A-Level · Physics · AQA · Mark scheme decoded
AQA A-Level Physics: de Broglie’s Hypothesis and Electron Diffraction — mark scheme explained
The short answer
De Broglie's hypothesis is a fundamental concept in quantum mechanics that suggests particles can exhibit wave-like properties. This idea was proposed by Louis de Broglie in 1924 and has significant implications for understanding the behavior of electrons, particularly in low-energy electron diffraction experiments.
The question
An electron is accelerated through a potential difference of 50 V. Calculate its de Broglie wavelength.
[Paraphrased for study — not reproduced from any exam paper.]
Mark scheme, decoded
How the examiner actually awards the marks on this topic.
Gradora's own decode of the marking approach — not the exam board's published mark scheme.
How marks are awarded
For derivation questions, show all steps clearly. For calculation questions, include units and check for consistency. For explanation questions, provide a detailed and coherent answer that addresses all aspects of the question.
What the command words demand
- Derive
- Show how to obtain a formula or result from given information.
- Explain
- Provide a clear and detailed account of a concept or phenomenon.
- Calculate
- Perform numerical calculations using appropriate equations.
- Interpret
- Analyze and explain the meaning of experimental results.
Model answer
A full-mark response to the question above, worked through step by step.
Timing: Allocate about 5-7 minutes per question to ensure you have enough time to derive equations, perform calculations, and write explanations.
- 1. Use the equation E k = eV to find the kinetic energy of the electron: E k = (1.602 × 10 -19 C) × 50 V = 8.01 × 10 -18 J.1 mark
- 2. Use the kinetic energy to find the momentum: E k = 1/2 mv 2 , so v = √(2E k /m) = √((2 × 8.01 × 10 -18 J) / (9.109 × 10 -31 kg)) ≈ 4.19 × 10 6 m/s.2 marks
- 3. Calculate the momentum: p = mv = (9.109 × 10 -31 kg) × (4.19 × 10 6 m/s) ≈ 3.82 × 10 -24 kg·m/s.1 mark
- 4. Use the de Broglie wavelength equation: λ = h / p = (6.626 × 10 -34 Js) / (3.82 × 10 -24 kg·m/s) ≈ 1.73 × 10 -10 m.2 marks
Final answer: 1.73 × 10 -10 m
Work through every step correctly and you earn all 6 marks.
Another worked example
An electron has a de Broglie wavelength of 2.5 × 10 -10 m. Calculate the kinetic energy of the electron.
- 1. Use the de Broglie wavelength equation to find the momentum: p = h / λ = (6.626 × 10 -34 Js) / (2.5 × 10 -10 m) ≈ 2.65 × 10 -24 kg·m/s.2 marks
- 2. Use the momentum to find the velocity: p = mv, so v = p / m = (2.65 × 10 -24 kg·m/s) / (9.109 × 10 -31 kg) ≈ 2.91 × 10 6 m/s.1 mark
- 3. Calculate the kinetic energy: E k = 1/2 mv 2 = 1/2 (9.109 × 10 -31 kg) × (2.91 × 10 6 m/s) 2 ≈ 3.87 × 10 -18 J.2 marks
Final answer: 3.87 × 10 -18 J
Work through every step correctly and you earn all 5 marks.
Common mistakes
Confusing the de Broglie wavelength equation with other equations, such as the kinetic energy equation.
Why it happens: Students may mix up different equations and use them incorrectly in calculations.
Fix: Practice deriving and using the de Broglie wavelength equation to reinforce its application.
Forgetting to convert units, especially when dealing with Planck's constant and electron charge.
Why it happens: Unit conversion is a common oversight that can lead to incorrect answers.
Fix: Always check the units of all constants and variables before performing calculations.
Misinterpreting the effect of increasing electron speed on the diffraction pattern.
Why it happens: Students may not fully understand the inverse relationship between wavelength and speed.
Fix: Visualize the relationship using graphs or diagrams to reinforce the concept.
Using the wrong value for the mass of an electron.
Why it happens: Students may use incorrect values from memory or reference materials.
Fix: Memorize the correct value (9.109 × 10 -31 kg) and double-check it during calculations.
Failing to explain the physical significance of the diffraction pattern in low-energy electron diffraction experiments.
Why it happens: Students may focus on the mathematical aspects without understanding the practical implications.
Fix: Practice explaining the physical meaning of experimental results and their importance in materials science.
Incorrectly applying the kinetic energy equation to find velocity or momentum.
Why it happens: Students may make algebraic errors when rearranging equations.
Fix: Practice solving for different variables in the kinetic energy equation and double-check each step.
Where the marks go
The question types you’ll meet on this topic and the marks each one carries — so you know what to expect and where to focus.
| Question type | What you’re asked to do | Marks |
|---|---|---|
| Calculate De Broglie Wavelength | Find an accelerated electron's wavelength by linking energy, momentum and the de Broglie relation. | 6 |
| Calculate Kinetic Energy | Find an electron's kinetic energy from its de Broglie wavelength using momentum. | 5 |
| Calculate Electron Mass | Combine the de Broglie and kinetic energy equations to find the electron's mass. | 6 |
| Calculate Kinetic Energy | Use the de Broglie wavelength to find the kinetic energy of accelerated electrons. | 5 |
| Total across these question types | 22 | |
Question types and mark tariffs are Gradora’s guidance based on how this topic is typically examined — not the board’s official paper structure.