AQA A-Level Physics Paper 1, June 2024: Question 12

1 mark · Medium difficulty · Multiple Choice

Calculate the ratio of the de Broglie wavelength of an electron to that of a proton when both move with the same speed.

Practise this question

Question

Multiple-choice question 12 asking to find the ratio of the de Broglie wavelength of an electron to that of a proton given they have the same speed. Four options are provided: A 5.5 x 10^-4, B 2.3 x 10^-2, C 42, D 1800.
Question text

12 An electron and a proton move with the same speed.

de Broglie wavelength of electron

What is ?

de Broglie wavelength of proton

[1 mark]

A 5.5 × 10−4

B 2.3 × 10−2

C 42

D 1800

Mark scheme

Show the mark scheme Mark scheme indicating the correct answer is D (1800) under assessment objective AO2.

12 D 1800 AO2

How to answer it

Comparing the de Broglie Wavelengths of an Electron and a Proton

AQA A-Level Physics • Particles and Radiation / Waves

What this question tests

This question assesses your understanding of particle wave-particle duality, specifically the de Broglie wavelength equation ( wavelength = h / mv ). It tests your ability to set up proportionality ratios, recognize constants, and correctly substitute the mass difference between subatomic particles (electrons vs. protons).

Question 1.2

An electron and a proton move with the same speed. What is the ratio of their de Broglie wavelengths?

✅ Correct Answer

D (1800)

The correct option is D because the de Broglie wavelength is inversely proportional to mass when speed is constant. Since a proton is roughly 1800 times more massive than an electron, the electron's wavelength is roughly 1800 times larger.

💡 Key Knowledge

  • The de Broglie equation is wavelength = h / p = h / (mv) .
  • Planck's constant ( h ) and speed ( v ) are constant for both particles in this scenario.
  • Therefore, wavelength is inversely proportional to mass (m) .
  • Mass of a proton is approximately 1.67 × 10⁻²⁷ kg ; mass of an electron is approximately 9.11 × 10⁻³¹ kg .

🧠 Exam Technique

For multiple-choice ratio questions, avoid full calculator inputs if you can use proportional reasoning. Set up an algebraic ratio fraction to see immediately which variable goes in the numerator versus the denominator, preventing inversion errors.

❌ Common Errors

Students frequently invert the ratio (calculating proton-to-electron instead of electron-to-proton), leading to an extremely small decimal value like 5.5 × 10⁻⁴ (Option A), or confuse mass values with charge ratios.

📐 Step-by-Step Calculation

  1. State the formula: wavelength = h / (mv)
  2. Set up the ratio required by the question:
    (wavelength of electron) / (wavelength of proton) = (h / (m_e × v)) / (h / (m_p × v))
  3. Cancel out common terms ( h and v ):
    Ratio = m_p / m_e
  4. Substitute standard particle masses from the data booklet:
    Ratio = (1.67 × 10⁻²⁷ kg) / (9.11 × 10⁻³¹ kg) ≈ 1833 (rounds to 1800 to 2 significant figures matching option D).
Mark Scheme Allocation: [1 mark] — Awarded for selecting option D. AO2 (Application of knowledge).

Topics

Physics · 3.2 Particles and radiation

Question and mark scheme from the AQA A-Level Physics examination, Paper 1, June 2024. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.