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
What each mark is really for — in plain English — and the wording trap that loses it.
- S1
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.
- S2
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.
- S3
3. Calculate the momentum: p = mv = (9.109 × 10 -31 kg) × (4.19 × 10 6 m/s) ≈ 3.82 × 10 -24 kg·m/s.
- S4
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.
Model answer
Worked through, with each step tagged to the mark it earns.
- S1
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.
- S2
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.
- S3
3. Calculate the momentum: p = mv = (9.109 × 10 -31 kg) × (4.19 × 10 6 m/s) ≈ 3.82 × 10 -24 kg·m/s.
- S4
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.
Final answer: 1.73 × 10 -10 m
Common mistakes
- Confusing the de Broglie wavelength equation with other equations, such as the kinetic energy equation. — 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. — Always check the units of all constants and variables before performing calculations.
- Misinterpreting the effect of increasing electron speed on the diffraction pattern. — Visualize the relationship using graphs or diagrams to reinforce the concept.
- Using the wrong value for the mass of an electron. — 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. — 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. — Practice solving for different variables in the kinetic energy equation and double-check each step.
Where the marks go
- Full worked solution (all marking points)6 marks