AQA A-Level Physics Paper 1, June 2024: Question 8

✅ Correct Answer: C

The correct option is C: the beta-plus decay of a ³⁹₂₀Ca nucleus.

💡 Key Knowledge

• Specific Charge Definition: Specific charge = Charge / Mass. For a nucleus, charge is proportional to proton number ($Z$) and mass is approximately proportional to nucleon number ($A$). Thus, specific charge ≈ Z / A .
• Beta-plus decay change: Proton number decreases by 1 ( Z - 1 ), nucleon number ($A$) stays constant.
• To maximize the specific charge ( Z / A ), you need a nucleus with a high initial ratio that either increases its numerator or, more effectively here, keeps $A$ small while maximizing $Z$.

🧠 Exam Technique

Don't waste time calculating full SI values (in C kg⁻¹) for all four options! Instead, evaluate the ratio Z / A for the resulting nucleus in each option:

• A: ²⁰⁹₈₂Po → Alpha decay loses 2 protons and 4 nucleons ( ²⁰⁵₈₀X ). Ratio: 80 / 205 ≈ 0.390
• B: ²⁸₁₂Mg → Beta-minus gains 1 proton, $A$ constant ( ²⁸₁₃X ). Ratio: 13 / 28 ≈ 0.464
• C: ³⁹₂₀Ca → Beta-plus loses 1 proton, $A$ constant ( ³⁹₁₉X ). Ratio: 19 / 39 ≈ 0.487
• D: ¹⁰⁵₄₇Ag → Electron capture loses 1 proton, $A$ constant ( ¹⁰⁵₄₆X ). Ratio: 46 / 105 ≈ 0.438

❌ Common Errors

• Confusing the change: Forgetting whether beta-plus increases or decreases the proton number. Remember: beta-plus emits a positive positron, so a proton turns into a neutron ( Z decreases by 1).
• Mass number confusion: Assuming alpha decay increases specific charge because it gets rid of heavy mass; while it reduces $A$ by 4, it also strips away 2 protons, drastically lowering the Z / A fraction for heavy nuclei.