Dawn of Modern Physics

By 1900 light was settled: it was a wave. Interference and diffraction had proved it, and a wave model explained everything anyone had measured. Then one experiment refused to fit.

Shine light on a clean metal surface and electrons are emitted. That much a wave model can allow. What it cannot allow is what actually happens.

Below a certain threshold frequency, no electrons come off at all — however bright the light, and however long you wait. Above it, electrons appear immediately, even with a very dim source. Making the light brighter produces more electrons, but never faster ones. Only raising the frequency raises their energy.

Every one of those is wrong on a wave model. A wave delivers energy continuously and spread out, so a dim light should simply take longer to accumulate enough — and brightness, not colour, should control the energy. That is not what nature does.

Drag the frequency below the dashed threshold and the emission stops dead — not "less", but none, at any brightness. Switch metals and the threshold moves, because each has its own work function. That cliff edge is what no wave model can produce.

Einstein's answer, in 1905, was that light arrives in discrete packets. Each packet — a photon — carries energy E = hf, fixed entirely by the frequency.

One photon is absorbed by one electron, all at once. If that single photon carries enough energy to free the electron from the metal, the electron leaves immediately; if it does not, nothing happens no matter how many such photons arrive.

The energy needed to free an electron is the work function φ, a property of the metal. Anything left over becomes the electron's kinetic energy, which gives Einstein's photoelectric equation.

Everything now fits. The threshold frequency is simply where hf equals φ. Brighter light means more photons, so more electrons — but each photon still carries the same energy, so the electrons are no faster. And emission is instant because it takes one photon, not an accumulation.

Energies here are small, so the electronvolt is used: the energy gained by an electron accelerated through one volt, 1 eV = 1.6 × 10⁻¹⁹ J.

h

Planck constantJ s

f

frequencyHz

φ

work functionJ or eV

KE_max

maximum kinetic energyJ or eV

Light now had two faces. Interference and diffraction still demanded a wave; the photoelectric effect demanded particles. Rather than one being wrong, both are needed — light behaves as a wave when it travels and as particles when it exchanges energy with matter.

In 1924 de Broglie asked the obvious opposite question: if a wave can behave as a particle, can a particle behave as a wave? He proposed that any object with momentum has an associated wavelength, λ = h/p.

For anything visible this is far too small to matter. A cricket ball has a de Broglie wavelength around 10⁻³⁴ m — smaller than any length that means anything. But an electron's is comparable to atomic spacing, and that is measurable.

It was measured. Fire electrons at a thin crystal and they produce a diffraction pattern, exactly as X-rays do. Electrons — indisputably particles, with mass and charge — diffract. The electron microscope is built on this: because the electron wavelength is far shorter than light, it resolves detail no optical microscope can reach.

λ

de Broglie wavelengthm

p

momentumkg m s⁻¹

V

accelerating voltageV