Light behaves like a wave — until it doesn't. Black body radiation, the photoelectric effect, and the Compton effect all forced physicists to accept that light comes in discrete packets called photons. Then de Broglie flipped the idea around: if waves can act like particles, maybe particles can act like waves too.
Every heated body radiates energy over a range of wavelengths, peaking at one dominant wavelength that shifts as temperature rises (hotter objects glow bluer). Classical wave theory predicted infinite energy at short wavelengths — the "ultraviolet catastrophe." Planck fixed this by proposing that atoms emit and absorb energy only in discrete packets, E = nhf, not continuously.
Planck's quantum idea explained the glow of a hot body — Einstein used the same idea to explain why light knocks electrons out of a metal.
Shining light on a metal plate can eject electrons, but only if each photon carries enough energy hf to overcome the metal's work function W. Below the threshold frequency, no electrons escape no matter how intense the light. Above it, each ejected electron carries maximum kinetic energy KEmax = hf − W, and a stopping voltage can just halt the fastest ones.
A photon doesn't just carry energy — it also carries momentum, and can bounce off an electron like a billiard ball.
When an X-ray photon collides with a loosely bound electron, momentum and energy are conserved just like a billiard-ball collision. The scattered photon emerges with less energy — hence a longer wavelength — by an amount that depends only on the scattering angle θ, confirming that photons carry momentum p = h/λ.
If light-waves can behave as particles, de Broglie asked: could particles like electrons behave as waves?
De Broglie proposed that any moving mass has an associated wavelength λ = h/(mv), just as a photon does. For everyday objects this wavelength is immeasurably small, but for electrons it's comparable to atomic spacing — enabling electron microscopes to resolve details far finer than any light microscope, since resolution improves as wavelength shrinks.
In the electron microscope, a beam of fast electrons has a de Broglie wavelength thousands of times shorter than visible light, letting it image structures like viruses that light microscopes cannot resolve.