AQA A-Level Physics Paper 1, June 2022: Question 10

✅ Correct Answer

Option A: 4.4 × 10⁷ C kg⁻¹

💡 Key Knowledge

• Definition: Specific charge is the charge-to-mass ratio, given by the formula:
  Specific Charge = Total Charge / Total Mass
• Nucleus properties: For a nucleus of ¹³₆C , the proton number is 6 and the nucleon number is 13 .
• Constants needed: Elementary charge e = 1.60 × 10⁻¹⁹ C and the unified atomic mass unit u = 1.66 × 10⁻²⁷ kg . (Mass of electrons in the atom's shell are ignored since it is a *nucleus*).

📐 Step-by-Step Calculation

1. Calculate total charge (Q):
   Q = 6 × 1.60 × 10⁻¹⁹ C = 9.60 × 10⁻¹⁹ C
2. Calculate total mass (m):
   m = 13 × 1.66 × 10⁻²⁷ kg = 2.158 × 10⁻²⁶ kg
3. Divide charge by mass:
   (9.60 × 10⁻¹⁹) / (2.158 × 10⁻²⁶) = 4.448 × 10⁷ C kg⁻¹
4. Round to appropriate sig figs:
   4.4 × 10⁷ C kg⁻¹

❌ Common Errors & Exam Technique

• Using nucleon number instead of proton number for charge: Students sometimes multiply the nucleon number (13) by e instead of the proton number (6), leading to incorrect answers like Option D ( 2.1 × 10⁸ C kg⁻¹ ). Remember: neutrons have zero charge!
• Including electron mass: The question asks for a nucleus, not a neutral atom. Do not add or subtract electron masses.
• Exam Technique: In multiple-choice calculations, always do a quick mental or rough-paper estimation to rule out absurd orders of magnitude before committing to full calculator steps.