AQA A-Level Physics Paper 1, June 2025: Question 27

1 mark · Medium difficulty · Multiple Choice

Calculate the de Broglie wavelength of an alpha particle travelling at a speed of 4.5 × 10⁵ m s⁻¹.

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Question

Question 27 asks: An alpha particle has a speed of 4.5 × 10⁵ m s⁻¹. What is the de Broglie wavelength of the alpha particle? Four options are given: A is 2.2 × 10⁻¹³ m, B is 4.4 × 10⁻¹³ m, C is 8.8 × 10⁻¹³ m, and D is 3.9 × 10⁻¹² m.
Question text

27 An alpha particle has a speed of 4.5 × 105 m s−1.

What is the de Broglie wavelength of the alpha particle?

[1 mark]

A 2.2 × 10−13 m

B 4.4 × 10−13 m

C 8.8 × 10−13 m

D 3.9 × 10−12 m

Mark scheme

Show the mark scheme Mark scheme for question 27 showing key 'A', corresponding value 2.2 × 10⁻¹³ m, with assessment objective AO1.

27 A 2.2 × 10−13 m AO1

How to answer it

de Broglie Wavelength of an Alpha Particle

📌 What this question tests

This question evaluates your ability to apply the de Broglie wavelength relationship to composite particles (matter waves). Specifically, it assesses:

  • Recalling and applying the de Broglie equation: λ = h / p = h / (mv)
  • Knowing the composition and calculating the rest mass of an alpha particle (2 protons + 2 neutrons, or 4 atomic mass units / nucleons)
  • Correctly handling fundamental physical constants from the AQA formula sheet (Planck constant h and nucleon mass / atomic mass unit u )
  • Accurate standard form calculation and selection of significant figures
Multiple Choice • Question 27 • 1 Mark

Question Walkthrough & Analysis

AQA Physics A-Level • Section A / Particles and Radiation

✅ Correct Answer

A (2.2 × 10⁻¹³ m)

Substituting the mass of an alpha particle ( m ≈ 4 × 1.66 × 10⁻²⁷ kg ) and given velocity into de Broglie's formula gives exactly 2.22 × 10⁻¹³ m , which rounds to 2 s.f. as 2.2 × 10⁻¹³ m.

💡 Key Knowledge

  • Alpha Particle (α): Helium-4 nucleus ( ⁴₂He ), consisting of 2 protons and 2 neutrons ( 4 nucleons).
  • Mass of α-particle:
    m ≈ 4 × 1.66 × 10⁻²⁷ kg = 6.64 × 10⁻²⁷ kg (or 6.646 × 10⁻²⁷ kg using individual nucleon masses).
  • Planck Constant:
    h = 6.63 × 10⁻³⁴ J s
  • Formula:
    λ = h / (m × v)

📐 Step-by-Step Calculation

  1. Identify values from the question and data booklet:
    • Speed, v = 4.5 × 10⁵ m s⁻¹
    • Planck constant, h = 6.63 × 10⁻³⁴ J s
    • Mass of one nucleon (or atomic mass unit, u ), u = 1.66 × 10⁻²⁷ kg
    • Mass of alpha particle, m = 4 × 1.66 × 10⁻²⁷ kg = 6.64 × 10⁻²⁷ kg
  2. Calculate momentum ( p = mv ):
    p = 6.64 × 10⁻²⁷ kg × (4.5 × 10⁵ m s⁻¹) = 2.988 × 10⁻²¹ kg m s⁻¹
  3. Calculate wavelength ( λ = h / p ):
    λ = (6.63 × 10⁻³⁴) / (2.988 × 10⁻²¹)
    λ = 2.219 × 10⁻¹³ m
  4. Round to 2 significant figures (consistent with given data):
    λ = 2.2 × 10⁻¹³ m → Option A

🧠 Exam Technique & Distractor Elimination

  • Notice the factor of 2 relationships: Look at the distractor choices:
    • B (4.4 × 10⁻¹³) is exactly 2× Option A (using mass of 2 nucleons instead of 4).
    • C (8.8 × 10⁻¹³) is exactly 4× Option A (using mass of 1 proton/neutron instead of 4).
  • Recognising these distractor ratios immediately alerts you that the mass/nucleon number of the particle is the key testing point!

❌ Common Errors & Pitfalls

  • Using proton number instead of mass number: Using m = 2 × 1.66 × 10⁻²⁷ kg gives 4.4 × 10⁻¹³ m (distractor B). Alpha has 2 protons and 2 neutrons.
  • Using a single nucleon mass: Forgetting that an alpha particle is a composite particle gives 8.8 × 10⁻¹³ m (distractor C).
  • Confusing charge with mass: Using the elementary charge value ( 1.60 × 10⁻¹⁹ C ) in place of mass.
Examiner Insight (AO1): This question assesses recall of basic particle properties combined with fundamental equation substitution. Students who memorize that an alpha particle has a nucleon number of 4 and can quickly grab u or mp from the formula sheet solve this question in under 45 seconds.

Topics

Physics · 3.2 Particles and radiation

Question and mark scheme from the AQA A-Level Physics examination, Paper 1, June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.