Wave-Particle Duality

The problem — light diffracts and interferes, which only waves do, yet the photoelectric effect requires it to arrive in discrete packets, which only particles do. Neither model alone accounts for all the evidence.

Wave–particle duality — matter and radiation both exhibit wave and particle behaviour, and which is observed depends on the experiment being performed. It is not that light is "really" one and pretending to be the other; both descriptions are needed and neither is complete on its own.

Evidence for light as a wave — diffraction, interference, and polarisation.

Evidence for light as a particle — the photoelectric effect, and the existence of a threshold frequency.

De Broglie's proposal — if waves can behave as particles, then particles should behave as waves, with wavelength

λ = h / p = h / mv

Why we do not notice it — h is about 6.63 × 10⁻³⁴ J s, so for anything of everyday mass the de Broglie wavelength is unimaginably small. A cricket ball has a wavelength around 10⁻³⁴ m, far too small to diffract through any gap that exists. Only for very light, slow-moving particles is the wavelength comparable to the spacing of atoms in a crystal.

Example: an electron with momentum 3.0 × 10⁻²⁴ kg m s⁻¹ has λ = (6.63 × 10⁻³⁴) ÷ (3.0 × 10⁻²⁴) = 2.2 × 10⁻¹⁰ m, which is about the spacing between atoms in a crystal — exactly the size of "gap" needed to diffract it.

Electron diffraction — firing electrons at a thin graphite film produces concentric rings on a screen, the same pattern a wave gives when diffracted by a regular lattice. Electrons are undeniably particles with mass and charge, so this is direct evidence that particles have wave properties.

Testing the relationship — increasing the accelerating voltage gives the electrons more momentum, so their de Broglie wavelength falls and the diffraction rings shrink. That the rings respond as λ = h/p predicts is what confirms the relationship rather than merely demonstrating that something wave-like happens.