Wave-particle duality

Physics A2 · Quantum physics. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

Light shows two kinds of behaviour. Interference and diffraction can only be explained if light is a wave. The photoelectric effect can only be explained if light arrives as particles called photons. Both pictures are needed, and this is called wave-particle duality.

The same is true for matter. When a beam of electrons passes through a thin film of graphite, a pattern of rings appears on a screen. This is electron diffraction, and diffraction is a wave property, so moving electrons behave as waves.

The wavelength linked to a moving particle is its de Broglie wavelength. It gets smaller as the momentum of the particle gets larger.

Rules to remember

Common mistake

Students use λ = h/p with the speed in place of the momentum, or with kinetic energy in place of momentum. Always find p = mv first.

Worked example

What is the de Broglie wavelength of a proton (mass 1.67 × 10−27 kg) moving at 2.0 × 105 m s−1?

  1. Momentum p = mv = 1.67 × 10−27 × 2.0 × 105 = 3.34 × 10−22 kg m s−1.
  2. λ = h/p = (6.63 × 10−34) ÷ (3.34 × 10−22) = 1.99 × 10−12 m.

Answer: About 2.0 × 10−12 m.

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