AQA A-Level Physics Paper 2, June 2023: Question 31

Nuclear Reactor Power from Mass Defect Rate

📌 What this question tests

This multiple-choice question assesses your ability to link Einstein's mass-energy relation to power and execute fundamental SI unit conversions:

Mass-Energy Equivalence: Applying ΔE = Δm c² in the context of nuclear fission.
Definition of Power: Relating energy rate to power via P = ΔE / Δt (where 1 W = 1 J s⁻¹ ).
Unit Conversion: Converting time from hours to SI base units (seconds).

Question 31

Calculation of Energy Transfer Rate (Power Output)

Multiple Choice • 1 Mark

✅ Correct Answer

B — 1.0 × 10⁸ W

The rate of decrease of mass converts to power by multiplying the mass loss per second by the speed of light squared ( c² ).

Mark Scheme Breakdown:
• 1 mark for selecting option B.

💡 Key Knowledge

Einstein's Equation: ΔE = Δm c² , where c = 3.00 × 10⁸ m s⁻¹ .
Power Definition: Power is the rate of energy transfer:
P = ΔE / Δt = (Δm / Δt) × c²
SI Units: Power in Watts ( W ) is strictly in Joules per second ( J s⁻¹ ). Therefore, the mass rate must be in kg s⁻¹ , not kg per hour .

📐 Step-by-Step Calculation

1 Identify Given Quantities and Units:
Mass decrease rate: Δm / Δt = 4.0 × 10⁻⁶ kg h⁻¹
Speed of light: c = 3.00 × 10⁸ m s⁻¹ (from the AQA Data Booklet)

2 Convert Mass Deficit Rate to SI Units (kg s⁻¹):
Since 1 hour = 60 × 60 = 3600 s :
Rate (kg s⁻¹) = (4.0 × 10⁻⁶ kg) / 3600 s = 1.111 × 10⁻⁹ kg s⁻¹

3 Calculate Power (Energy per Second):
P = (Δm / Δt) × c²
P = (1.111 × 10⁻⁹ kg s⁻¹) × (3.00 × 10⁸ m s⁻¹)²
P = (1.111 × 10⁻⁹) × (9.00 × 10¹⁶) = 1.0 × 10⁸ W

🧠 Exam Technique

Watch the Denominator: Whenever you see rates expressed "per minute", "per hour", or "per day", underline the time unit immediately. A watt is a Joule per second.
Square the Constant: Don't forget to square c . Remember that (3.00 × 10⁸)² = 9.00 × 10¹⁶ .
Mental Sanity Check: Power stations typically output hundreds of megawatts ( MW = 10⁶ W ) to gigawatts ( GW = 10⁹ W ). An answer of 1.0 × 10⁸ W = 100 MW makes total physical sense.

❌ Common Calculation Traps

Forgetting to divide by 3600: Calculating (4.0 × 10⁻⁶) × (3.00 × 10⁸)² = 3.6 × 10¹¹ J h⁻¹ . Students who then make an arithmetic order-of-magnitude slip often gravitate towards D ( 3.6 × 10¹⁰ W ).
Dividing by 60 instead of 3600: Only converting hours to minutes leads to an answer with an incorrect factor of 60.
Forgetting to square c: Multiplying m directly by c instead of c² leads to meaningless orders of magnitude.

AQA A-Level Physics Paper 2, June 2023: Question 31

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