The Photoelectric Puzzle (Setup)

Light strikes metal — something unexpected happens

Shine ultraviolet light on a clean metal surface and electrons are ejected. That much was known by 1887, when Heinrich Hertz first noticed it while studying spark discharges. The effect was called photoemission, and within two decades Philipp Lenard had measured its properties carefully enough to expose a deep conflict with classical wave theory.

What classical electromagnetism predicts

In classical physics, light is a continuous electromagnetic wave. Its energy is spread smoothly over the wavefront and characterised by two quantities: frequency $\nu$ (oscillations per second) and intensity $I$ (power per unit area). The energy delivered to a patch of metal grows with intensity and with time — more light, more energy, eventually enough to free an electron regardless of frequency.

Three concrete classical predictions follow:

Any frequency should work — given a sufficiently intense beam, even red light or radio waves should eventually supply enough energy to eject electrons.
Dim light should produce a time delay — if the beam is faint, you must wait while the metal accumulates energy before any electrons can escape. Classical estimates put this delay at seconds to hours for a typical beam.
Higher intensity should give faster electrons — a brighter wave carries more energy and should push electrons out with greater kinetic energy.

What experiment actually shows

Lenard's careful measurements, confirmed many times since, flatly contradict all three:

There is a sharp threshold frequency. Below a critical frequency $\nu_0$ — which depends on the metal but not on the beam intensity — no electrons are emitted at all, however intense the light. Sodium metal, for instance, shows no emission for visible red or orange light; only wavelengths shorter than roughly $540\,\text{nm}$ (green) suffice.
There is no measurable time delay. Electrons appear within nanoseconds of the beam being turned on, even when the intensity is so low that classical theory predicts a delay of hours. The energy arrives all at once, not spread over time.
Intensity controls the number of electrons, not their speed. Doubling the brightness doubles the rate of emission, but the maximum kinetic energy of the ejected electrons does not change. Only increasing the frequency increases the maximum speed.

Each of these facts is inexplicable within the wave picture. A wave model that is continuous and spread out simply cannot concentrate all its energy at one electron instantaneously, and has no mechanism to enforce a frequency cut-off.

The puzzle stated cleanly

Summarising the conflict: classical wave theory gives a consistent, mathematically precise account of interference, diffraction, and polarisation (as the rest of this module has shown), but it predicts photoemission behaviour that experiment simply does not observe. The failures are not quantitative edge-cases; they are qualitative contradictions — the wrong sign, an absent delay, a missing threshold.

This is the photoelectric puzzle: the data fit a model in which light carries energy in discrete units proportional to frequency, not in a continuous wave that any detector can soak up over time. Resolving this puzzle is the step that forced physicists to abandon classical electromagnetism at the microscopic scale and begin building quantum theory. The resolution — Einstein's photon hypothesis — is developed in the next module.