AQA A-Level Physics Paper 2, June 2025: Question 28

AQA A-Level Physics • Nuclear Physics

Alpha Decay Energy Release & Mass Defect

What this question tests

This question evaluates your ability to apply Einstein's mass-energy equivalence to a radioactive decay reaction. Specifically, it assesses:

Calculating the mass defect (Δm) of an alpha decay reaction from rest masses given in atomic mass units (u).
Converting mass defect in u directly into released kinetic energy in MeV using the data sheet equivalence ( 1 u = 931.5 MeV ).
Understanding conservation of momentum and energy approximations (why negligible recoil speed implies the alpha particle carries essentially all the released kinetic energy).
Spotting metric prefix traps ( meV vs MeV ).

Question 28 Walkthrough

Calculation of Alpha Particle Kinetic Energy

✅ Correct Answer

C — 4.7 MeV

The mass defect is 0.005 u . Multiplying by 931.5 MeV u⁻¹ yields 4.66 MeV ≈ 4.7 MeV .

💡 Key Knowledge

Nuclear Equation: ²¹⁰₈₄Po → ²⁰⁶₈₂Pb + ⁴₂α
Mass-Energy Conversion: On the AQA data sheet, 1 u = 931.5 MeV . You do not need to convert to kg and J first!
Recoil Assumption: Since the daughter lead nucleus is ~51 times heavier than the alpha particle and recoil speed is stated as negligible, virtually 100% of the decay energy goes to the kinetic energy of the alpha particle.

📐 Step-by-Step Calculation

Step 1: Calculate total initial mass (Reactants) Mass of ²¹⁰Po nucleus = 209.983 u

Step 2: Calculate total final mass (Products) Mass of ²⁰⁶Pb + Mass of α = 205.975 u + 4.003 u = 209.978 u

Step 3: Calculate the mass defect (Δm) Δm = Initial Mass − Final Mass
Δm = 209.983 u − 209.978 u = 0.005 u

Step 4: Convert mass defect to energy in MeV Using the data sheet equivalence factor 1 u = 931.5 MeV :
E = Δm × 931.5 MeV u⁻¹
E = 0.005 × 931.5 = 4.6575 MeV
Rounding to 2 significant figures: 4.7 MeV

🧠 Exam Technique & Shortcuts

Use 931.5 MeV: Avoid converting u → kg → J → eV → MeV . That 4-step route wastes 2–3 minutes in a multiple-choice section and introduces rounding errors.
Inspect orders of magnitude: Typical alpha particles emitted from radioactive decays have energies between 4 MeV and 9 MeV . Even without calculation, GeV (option D) is astronomical for alpha decay, and meV (option A) is far too tiny.

❌ Common Traps & Distractors

Prefix Blindness (Option A: 5.0 meV): Lowercase m means milli (10⁻³ eV), while uppercase M means mega (10⁶ eV). A difference of 9 orders of magnitude!
Rough Rounding Error: Rounding 0.005 × 931.5 very crudely as ~5 and picking A without reading the prefix.
Unit Mix-up (Option D: 3.7 GeV): Using speed of light squared ( c² ) incorrectly on values already expressed in mass units.