Wave-Particle Duality

The photoelectric effect showed that light, normally described as a wave, sometimes has to be treated as a stream of particles. The evidence here runs the other way: electrons, normally pictured as tiny point-like particles, show wave behaviour too. Neither description alone is the full story.

Two pieces of evidence, pointing in opposite directions

The previous lesson covered the first half of this argument: the photoelectric effect only makes sense if electromagnetic radiation — normally a wave, given how naturally it produces diffraction and interference — sometimes behaves as discrete particles, photons, each carrying a fixed packet of energy $hf$. That's a wave showing particle-like behaviour.

The second half runs the opposite direction. Electron diffraction demonstrates that electrons — normally pictured as tiny charged particles with a definite position and mass — produce diffraction patterns when directed at a suitably sized obstacle or aperture. Diffraction is a wave phenomenon: the spreading and interference of a wave after passing a gap, not something a stream of classical particles travelling in straight lines should produce. Yet a beam of electrons fired at a thin crystalline sample produces rings and patterns unmistakably identical in form to diffraction patterns from light or X-rays passing through a similarly sized structure. AQA doesn't require the details of any specific method — what matters is the conceptual result: a particle beam diffracts, and diffraction is characteristically wave behaviour.

Together, these two pieces of evidence say the strict separation between "wave" and "particle" doesn't hold at this scale. Light, usually a wave, can behave like particles; electrons, usually particles, can behave like waves. This dual behaviour is called wave-particle duality.

The de Broglie wavelength

If electrons can behave like waves, it's natural to ask what "wavelength" means for something normally thought of as a particle. De Broglie's proposal, now well confirmed experimentally, is that every moving particle has an associated wavelength set by its momentum.

This $\lambda = \dfrac{h}{mv}$ is the de Broglie wavelength. It applies to every moving object with mass, not just electrons — but because $h$ is so small, the de Broglie wavelength of anything with everyday mass and speed is absurdly tiny, far too small to produce a noticeable diffraction effect. Only for particles as light as electrons, at typical laboratory speeds, does the wavelength become comparable to atomic spacing in a crystal — exactly the scale needed for an observable diffraction pattern.

Why momentum controls the amount of diffraction

Diffraction — how much a wave spreads after passing a gap or obstacle — is most significant when wavelength is comparable to the size of the gap. A wave much smaller than the gap barely spreads; one comparable to (or larger than) the gap spreads substantially.

From $\lambda = \dfrac{h}{mv}$, increasing a particle's momentum decreases its de Broglie wavelength, since the two are inversely proportional. A shorter wavelength means less pronounced diffraction — a narrower pattern. Lowering momentum has the opposite effect: a longer wavelength, closer to (or larger than) the gap, producing a more widely spread pattern. This is why higher-energy electron beams probe finer structures: a faster electron has a shorter wavelength, resolving smaller gaps before diffraction washes out the detail.

A changing picture of matter

Wave-particle duality is a genuinely strange conclusion, and it only became accepted because the evidence — the photoelectric effect on one side, electron diffraction on the other — was independently reproduced and scrutinised by many physicists before being trusted rather than dismissed as an anomaly. That process, of new evidence being tested by the wider scientific community before it reshapes an accepted model, is how understanding of matter has genuinely changed over time.