AQA AS Level Physics Paper 2, June 2025: Question 6

📋 What this question tests

Wave-particle duality: Using the de Broglie equation λ = h / p = h / (mv) .
Proportional reasoning: Relating momentum and velocity when wavelengths are identical.
Data Booklet retrieval & estimation: Recalling or looking up the rest masses of protons and electrons, then evaluating an order of magnitude calculation without getting bogged down in unnecessary precision.

Question 06 (1 Mark)

D (10³)

Mark Scheme: 1 mark for option D. AO1 (recall and application of fundamental physical constants and relationships).

de Broglie wavelength: λ = h / mv
If two particles have the same wavelength λ , they must have the same momentum:
p_e = p_p ⇒ m_ev_e = m_pv_p
Rearranging for the ratio of speeds gives an inverse mass ratio:
v_e / v_p = m_p / m_e
From the AQA Data Booklet:
- Rest mass of proton, m_p ≈ 1.67 × 10⁻²⁷ kg
- Rest mass of electron, m_e ≈ 9.11 × 10⁻³¹ kg

Equate momenta:
Since λ = h / p and h is constant, equal wavelengths mean equal momenta:
m_e × v_e = m_p × v_p
Set up the required ratio:
The question asks for v_e / v_p :
v_e / v_p = m_p / m_e
Substitute mass values from the Data Booklet:
v_e / v_p = (1.67 × 10⁻²⁷ kg) / (9.11 × 10⁻³¹ kg)
Compute to an order of magnitude:
v_e / v_p ≈ 1833 ≈ 1.83 × 10³
To the nearest power of ten (order of magnitude), this is 10³.

Sanity check your answer: A proton is nearly 2000 times heavier than an electron. For a tiny electron to carry the exact same momentum as a massive proton, it must be travelling far faster! Therefore:
v_e >> v_p ⇒ v_e / v_p > 1
This qualitative check immediately eliminates options A ( 10⁻³ ) and B ( 10⁻² ) in under 5 seconds!
Between 10¹ and 10³ , recall that a proton is ~1800 times heavier than an electron, which points directly to 10³ .

Inverting the ratio (choosing A): Confusing v_e / v_p with m_e / m_p leads directly to ~10⁻³ . Always write down m_ev_e = m_pv_p explicitly.
Forgetting mass difference: Guessing option C ( 10¹ ) by underestimating the vast mass difference between leptons and baryons.
Wasting time with full calculations: Multiple-choice questions are 1 mark each (~1 minute). Do not calculate to 3 significant figures when order-of-magnitude powers of 10 are all that is required.

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