AQA AS Level Physics Paper 2, June 2024: Question 17

1 mark · Medium difficulty · Multiple Choice

Calculate the de Broglie wavelength of a positron travelling at 5% of the speed of light.

Practise this question

Question

Multiple choice question 17 asking for the de Broglie wavelength of a positron travelling at 5% of the speed of light, with four options A, B, C, and D ranging from 2.7 x 10^-16 m to 4.9 x 10^-11 m.
Question text

17 What is the de Broglie wavelength of a positron travelling at 5% of the speed of light?

[1 mark]

A 2.7 × 10−16 m

B 2.7 × 10−14 m

C 4.9 × 10−13 m

D 4.9 × 10−11 m

Mark scheme

Show the mark scheme Mark scheme for question 17 indicating the correct answer is D, corresponding to a value of 4.9 x 10^-11 m.

17 D 4.9 × 10−11 m

How to answer it

Calculating the De Broglie Wavelength of a High-Speed Positron

Question 17 [1 mark]

What this question tests

This question assesses your ability to recall and apply the de Broglie wavelength equation, handle particle properties (specifically the mass of a positron/electron from the data booklet), and correctly perform unit conversions involving percentages and the speed of light.

Question Breakdown

✅ Correct Answer

Option D: 4.9 × 10⁻¹¹ m

Awarded for selecting option D based on correct application of the de Broglie formula.

💡 Key Knowledge

  • The de Broglie equation is λ = h / (m v) .
  • A positron has the exact same rest mass as an electron: m = 9.11 × 10⁻³¹ kg (found in your AQA data booklet).
  • The speed of light in a vacuum is c = 3.00 × 10⁸ m s⁻¹ .

🧠 Exam Technique

In multiple-choice calculations, do not clear your calculator intermediate steps. Keep full precision until the final rounding stage to avoid rounding errors matching distractor options.

❌ Common Errors

  • Forgetting to convert 5% into a decimal (using 5 instead of 0.05).
  • Confusing a positron with a proton and using the wrong mass ( 1.67 × 10⁻²⁷ kg ), which leads to drastically incorrect powers of ten.
  • Failing to multiply c by 0.05 correctly.

📐 Step-by-Step Calculation

  1. Identify the parameters:
    Planck constant ( h ) = 6.63 × 10⁻³⁴ J s (or Js⁻¹)
    Mass of positron ( m ) = 9.11 × 10⁻³¹ kg
    Velocity ( v ) = 5% of c = 0.05 × 3.00 × 10⁸ m s⁻¹ = 1.50 × 10⁷ m s⁻¹
  2. Substitute values into the de Broglie equation:
    λ = (6.63 × 10⁻³⁴) / ((9.11 × 10⁻³¹) × (1.50 × 10⁷))
  3. Evaluate the denominator:
    Denominator = 1.3665 × 10⁻²³ kg m s⁻¹
  4. Calculate final wavelength:
    λ = 4.85... × 10⁻¹¹ m , which rounds to 4.9 × 10⁻¹¹ m (matching Option D).

Topics

Physics · 3.2 Particles and radiation

Question and mark scheme from the AQA AS Level Physics examination, Paper 2, June 2024. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.