A scientist is investigating the wave and particle properties of electrons. When a beam of electrons is directed at a thin crystal, a pattern of alternating bright and dark rings is observed on a detector screen behind the crystal. The scientist then increases the speed of the electrons in the beam. State what change is observed in the ring pattern and explain, in terms of de Broglie wavelength, why this change occurs.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
Electrons can behave as both particles and waves. The de Broglie wavelength of a particle depends on its momentum.
Model answer (5 marks)
The rings become closer together.
When the speed of the electrons is increased their momentum p=m v increases.
According to de Broglie, λ=h/p, so a larger p gives a smaller λ.
A smaller wavelength means the electrons are diffracted through a smaller angle.
With a smaller diffraction angle the bright and dark rings on the screen are spaced more closely.
When the speed of the electrons is increased their momentum p=m v increases.
According to de Broglie, λ=h/p, so a larger p gives a smaller λ.
A smaller wavelength means the electrons are diffracted through a smaller angle.
With a smaller diffraction angle the bright and dark rings on the screen are spaced more closely.
Examiner tips
- Use the command word ‘explain’ – give a clear cause–effect chain. Mention the de Broglie relation λ=h/p. Show that increasing v → larger p → smaller λ → smaller diffraction angle → rings closer together.
Common mistakes
- Saying the rings become further apart. Forgetting to link momentum to wavelength. Using the wrong equation (e.g. λ=hv) instead of λ=h/p.
Mark scheme (5 marks)
- The rings become closer together (the pattern becomes more compressed / narrower spacing between rings)
- Increasing the speed of the electrons increases their momentum
- A greater momentum means a smaller de Broglie wavelength
- A smaller wavelength produces less diffraction / the electrons are diffracted through smaller angles
- Less diffraction results in the rings being closer together on the screen
Key terms in this question
Related
- All WJEC A-Level Physics (Wales) revision notes →
- How to answer a "Explain" question →
- Decode the mark scheme abbreviations →
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