The Photoelectric Effect Experiment: Einstein, Photons, and the Birth of Quantum Physics

Shine light on a metal and, if the light's frequency is high enough, electrons fly off the surface. That sentence sounds simple. It nearly broke nineteenth-century physics. When careful experiments in the 1880s and 1890s revealed that the energy of the ejected electrons depended on the color of the light rather than its brightness, classical wave theory had no explanation. Albert Einstein solved it in 1905 by proposing that light itself comes in discrete packets — photons. That idea, not relativity, won him the Nobel Prize, and it launched modern quantum mechanics.

What Hertz Found — and Did Not Understand

Heinrich Hertz was not looking for anything strange in 1887. He was testing James Clerk Maxwell's electromagnetic theory by generating and detecting radio waves in his Karlsruhe laboratory. One of his detectors was a spark-gap device: two metal balls separated by a small air gap, connected to a resonating circuit. When the transmitter fired, the receiver gap sparked.

Hertz noticed that the receiver sparked more reliably when ultraviolet light from the transmitter arc fell on the detector's electrodes. He published the observation that year, careful to document what he saw and equally careful not to over-interpret it.

Source: Hertz, H. (1887), "Über einen Einfluss des ultravioletten Lichtes auf die electrische Entladung," Annalen der Physik, 267(8), 983–1000 — the original paper describing the observation that UV light facilitated electrical discharge.

Hertz had no explanation for the effect. He never proposed one. He moved on to other experiments and died of a bone disease in 1894 at the age of 36. The phenomenon he had stumbled on would take another eighteen years to explain, and the explanation would overthrow the classical picture of light.

Wilhelm Hallwachs, working in Dresden in 1888, simplified the observation to its bare essentials. A freshly polished zinc plate connected to an electroscope lost its charge when illuminated with ultraviolet light — but only if the plate was negatively charged. Positive charge was unaffected. This meant the light was ejecting negatively charged particles from the metal, not attracting positive ones. The particles were whatever made up negative electricity — though the word "electron" did not yet exist.

Source: Hallwachs, W. (1888), "Über den Einfluss des Lichtes auf electrostatisch geladene Körper," Annalen der Physik, 269(2), 301–312 — the Hallwachs experiment establishing that negative charge, not positive, was being removed by the light.

Lenard's Careful Measurements — and Their Disturbing Implications

Philipp Lenard picked up the problem in the late 1890s. He was a better experimentalist than theorist, meticulous and systematic, and he had the right equipment. Using a metal cathode in a vacuum tube, he could not only detect the ejected particles but measure their energy by applying a retarding voltage between two electrodes. If you apply a reverse voltage large enough to stop the fastest electrons from reaching the collector, you can read off the maximum kinetic energy of the ejected particles from the stopping potential.

Stopping potential — the reverse voltage just large enough to halt the most energetic photoelectrons. If stopping potential is V₀ and the electron charge is e, the maximum kinetic energy is eV₀.

Lenard's results from 1899 to 1902 were unsettling. Classical wave theory predicted that brighter light should deliver more energy per unit area to the metal surface, so electrons ejected by bright light should have more kinetic energy than those ejected by dim light. Lenard found the opposite was true: the stopping potential — and thus the maximum electron energy — did not change when he increased the brightness of the light. More electrons were ejected, but they were not faster.

What did change the electron energy was the frequency (color) of the light. Higher frequency light ejected faster electrons. And below a certain threshold frequency, no electrons were emitted at all, regardless of how bright the light was.

Source: Lenard, P. (1902), "Ueber die lichtelektrische Wirkung," Annalen der Physik, 313(5), 149–198 — the definitive experimental paper establishing that electron energy depends on light frequency, not intensity, and that a minimum threshold frequency exists.

This was inexplicable on classical wave theory. A wave's energy is proportional to its amplitude (brightness). A bright wave should hit the metal with more energy than a dim one. Yet the electrons could not tell the difference. Lenard received the Nobel Prize in Physics in 1905 specifically for this experimental work — the observation that classical physics could not explain.

The Three Unexplained Facts

By 1905, three experimental facts about the photoelectric effect had no classical explanation:

Observation	Classical prediction	What actually happened
Brighter light → faster electrons?	Yes — more wave energy per area	No — more electrons, same maximum speed
Higher frequency → faster electrons?	Not especially	Yes — linear relationship
Threshold frequency below which nothing happens?	Should not exist — waves of any frequency carry energy	Exists for every metal
Delay before first emission?	Yes — electrons must absorb energy gradually	No — emission is essentially instantaneous

Each discrepancy was a stab in classical physics. The fourth one — the absence of a time delay — was particularly pointed. A wave arriving at a metal surface should take time to deposit enough energy to eject an electron, especially if the light is very dim. Even with extraordinarily faint ultraviolet light, the first electrons appear within nanoseconds. They do not wait.

Einstein's 1905 Paper — Light as Quanta

Albert Einstein's paper "On a Heuristic Viewpoint Concerning the Production and Transformation of Light" was published on June 9, 1905, in Annalen der Physik. It was one of four extraordinary papers he published that year — the others being on Brownian motion, special relativity, and mass-energy equivalence — but Einstein himself called this one "very revolutionary."

Source: Einstein, A. (1905), "Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt," Annalen der Physik, 322(6), 132–148 — the paper proposing light quanta to explain the photoelectric effect.

Einstein's proposal was radical: light does not behave as a continuous wave when it interacts with matter. Instead, it comes in discrete packets of energy, each with energy proportional to the light's frequency:

E = hf

where h is Planck's constant (6.626 × 10⁻³⁴ J·s) and f is the frequency of the light. Each packet — which we now call a photon — either has enough energy to eject an electron or it does not. No accumulation. No delay. One photon interacts with one electron.

This single equation explains every anomaly:

• Why brightness doesn't change electron energy: More photons arrive per second, but each has the same energy. More electrons are ejected, but none faster.
• Why frequency determines electron energy: Higher frequency means higher energy per photon, so the electron receives more energy from each collision.
• Why there's a threshold frequency: Each metal has a characteristic minimum energy, called the work function (symbol φ), needed to pull an electron free of the surface. If hf < φ, no electron can escape regardless of how many photons arrive.
• Why there's no time delay: Each ejection is a single photon-electron collision, complete in less than a femtosecond (10⁻¹⁵ s).

The full Einstein photoelectric equation is:

KE_max = hf − φ

where KE_max is the maximum kinetic energy of the ejected electrons and φ is the work function of the specific metal.

This is a line with slope h and intercept −φ when KE_max is plotted against f. Einstein's equation makes a specific, testable prediction: if you plot maximum electron energy against light frequency for different frequencies, you get a straight line, and the slope of that line is Planck's constant — a number that had been determined from blackbody radiation and could be checked against the photoelectric data.

Millikan's Decade of Determined Opposition

Robert Millikan was the leading American experimental physicist of his era, famous for measuring the electron's charge with his oil-drop experiment (completed in 1909). He was also, in 1905, deeply skeptical of Einstein's light-quantum hypothesis.

Millikan believed Einstein's idea was physically untenable. Maxwell's electromagnetic theory was one of the great triumphs of nineteenth-century physics. The idea that light — a wave phenomenon, produced and detected through wave interactions, showing beautiful interference patterns — actually came in localized particles struck Millikan as a step backward to the discredited corpuscular theory of Newton.

He set out to disprove Einstein's equation.

Source: Millikan, R. A. (1916), "A direct photoelectric determination of Planck's 'h'," Physical Review, 7(3), 355–388 — the definitive 1916 paper reporting Millikan's precise measurement of h through the photoelectric effect, and the reluctant confirmation of Einstein's equation.

Millikan spent roughly a decade on the problem, from around 1905 to 1916. The technical challenges were severe. To measure stopping potentials accurately, the metal surface had to be atomically clean — even a single oxide layer changed the work function enough to corrupt the measurement. Millikan solved this by machining fresh metal surfaces inside his vacuum apparatus using a small cutting tool, so the surface was never exposed to air.

He measured stopping potentials for sodium, lithium, and potassium using monochromatic light at several frequencies. He plotted KE_max against frequency. He got a straight line. He measured the slope. It matched Planck's constant to within 0.5%.

He was not happy about it. His 1916 paper contains one of the great concessions in the history of science: after presenting the measurements that confirmed Einstein's equation in every particular, Millikan wrote that while the equation was verified, Einstein's "bold, not to say reckless" hypothesis about light quanta still seemed physically unwarranted. He accepted the equation without accepting the model behind it.

The slope of Millikan's stopping-potential graph gave h = 6.57 × 10⁻²⁷ erg·second (6.57 × 10⁻³⁴ J·s). The modern value is 6.626 × 10⁻³⁴ J·s. Millikan was within 0.8%.

The Timeline

Year	Event
1887	Hertz notices ultraviolet light enhances spark-gap discharge in Karlsruhe
1888	Hallwachs shows UV removes negative charge from zinc plates
1897	J.J. Thomson identifies the electron as the carrier of negative electricity
1899	Lenard begins systematic photoelectric measurements
1902	Lenard publishes: electron energy depends on light frequency, not intensity; threshold exists
1905	Lenard receives Nobel Prize in Physics for cathode-ray and photoelectric work
June 9, 1905	Einstein publishes the light-quantum (photon) hypothesis in Annalen der Physik
1909–1916	Millikan conducts systematic stopping-potential measurements with freshly-machined metal surfaces
1916	Millikan publishes confirmation of Einstein's equation; measures h to within 0.5%
1921	Einstein awarded 1921 Nobel Prize in Physics "for his discovery of the law of the photoelectric effect"
1923	Millikan awarded 1923 Nobel Prize in Physics for the electron charge and photoelectric measurements
1926	Lewis coins the word "photon" for the light quantum

Source: NobelPrize.org — Nobel Prize in Physics 1921 awarded to Albert Einstein; Nobel Prize in Physics 1923 awarded to Robert A. Millikan.

What the Experiment Established About Light and Matter

The photoelectric effect experiment, through its four-decade arc from Hertz's observation to Millikan's confirmation, established two things of extraordinary importance.

First, light has particle-like properties at the quantum scale. This does not mean light is a particle in the classical sense — it still shows interference and diffraction, which are wave phenomena. It means the energy exchange between light and matter is quantized. Light does not smoothly deposit energy like water filling a bucket; it delivers energy in lumps, one photon at a time. This is the central insight of quantum mechanics, and the photoelectric effect is its clearest early demonstration.

Second, the relationship between energy and frequency — E = hf — is universal. The same constant h that Planck introduced in 1900 to fix the blackbody radiation problem appears here, in a completely different physical context. Two apparently unrelated phenomena — the spectrum of thermal radiation and the ejection of electrons from metals — are connected by the same fundamental constant. This universality was a sign that something deep was going on, not a coincidence.

The work function values Millikan and others measured are specific to each metal because they depend on the electron binding energy in that material's lattice structure:

Metal	Work function (eV)	Threshold frequency (Hz)
Cesium	2.1	~5.1 × 10¹⁴
Sodium	2.3	~5.6 × 10¹⁴
Aluminum	4.1	~9.9 × 10¹⁴
Copper	4.7	~1.1 × 10¹⁵
Gold	5.1	~1.2 × 10¹⁵

Work function (φ) — the minimum energy, measured in electron volts (eV), required to remove an electron from the surface of a specific metal. One electron volt equals 1.602 × 10⁻¹⁹ joules.

Visible light (frequencies roughly 4–7 × 10¹⁴ Hz) can only produce the photoelectric effect in metals with low work functions like cesium or sodium. This is why ultraviolet light was needed in Hertz's and Lenard's original experiments — most common metals have work functions above the visible range.

Why Millikan Resisted and What That Tells Us

The spectacle of a brilliant experimenter spending a decade trying to disprove a theory and instead confirming it is worth sitting with. Millikan's resistance was not irrational — it was scientifically motivated. Maxwell's equations had been verified to extraordinary precision. Hertz himself had confirmed that electromagnetic waves travel at the speed of light. Waves and interference were bedrock.

The concept of a photon was not just a new particle; it was a claim that the nature of light was fundamentally different from what Maxwell's beautiful equations suggested. Millikan's skepticism reflected the appropriate weight of existing evidence. That he eventually published a paper that rigorously confirmed Einstein's equation — despite his personal theoretical objections — is a model of scientific integrity.

Einstein, for his part, had been even more radical than his paper let on. He described his own hypothesis as "heuristic" — meaning useful as a working assumption, not necessarily a deep truth. He understood that proposing that light was quantized contradicted the best theory of his era. He proposed it anyway because the experimental evidence — specifically, Lenard's measurements — demanded an explanation that wave theory could not provide.

Source: Pais, A. (1982), Subtle is the Lord: The Science and Life of Albert Einstein, Oxford University Press — comprehensive intellectual biography detailing Einstein's attitude toward the light-quantum paper and his subsequent discomfort with the full implications of quantum mechanics.

Applications Downstream of This Experiment

The photoelectric effect is not a historical curiosity. Every solar cell operates on a variant of it: photons from sunlight strike a semiconductor, ejecting electrons that flow as current. The efficiency and voltage of a solar cell depend directly on the work function of the semiconductor material and the frequency distribution of incoming light.

Photodetectors in cameras, phototubes in laboratory spectroscopy, and the image sensors in every digital camera and phone exploit the same physical mechanism that puzzled Hertz in 1887.

Photomultiplier tubes — used in particle physics detectors and astronomical instruments — amplify the signal from a single photon into a detectable electrical pulse through a cascade of photoelectric ejections inside a vacuum tube. The Cherenkov detector arrays at CERN and in neutrino observatories like Super-Kamiokande in Japan rely on arrays of photomultiplier tubes.

Source: Super-Kamiokande Collaboration (2003), "The Super-Kamiokande detector," Nuclear Instruments and Methods in Physics Research A, 501, 418–462 — describes the 11,146 photomultiplier tubes lining the 50,000-ton water tank used to detect neutrino-induced Cherenkov light.

The Wave-Particle Duality Problem — Light After Einstein

Einstein's 1905 paper did not resolve the nature of light; it deepened the mystery. Before 1905, light was a wave — the evidence from interference experiments was overwhelming. After 1905, light was also a particle — the evidence from the photoelectric effect was becoming undeniable. But a thing cannot be both a wave and a particle in classical physics. Waves spread out; particles are localized. Waves interfere with each other; particles collide.

The resolution, which took another two decades to formalize, is that light is neither a classical wave nor a classical particle. It is a quantum field — a physical entity that exhibits wave properties when propagating (interference, diffraction, polarization) and particle properties when interacting (discrete energy exchange, momentum transfer in Compton scattering). The wave-particle duality is not a compromise between two contradictory descriptions; it is a feature of quantum mechanics itself, which has no classical analog.

Wave-particle duality — the principle that quantum objects exhibit both wave-like properties (interference, diffraction) and particle-like properties (discrete energy and momentum exchanges), depending on how they are observed. Neither description is complete without the other.

Einstein's light-quantum paper set the problem in motion. Louis de Broglie extended it in 1924 by proposing that matter — electrons, protons, atoms — also has a wave nature, with wavelength λ = h/p (where p is momentum). The Davisson-Germer experiment in 1927 confirmed electron diffraction, validating de Broglie's hypothesis. By 1927, the wave-particle duality applied not just to light but to all quantum objects.

Source: de Broglie, L. (1924), "Recherches sur la théorie des quanta," doctoral thesis, University of Paris — the thesis proposing matter waves, building on Einstein's light-quantum hypothesis. Published in Annales de Physique, 10(3), 22–128 (1925).

The photoelectric effect is the historical hinge between the classical world of waves and particles and the quantum world where both are simultaneously real. No other single experiment makes this transition as cleanly visible.

What the 1921 Nobel Prize Statement Really Said

Einstein's Nobel citation was "for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect." The word "law" is important — the Prize recognized a mathematical relationship verified by experiment, not a theoretical model. The Nobel Committee in 1921 remained cautious about the photon as a physical object, even while endorsing Einstein's equation KE_max = hf − φ as an established fact.

This caution was not unreasonable. In 1921, several alternative theories could reproduce Einstein's equation without requiring photons — semiclassical models in which light was still a wave but electrons responded to its frequency through quantum rules built into the metal. It was not until 1926–1927, with the development of quantum electrodynamics (QED), that the photon was established on the solid theoretical footing that made denial impossible.

Source: Pais, A. (1982), Subtle is the Lord, Oxford University Press — analysis of the Nobel Committee's deliberations and the reasons for the specific wording of Einstein's 1921 prize citation.

Einstein received the prize in 1922 (presented in November 1922 for the 1921 prize), when he was on a lecture tour of Japan and could not attend the ceremony. The prize money — 121,572 Swedish kronor — went, as Einstein had agreed in divorce proceedings, to his first wife Mileva Marić.

What People Get Wrong About the Photoelectric Effect

"Einstein discovered the photoelectric effect." Hertz discovered it in 1887. Lenard characterized its key properties by 1902. Einstein explained it in 1905. Discovery and explanation are different contributions.

"Einstein won the Nobel for relativity." The 1921 Nobel Prize citation is explicit: "for his discovery of the law of the photoelectric effect." Relativity was controversial in 1921, and several Nobel Committee members were uncertain about it. The photoelectric effect was experimentally confirmed and unambiguous.

"Millikan confirmed Einstein right away." Millikan spent roughly a decade on the problem and confirmed Einstein's equation in 1916 — eleven years after Einstein published. Even then, Millikan publicly questioned the physical interpretation (photons) while accepting the mathematical result.

"The photoelectric effect proves light is a particle." More precisely, it proves that light's interaction with matter is quantized — energy is exchanged in discrete amounts. Light also shows wave behavior in interference experiments. The concept of wave-particle duality, which emerged from precisely this tension, is the correct framing. Neither "pure wave" nor "pure particle" describes light fully.

FAQs

Q: Why does light frequency affect electron energy but light intensity does not?
A: In Einstein's photon model, each electron is struck by one photon at a time. The photon's energy is hf — determined entirely by its frequency. A brighter light beam delivers more photons per second, so more electrons are ejected, but each electron still receives energy from only one photon. Increasing intensity means more electrons ejected, not faster ones. Increasing frequency means each photon carries more energy, so each ejected electron moves faster.

Q: What is the work function and why does it vary by metal?
A: The work function is the minimum energy needed to pull a conduction electron completely free from the metal surface. It varies because different metals hold their electrons with different strengths, depending on the metal's crystal structure, electron density, and surface properties. Cesium's work function is about 2.1 eV; gold's is about 5.1 eV. Only photons with energy exceeding the work function can cause photoemission.

Q: How did Millikan measure the stopping potential so precisely?
A: Millikan's key innovation was machining fresh metal surfaces inside his vacuum apparatus using a motor-driven cutter. Earlier attempts were ruined by oxide layers that changed the work function unpredictably. With clean surfaces, he could apply a precise reverse voltage between two electrodes and read the minimum voltage that stopped the photocurrent entirely. That voltage, multiplied by the electron charge, gave the maximum kinetic energy.

Q: What is a photon, exactly?
A: A photon is a quantum of electromagnetic energy — the smallest indivisible unit of a light field at a given frequency. It has energy E = hf, momentum p = h/λ (where λ is wavelength), zero rest mass, and always travels at the speed of light in vacuum. The word "photon" was coined by chemist Gilbert Lewis in 1926, twenty-one years after Einstein's paper.

Q: Did Einstein believe his own photon hypothesis?
A: He proposed it, but he also called it "heuristic" — a working assumption rather than a physical truth he fully committed to. Even after his 1905 paper, Einstein remained uneasy about the full implications of quantization. In 1909 he wrote that the next phase of physics would have to account for both the wave and particle properties of light simultaneously. That task consumed much of twentieth-century physics.

Q: How does the photoelectric effect differ from the Compton effect?
A: Both involve photons interacting with electrons, but in different ways. In the photoelectric effect, a photon is completely absorbed by a bound electron in a metal, which is then ejected. In the Compton effect (1923), a photon scatters off an electron, transferring some — but not all — of its energy. The photon survives with reduced frequency. Compton's result provided additional evidence that photons have momentum as well as energy.

The Takeaway

Hertz's 1887 observation was a loose thread. Lenard pulled it hard enough by 1902 that classical physics started to unravel. Einstein's 1905 paper did not patch the unraveling — it acknowledged that the wave theory of light, however successful in other contexts, was inadequate to describe how light and matter exchange energy. Light comes in lumps, and the lump size depends on frequency. That insight, delivered to a skeptical physics community and verified only after a decade of adversarial experimentation by Millikan, started the chain of reasoning that eventually produced quantum mechanics, quantum electrodynamics, and semiconductor physics. Every solar panel, digital camera sensor, and photomultiplier tube operating today is doing exactly what Lenard's electrons did — responding to individual photons, one at a time.

---

Read next:

• The Millikan Oil Drop Experiment
• The Davisson-Germer Experiment
• The Double-Slit Experiment