IB · E · extended response
A shielding decision needs more than a half-life
Nuclear and quantum physics · Original GioPhysics question with a detailed, mark-by-mark answer guide.
- Demand
- discriminating
- Marks
- 6
- Topics
- 1
- Answer
- Complete
Remaining activity fraction
Supplied question data. Read the labelled axes and use the observations to test the physical model.
Vertical axis (y): Activity / initial activity
Horizontal axis (x): Elapsed half-lives
Read the exact data as a table
| Elapsed half-lives | Activity / initial activity |
|---|---|
| 0 | 1 |
| 1 | 0.5 |
| 2 | 0.25 |
| 3 | 0.125 |
| 4 | 0.0625 |
These are the supplied values, not a worked answer. Lines join the supplied values; they are not a fitted model.
Two sealed waste samples each have initial activity 800 Bq. Sample A has half-life 2 days and sample B 20 years. Their activity fractions after successive half-lives are supplied. For a simplified external gamma-shielding estimate, each 1 cm of a material halves transmitted intensity. This model ignores buildup and other radiation types. Supplied data (Elapsed half-lives; Activity / initial activity): (0, 1), (1, 0.5), (2, 0.25), (3, 0.125), (4, 0.0625).
- (a)
Find each sample's activity after 8 days or 80 years respectively and the ideal shielding thickness for a 1/32 intensity factor.
3 marks - (b)
Evaluate the claim that equal activity means equal risk, and propose a defensible waste-management comparison.
3 marks
Ready to self-mark?Reveal the detailed answer guide
(a)
Find each sample's activity after 8 days or 80 years respectively and the ideal shielding thickness for a 1/32 intensity factor.
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
Eight days is four half-lives for A; 80 years is four for B. Each activity becomes 800/2⁴ = 50 Bq, despite very different calendar times.
- 2
A transmission factor 1/32 is (1/2)⁵, so five 1 cm layers are needed in the simplified shielding model.
- 3
Decay storage and shielding reduce different aspects of exposure: elapsed time reduces activity, while shielding reduces radiation reaching a location without changing the decay rate.
(b)
Evaluate the claim that equal activity means equal risk, and propose a defensible waste-management comparison.
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
A becquerel is one decay per second, not a unit of absorbed or biologically weighted dose. Decay energy, radiation type and uptake can differ.
- 2
A long-lived sample may need containment for far longer, while a short-lived sample can have intense early emission. Daughter products can complicate both histories.
- 3
Compare measured dose rates under specified geometry, containment integrity, transport and storage requirements, and credible contamination pathways. The simple half-value model alone cannot certify a storage design.
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.
- Eight days is four half-lives for A; 80 years is four for B. Each activity becomes 800/2⁴ = 50 Bq, despite very different calendar times.
- A transmission factor 1/32 is (1/2)⁵, so five 1 cm layers are needed in the simplified shielding model.
- Decay storage and shielding reduce different aspects of exposure: elapsed time reduces activity, while shielding reduces radiation reaching a location without changing the decay rate.
- A becquerel is one decay per second, not a unit of absorbed or biologically weighted dose. Decay energy, radiation type and uptake can differ.
- A long-lived sample may need containment for far longer, while a short-lived sample can have intense early emission. Daughter products can complicate both histories.
- Compare measured dose rates under specified geometry, containment integrity, transport and storage requirements, and credible contamination pathways. The simple half-value model alone cannot certify a storage design.
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