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EnglandPhysicsSyllabus dot point

How can light and electrons behave as both waves and particles, and what evidence supports each description?

The evidence for the wave nature of light and the particle nature of light, the de Broglie wavelength of a particle, electron diffraction as evidence for the wave nature of matter, and the link between momentum and wavelength.

A focused answer to AQA A-Level Physics 3.2.2.4, covering the evidence for the wave and particle natures of light, the de Broglie equation, electron diffraction as proof of the wave nature of matter, and how wavelength depends on momentum.

Generated by Claude Opus 4.89 min answer

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  1. What this dot point is asking
  2. The dual nature of light
  3. The de Broglie hypothesis
  4. Electron diffraction
  5. Try this

What this dot point is asking

AQA specification point 3.2.2.4 wants you to know the evidence that light behaves as a wave and as a particle, state and use the de Broglie equation, explain electron diffraction as evidence for the wave nature of matter, and show how a particle's wavelength depends on its momentum.

The dual nature of light

The two models are used in different situations: the wave model explains how light spreads and superposes, while the photon model explains how it delivers energy in quantised lumps. Both are needed for a complete picture. Crucially, the same beam of light can show wave behaviour in one experiment (diffraction) and particle behaviour in another (the photoelectric effect), so duality is a genuine feature of light, not just a choice of description. De Broglie's insight was to extend this symmetry to matter, predicting that particles should also diffract.

The de Broglie hypothesis

For everyday objects the momentum is so large that the wavelength is far too small to detect (a thrown ball has a wavelength around 10−34 m10^{-34} \text{ m}), which is why wave behaviour of matter is only seen for tiny particles like electrons.

Electron diffraction

When a beam of electrons passes through a thin polycrystalline film, it produces a diffraction pattern of rings, just as waves do through a regular structure. Since diffraction is a wave property, this is direct evidence that electrons (matter) behave as waves. Reducing the electron speed lowers the momentum, increasing λ\lambda and making the rings spread out, while increasing the speed shrinks the wavelength and tightens the pattern. The electron wavelength must be comparable to the atomic spacing for the diffraction to be observable.

Try this

Q1. State the de Broglie equation and define each symbol. [2 marks]

  • Cue. λ=hp\lambda = \dfrac{h}{p}: λ\lambda wavelength, hh Planck constant, pp momentum.

Q2. Explain how electron diffraction provides evidence for the wave nature of matter. [2 marks]

  • Cue. Electrons passing through a crystal form a diffraction pattern, and diffraction is a property only of waves.

Q3. State what happens to the de Broglie wavelength of an electron if its speed increases. [1 mark]

  • Cue. The wavelength decreases.

Exam-style practice questions

Practice questions written in the style of AQA exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

AQA 20194 marksAn electron is accelerated to a speed of 3.0×106 m s−13.0 \times 10^6 \text{ m s}^{-1}. Calculate its de Broglie wavelength. Take the electron mass as 9.11×10−31 kg9.11 \times 10^{-31} \text{ kg} and h=6.63×10−34 J sh = 6.63 \times 10^{-34} \text{ J s}.
Show worked answer →

Find the momentum: p=mv=(9.11×10−31)(3.0×106)=2.73×10−24 kg m s−1p = mv = (9.11 \times 10^{-31})(3.0 \times 10^6) = 2.73 \times 10^{-24} \text{ kg m s}^{-1}.

Apply the de Broglie equation λ=hp=6.63×10−342.73×10−24\lambda = \dfrac{h}{p} = \dfrac{6.63 \times 10^{-34}}{2.73 \times 10^{-24}}.

λ=2.4×10−10 m\lambda = 2.4 \times 10^{-10} \text{ m}, comparable to atomic spacing, which is why electrons diffract through crystals.

Markers reward finding the momentum, applying λ=hp\lambda = \dfrac{h}{p}, and the correct wavelength.

AQA 20214 marksExplain how electron diffraction provides evidence for the wave nature of matter, and describe what happens to the diffraction pattern when the electrons are slowed down.
Show worked answer →

When a beam of electrons passes through a thin polycrystalline film, it produces a diffraction pattern of concentric rings on a screen. Diffraction is a property only of waves, so this shows that electrons (matter) behave as waves.

Slowing the electrons reduces their momentum p=mvp = mv. From λ=hp\lambda = \dfrac{h}{p}, a smaller momentum means a longer de Broglie wavelength, so the diffraction rings spread out (the diffraction angle increases).

Markers reward the ring pattern as evidence of wave behaviour, the link to the de Broglie wavelength, and the rings spreading out for slower (lower-momentum) electrons.

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