duration measurement windows at the supplied times. Background measured without the source is 40 counts per window. Geometry and detector efficiency are fixed. Assume one radionuclide dominates and counting windows are short compared with its half-life. Supplied data (Time / min; Counts per window): (0, 360), (5, 200), (10, 120), (15, 80), (20, 60).
- (a)
Correct for background, infer half-life and predict the raw count after 30 min.
3 marks - (b)
Evaluate the inference that the source is harmless when raw counts approach background, and explain how to improve confidence in a weak signal.
3 marks
Ready to self-mark?Reveal the detailed answer guide
(a)
Correct for background, infer half-life and predict the raw count after 30 min.
Build a chain of claim, evidence and physics reasoning. Address more than one relevant factor, identify a limitation or assumption, and finish with a conclusion that is conditional on the evidence rather than absolute.
- 1
Subtract 40 from each raw reading before analysing source decay. The corrected signal halves every 5 min.
- 2
At 30 min six half-lives have elapsed, giving expected net counts 320/2⁶ = 5.
- 3
The detector still records background, so expected raw counts are 5+40 = 45. A real individual reading will fluctuate randomly about this expectation.
(b)
Evaluate the inference that the source is harmless when raw counts approach background, and explain how to improve confidence in a weak signal.
Build a chain of claim, evidence and physics reasoning. Address more than one relevant factor, identify a limitation or assumption, and finish with a conclusion that is conditional on the evidence rather than absolute.
- 1
Activity describes decays per second, while counts depend on detector efficiency, radiation type, shielding and geometry. The source can remain active when this setup cannot clearly distinguish it from background.
- 2
Longer matched source and background counting periods reduce relative random uncertainty, while repeated readings reveal scatter. Keep distance and shielding fixed for a fair decay comparison.
- 3
Risk also depends on exposure time, energy, biological uptake and contamination pathways. Use the relevant handling controls rather than inferring safety from one low count.
Complete marking guidance
Use these worked steps alongside the part-by-part answers. They explain the method and mark allocation; they do not add extra marks.
- Subtract 40 from each raw reading before analysing source decay. The corrected signal halves every 5 min.
- At 30 min six half-lives have elapsed, giving expected net counts 320/2⁶ = 5.
- The detector still records background, so expected raw counts are 5+40 = 45. A real individual reading will fluctuate randomly about this expectation.
- Activity describes decays per second, while counts depend on detector efficiency, radiation type, shielding and geometry. The source can remain active when this setup cannot clearly distinguish it from background.
- Longer matched source and background counting periods reduce relative random uncertainty, while repeated readings reveal scatter. Keep distance and shielding fixed for a fair decay comparison.
- Risk also depends on exposure time, energy, biological uptake and contamination pathways. Use the relevant handling controls rather than inferring safety from one low count.
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