The photoelectric effect

In 1902, Philipp Lenard illuminated a metal surface in vacuum and measured the electrons it ejected — the photoelectric effect, first noticed by Hertz in 1887. Lenard's results were strange by the standards of classical wave optics. Cranking up the light's intensity ejected more electrons, which made sense — more energy in, more electrons out — but it did nothing to their individual kinetic energies; the fastest ejected electrons came out just as fast under dim light as under bright light of the same color. What did change their speed was the light's frequency: bluer light produced faster electrons, redder light produced slower ones, and below some sharply-defined threshold frequency f₀ — different for every metal — no electrons came out at all, no matter how intense the light or how long you waited.

None of that fits a classical wave picture of light. In wave theory, a light wave's energy is spread continuously across its wavefront and is proportional to intensity — brighter light means a bigger-amplitude wave delivering energy faster, and that energy should be absorbable by an electron at any frequency, given enough time to accumulate it. Wave theory therefore predicts three things that all failed the test: kinetic energy should scale with intensity, not frequency; there should be no sharp threshold frequency — even feeble red light should eventually shake an electron loose if you wait; and for very dim light there should be a measurable time lag while the electron slowly soaks up enough energy to escape. None of these were observed. Electrons at threshold appeared within nanoseconds of the light switching on, at any intensity, and dim blue light above f₀ ejected electrons instantly while intense red light below f₀ ejected none, ever.

Einstein's 1905 resolution — the work that won him the Nobel Prize, not relativity — was to take Planck's quantization further than Planck himself was willing to. Rather than treating quantization as a bookkeeping property of the oscillators that emit and absorb light, Einstein proposed that light itself travels and delivers its energy in discrete, localized quanta — photons — each carrying energy E = hf, fixed by frequency alone. A photoelectric collision is then a one-to-one event: a single photon strikes a single electron and hands over its entire energy hf in one shot; intensity just controls how many photons arrive per second, not how much energy each one carries. That single reframing explains every feature of Lenard's data at once — frequency, not intensity, sets the energy budget, so there's no time lag and no continuous scaling with brightness.

Getting the electron out of the metal costs a fixed energy — the work function φ, the minimum energy binding the least-tightly-held electrons to the surface, different for every material. Whatever energy the photon delivers beyond that price is left over as the electron's kinetic energy, giving Einstein's photoelectric equation below. Experimentally, K_max is measured by applying a retarding voltage V₀ — the stopping potential — just large enough to turn back even the fastest electrons, so eV₀ = K_max. Plot K_max against frequency for a given metal and Einstein's equation says you should get a straight line: slope h (the same h from Planck's blackbody formula, now confirmed as a genuine universal constant, not a curve-fitting trick), y-intercept −φ, and x-intercept exactly at the threshold frequency f₀ = φ/h. Robert Millikan spent a decade trying to disprove Einstein's photon hypothesis experimentally and instead confirmed it to high precision in 1916 — measuring h photoelectrically to within 0.5% of Planck's blackbody value, the first hard evidence that light's particle-like graininess was real, not just a useful fiction.