A-Level · Physics · AQA · Mark scheme decoded
AQA A-Level Physics: Wave-Particle Duality and Electron Diffraction — mark scheme explained
The short answer
The concept of wave-particle duality is a fundamental principle in modern physics, suggesting that particles can exhibit both wave-like and particle-like properties. This idea was revolutionary when it was first proposed and has profound implications for our understanding of the nature of matter and electromagnetic radiation.
The question
An electron has a momentum of 5 × 10 -24 kg m/s. 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
Step 1: Identify the given values and the formula to use.
- S2
Given: Momentum (mv) = 5 × 10 -24 kg m/s, Planck's constant (h) = 6.626 × 10 -34 Js
- S3
Step 2: Substitute the values into the de Broglie wavelength equation λ = h / mv.
- S4
λ = (6.626 × 10 -34 Js) / (5 × 10 -24 kg m/s)
- S5
Step 3: Perform the division to find the wavelength.
- S6
λ = 1.3252 × 10 -10 m
- S7
Step 4: Express the answer in a suitable unit, such as nanometers (nm).
- S8
1.3252 × 10 -10 m = 0.13252 nm
Model answer
Worked through, with each step tagged to the mark it earns.
- S1
Step 1: Identify the given values and the formula to use.
- S2
Given: Momentum (mv) = 5 × 10 -24 kg m/s, Planck's constant (h) = 6.626 × 10 -34 Js
- S3
Step 2: Substitute the values into the de Broglie wavelength equation λ = h / mv.
- S4
λ = (6.626 × 10 -34 Js) / (5 × 10 -24 kg m/s)
- S5
Step 3: Perform the division to find the wavelength.
- S6
λ = 1.3252 × 10 -10 m
- S7
Step 4: Express the answer in a suitable unit, such as nanometers (nm).
- S8
1.3252 × 10 -10 m = 0.13252 nm
Final answer: 0.13252 nm
Common mistakes
- Confusing the de Broglie equation with the speed of light equation (c = λf). — Review and memorize the specific form of the de Broglie equation: λ = h / mv. Practice using it in various contexts to reinforce its application.
- Forgetting to convert units when necessary, such as converting meters to nanometers or picometers. — Always check the units required in the question and perform necessary conversions. Practice problems that involve different units to build familiarity.
- Using the wrong value for Planck's constant (h). — Memorize the exact value of Planck's constant: 6.626 × 10 -34 Js. Double-check your work to ensure you are using the correct value.
- Misinterpreting the relationship between momentum and wavelength in the de Broglie equation. — Review the inverse relationship between momentum (mv) and wavelength (λ) as described by λ = h / mv. Practice problems that involve changing momentum to see how it affects the wavelength.
- Failing to explain the significance of electron diffraction in supporting wave-particle duality. — Understand that electron diffraction provides strong evidence for the wave-like properties of particles. Practice explaining this concept in both written and verbal contexts.
- Not recognizing the role of peer review in scientific research. — Study the process of peer review and its significance in advancing scientific knowledge. Practice explaining how peer review contributes to the credibility of new discoveries.
Where the marks go
- Full worked solution (all marking points)4 marks