The Photoelectric Effect: How Einstein Proved Light Is Made of Particles

By 1902, experimenters had noticed something deeply strange. Shining ultraviolet light on a zinc plate caused the plate to emit electrons — a phenomenon Heinrich Hertz had first observed in 1887. But when the experiments were done carefully, the results defied every expectation that classical physics offered. Increasing the light intensity produced more electrons but did not increase their maximum speed. Using light below a certain frequency produced no electrons at all, no matter how bright the beam. These observations had no explanation in classical physics. In 1905, Albert Einstein provided one — and the explanation required him to argue that light itself was made of discrete packets of energy. That paper, not his relativity papers, is the one that won him the Nobel Prize in Physics in 1921.

Three Puzzles That Classical Physics Could Not Explain

Classical electromagnetism treated light as a continuous wave. A wave can carry any amount of energy continuously — given enough time, even a feeble beam of light should deliver enough energy to eject an electron from any metal. That prediction is simply wrong.

• The threshold frequency puzzle: Below a certain frequency ν₀, light ejects no electrons regardless of intensity. Classical waves have no threshold; any frequency should work given enough time.
• The instantaneous response puzzle: Electrons are ejected within nanoseconds of the light striking the metal, even at very low intensities. Classical theory predicted that weak light would take seconds or minutes to accumulate enough energy to free an electron.
• The intensity-energy puzzle: Brighter light produces more electrons but does not increase the maximum kinetic energy of the ejected electrons. Only increasing the frequency increases their kinetic energy. Classically, a brighter (higher amplitude) wave should deliver more energy to each electron.

Einstein's Quantum Hypothesis

Einstein's 1905 paper proposed that light is not a continuous wave but a stream of discrete energy packets, each carrying energy E = hν, where h is Planck's constant (6.626 × 10⁻³⁴ J·s) and ν is the frequency. These packets were later named photons by Gilbert Lewis in 1926.

Each photon interacts with one electron. The photon's energy goes entirely to the electron. Part of that energy — the work function W — is used to overcome the binding energy holding the electron in the metal. The rest becomes kinetic energy. Einstein's equation for the maximum kinetic energy of ejected electrons is:

KE_max = hν − W

This single equation explained all three puzzles at once. Below the threshold frequency (ν₀ = W/h), even one photon carries insufficient energy to liberate any electron. Above the threshold, every photon that is absorbed immediately frees one electron — no energy accumulation required, hence instantaneous response. Increasing intensity means more photons (more electrons), but each photon still carries only hν energy, so the maximum kinetic energy is unchanged by intensity alone.

Millikan's Verification and the Measurement of h

Robert Millikan spent ten years trying to disprove Einstein's equation. Working in vacuum with carefully cleaned metal surfaces, he measured the stopping potential V_s — the voltage needed to bring the fastest electrons to rest — as a function of frequency. KE_max = eV_s, so Einstein's equation predicts V_s = (h/e)ν − W/e: a straight line when plotted against frequency, with slope h/e.

Millikan's 1916 results were precise and unambiguous. The graphs were perfectly straight lines. The slope gave h = 6.57 × 10⁻³⁴ J·s — within 1% of the modern value. Millikan believed Einstein's physical interpretation was wrong, but he could not argue with his own data. He later received the 1923 Nobel Prize partly for this work. The photoelectric effect became the most direct measurement of Planck's constant for decades.

Metal	Work Function W (eV)	Threshold Frequency ν0 (Hz)	Threshold Wavelength (nm)
Cesium	2.1	5.1 × 1014	590 (visible, orange)
Sodium	2.36	5.7 × 1014	540 (visible, green)
Aluminum	4.08	9.9 × 1014	304 (UV)
Copper	4.7	1.14 × 1015	264 (UV)
Gold	5.1	1.23 × 1015	243 (UV)
Platinum	5.65	1.37 × 1015	219 (UV)

The Photon Concept and Its Resistance

Einstein's photon concept was controversial for years. Max Planck himself — who had introduced energy quanta in 1900 to explain blackbody radiation — thought the idea of quantized light went too far. Niels Bohr resisted it even longer. The concept seemed to abandon the beautiful wave theory of light that Maxwell had built and that explained interference, diffraction, and polarization so perfectly. How could light be both a wave (explaining interference) and a particle (explaining the photoelectric effect)?

The resolution came with quantum mechanics in 1925–1926. Light is neither purely a wave nor purely a particle. It is a quantum field whose excitations (photons) behave like particles in some experiments and like waves in others, depending on what is measured. The photoelectric effect detects the particle aspect. Double-slit interference detects the wave aspect. Both are real. This is wave-particle duality — a concept that extends to electrons, protons, and all other quantum objects as well.

Applications of the Photoelectric Effect

Application	How the Photoelectric Effect Is Used
Solar cells (photovoltaic)	Photons in silicon excite electrons across the band gap, generating current at a p-n junction
Photomultiplier tubes	Single photons eject electrons from a photocathode; amplified by a cascade of dynodes; used in particle physics detectors
CCD and CMOS image sensors	Photons create electron-hole pairs in silicon pixels; accumulated charge encodes the image
X-ray photoelectron spectroscopy (XPS)	X-ray photons eject core-level electrons whose binding energies identify atomic species and chemical bonding
Night-vision photocathodes	Low-light photons eject electrons from multi-alkali photocathodes; electrons are amplified by microchannel plates

From Annus Mirabilis to Modern Quantum Optics

Einstein's 1905 paper on the photoelectric effect appeared in the same journal (Annalen der Physik) and the same year as his papers on special relativity and Brownian motion. That year is called his annus mirabilis — miracle year. Of the three papers, the photoelectric paper was the most conceptually radical. Relativity reorganized space and time but preserved the deterministic structure of classical physics. The photoelectric paper introduced irreducible discreteness into the nature of light — the first step toward a fully probabilistic description of physical reality.

Modern quantum optics has taken photon physics to extraordinary levels of precision. Individual photons can now be generated on demand, detected with near-unit efficiency, and entangled with other photons to test the foundations of quantum mechanics. The photoelectric effect that Hertz noticed in a laboratory in 1887 now underlies every digital image, every solar panel, and every optical fiber communication system on Earth.