AQA A-Level Physics Paper 2, June 2023: Question 25

What This Question Tests

This question assesses your understanding of nuclear fission waste management and the link between half-life and the decay constant (λ):

The penetrating power of different types of ionising radiation (α vs γ).
Why high-level waste (HLW) presents long-term hazards requiring deep geological repository storage.
The mathematical relationship T½ = ln(2) / λ , specifically recognizing that long-lived isotopes possess small decay constants.

D: gamma radiation from nuclides with a small decay constant.

Mark Scheme: 1 mark for option D.

Penetrating Power: Alpha (α) particles are stopped by paper or dead skin and have a range of only a few centimetres in air. Underground rock shielding is not needed for external alpha shielding; it is required for highly penetrating gamma (γ) rays.
Decay Constant & Half-Life: The decay constant λ is inversely proportional to half-life:
λ = ln(2) / T½
Long-Term Hazard: Short-lived isotopes (large λ) decay rapidly while the waste sits in cooling ponds (months to years). The isotopes that persist for thousands of years in deep underground storage have very long half-lives, which means they have a small decay constant (λ).

Step 1: Determine the type of radiation (Alpha vs Gamma)
Alpha radiation cannot penetrate standard container walls (or even a sheet of paper or human skin). To protect workers from external radiation through heavy rock strata or deep caverns, the concern is high-energy, highly penetrating gamma radiation. This eliminates options A and B.
Step 2: Relate storage timeframe to decay constant
By the time spent fuel leaves the initial cooling ponds, isotopes with high activity and short half-lives have already decayed. The waste placed in underground caves remains dangerous for hundreds to thousands of years.
Step 3: Connect long half-life to decay constant magnitude
Because λ = 0.693 / T½ , an extremely long half-life corresponds to an exceptionally small decay constant.
Conclusion:
Protection is needed against gamma radiation from isotopes with a small decay constant (Option D).

Divide and Conquer: Split 2×2 multiple choice questions into two independent halves:
1. Alpha vs Gamma? → Choose Gamma.
2. Large λ vs Small λ? → Choose Small λ.
Contextual Clue: Look at the timeline: "cooling pond" → handles the intense heat and decay of nuclides with large λ (short half-life). "Underground caves" → long-term isolation for nuclides with small λ (long half-life).

Confusing λ with half-life: Students often intuitively associate "small decay constant" with "small danger" or "short time", forgetting that a smaller decay constant means a longer half-life.
Selecting Option C: Choosing large decay constant because they believe high initial activity is the reason for permanent repository storage, ignoring that nuclides with large λ burn out very quickly in the pond stage.
Focusing on Alpha toxicity: While alpha emitters (like plutonium) are dangerous if ingested/inhaled, underground rock provides external shielding against penetrating gamma emitters.

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