One of the most profound discoveries of modern physics is that light and matter both exhibit wave-like and particle-like behaviour depending on the experimental setup. This is called wave-particle duality. Classical physics treated waves and particles as fundamentally different — waves spread out and interfere, particles have definite positions and momenta. Quantum mechanics showed that this distinction breaks down at the atomic scale.

Light shows wave nature in phenomena like reflection, refraction, diffraction, interference, and polarisation. It shows particle nature in the photoelectric effect, Compton effect, and emission/absorption spectra. Similarly, matter particles like electrons show particle nature in normal motion but wave nature in diffraction experiments.

Max Planck proposed in 1900 that energy is not continuous but comes in discrete packets called quanta. The energy of each quantum (photon for light) is E = hν, where h = 6.626 × 10⁻³⁴ J·s is Planck's constant and ν is the frequency of radiation.

Higher frequency (shorter wavelength) means higher energy per photon. UV photons have more energy than visible photons, which have more energy than infrared photons. This explains why UV light causes sunburn but visible light does not — UV photons have enough energy to break chemical bonds in skin molecules.

The photoelectric effect is the emission of electrons from a metal when light of sufficient frequency falls on it. Einstein explained it using E = hν: each photon gives its energy to one electron. If hν > work function (φ), the electron is emitted with kinetic energy KE = hν − φ. Key observations that prove particle nature: (1) There is a threshold frequency below which no emission occurs regardless of intensity. (2) Emission is instantaneous. (3) KE of emitted electrons depends on frequency, not intensity. (4) Intensity only affects the number of electrons emitted, not their energy. Wave theory fails to explain all these observations.

In 1923, Arthur Compton showed that when X-rays are scattered by free electrons, the scattered X-rays have a longer wavelength (lower energy) than the incident X-rays. The change in wavelength (Compton shift) is:

This can only be explained if photons behave like particles with momentum p = h/λ = hν/c, colliding with electrons and transferring some momentum. The maximum Compton shift (λ_c = h/m_e c = 2.43 × 10⁻¹² m) occurs at θ = 180° (backscattering). This definitively proved that photons carry momentum — a particle property.

In 1924, Louis de Broglie proposed that if waves (light) can show particle nature, then particles (electrons, protons, etc.) should also show wave nature. He proposed that every moving particle has an associated wavelength:

For a particle accelerated through potential V: KE = ½mv² = eV, so mv = √(2meV), giving λ = h/√(2meV). This is the de Broglie wavelength of an accelerated electron. For macroscopic objects (like a cricket ball), the de Broglie wavelength is incredibly tiny (~ 10⁻³⁴ m) — far too small to observe. This is why quantum effects are not seen in daily life.

Davisson and Germer (1927) fired a beam of electrons at a nickel crystal and observed diffraction patterns — exactly as expected for waves. The wavelength calculated from diffraction matched the de Broglie wavelength perfectly. This landmark experiment confirmed that electrons have wave nature, validating de Broglie's hypothesis.

G.P. Thomson also observed electron diffraction using thin metal foils around the same time. Both Davisson-Germer and G.P. Thomson received Nobel Prizes for their experimental confirmation of de Broglie's theory.