4.5QuantumStretch

Wave-Particle Duality

Light diffracts and interferes like a wave, yet knocks electrons out of metal like a stream of particles. Louis de Broglie’s radical suggestion was that this duality runs both ways — that matter itself, not just light, should show wave-like behaviour, an idea confirmed by firing electrons through a thin metal film.

35 min Video by Physics Online Module 4.5 Quantum physics

The de Broglie Wavelength and Wave Particle Duality — A Level PhysicsWatch the full walkthrough before the notes below.

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What you'll be able to do

Explain what is meant by wave-particle duality
State and use the de Broglie equation $λ = \frac{h}{p}$
Describe electron diffraction as evidence for the wave nature of matter
Explain why wave behaviour is never observed for everyday macroscopic objects

Wave-particle duality

Diffraction and interference only make sense if light behaves as a wave; the photoelectric effect only makes sense if light arrives as discrete photon particles. Depending on the experiment, light displays one behaviour or the other — never both in the same measurement — and both models are needed to fully describe it. This is $wave-particle duality$ .

The de Broglie wavelength

In 1924, de Broglie proposed that every moving particle has an associated wavelength related to its momentum. Faster or more massive particles have greater momentum, giving a shorter de Broglie wavelength — which is why the effect is only ever noticeable for very light, fast particles like electrons.

λ = \frac{h}{p} = \frac{h}{m v}

De Broglie wavelength (non-relativistic).

1Momentum:

p = m v = 9.11 \times 1 0^{- 31} \times 3.0 \times 1 0^{7} = 2.73 \times 1 0^{- 23}

kg m s⁻¹.

2De Broglie wavelength:

λ = \frac{h}{p} = \frac{6.63 \times 1 0 ^{- 34}}{2.73 \times 1 0 ^{- 23}}

Answer

λ \approx 2.43 \times 1 0^{- 11}

Tip — A larger momentum always gives a SHORTER de Broglie wavelength — this is exactly why electrons show observable wave effects but a thrown ball never does.

Electron diffraction: the evidence

Firing a beam of electrons through a thin film of polycrystalline graphite produces a pattern of concentric bright and dark rings on a detecting screen — a diffraction pattern, exactly as X-rays (known waves) produce through the same crystal structure. This is direct experimental evidence that matter genuinely has wave properties.

Increasing the electron beam’s accelerating voltage increases electron speed and momentum, shortening the de Broglie wavelength and producing a smaller, tighter diffraction pattern.

Tip — A higher accelerating voltage → faster electrons → greater momentum → shorter wavelength → LESS diffraction (smaller rings) — the same wavelength-diffraction relationship you’ve already met for light.

Equation recap

λ = \frac{h}{p} = \frac{h}{m v}

De Broglie wavelength.

Common mistakes to avoid

Believing wave-particle duality means light is a wave AND a particle in the very same measurement.

Duality means each behaviour shows up in different experiments — wave behaviour in diffraction, particle behaviour in the photoelectric effect — never both simultaneously in one observation.

Assuming every object has a measurable de Broglie wavelength.

Only very light, fast particles (like electrons) have a de Broglie wavelength large enough to observe — everyday objects have momenta far too large for any detectable wave effect.

Thinking increasing electron speed increases the size of the diffraction pattern.

Faster electrons have a SHORTER de Broglie wavelength, producing LESS diffraction — a smaller, not larger, pattern.

Key takeaways

Wave-particle duality: light (and matter) show wave or particle behaviour depending on the experiment, never both at once.
De Broglie wavelength: λ = h/p = h/(mv).
Electron diffraction through graphite produces rings, direct evidence for the wave nature of matter.
A higher accelerating voltage increases momentum, shrinking the de Broglie wavelength and the diffraction pattern.

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Wave-Particle Duality

35 min Video by Physics Online Module 4.5 Quantum physics