How the Photoelectric Effect Works and Why Light Comes in Packets

In the late nineteenth century, physicists observed that shining light on a metal surface could knock electrons loose. The puzzling part was that the results did not match the wave theory of light, which had been successful for a century. Brighter light did not always produce faster electrons, and very dim blue light could eject electrons that dim red light never could. In 1905, Albert Einstein explained the pattern by proposing that light arrives in packets of energy, now called photons. That idea helped launch quantum theory.

This post explains the experiment, the rules it obeys, the equation Einstein used and how to calculate the threshold for any metal.

The basic setup

Place two metal plates inside a vacuum tube, with a voltage between them and a light source aimed at one plate. When light hits the plate, electrons can escape from its surface. If the other plate is positive, it attracts the electrons, and a current flows through an external circuit. Reversing the voltage slows the electrons down. At a particular negative voltage, called the stopping potential, even the fastest electrons cannot reach the other plate, and the current stops.

The stopping potential gives a direct measure of the maximum kinetic energy of the ejected electrons. Multiply it by the electron charge and you have the energy each electron carries away.

What the experiment showed

Three observations defined the puzzle.

First, electrons are ejected immediately when light arrives, even at very low intensity. Wave theory predicted a delay of seconds or more while the electrons soaked up enough energy from a dim wave.

Second, below a certain frequency, called the threshold frequency, no electrons are ejected at all, no matter how bright the light is. Wave theory predicted that enough intensity should eventually free electrons at any frequency.

Third, the maximum kinetic energy of the electrons depends on the frequency of the light, not its brightness. Doubling the intensity doubles the number of electrons ejected, but it does not change how fast each one moves. Wave theory predicted the opposite.

Einstein's explanation

Einstein proposed that light energy comes in discrete units. The energy of each unit, or photon, depends only on frequency:

E = h f

Here E is the photon energy, f is the frequency and h is Planck's constant, approximately 6.63 × 10^-34 joule seconds. Max Planck had introduced this relation in 1900 to explain black-body radiation, but Einstein took it seriously as a property of light itself.

When one photon hits an electron in the metal, the electron absorbs the whole photon at once. Part of that energy is needed to escape from the metal. This amount is called the work function, written φ. Any leftover energy becomes the electron's kinetic energy:

K_max = h f − φ

This equation contains the entire story. Frequency sets the energy per photon. The work function sets the minimum energy needed. Brightness only sets how many photons arrive, and therefore how many electrons leave.

Why there is a threshold

If h f is smaller than φ, a single photon cannot free an electron, no matter how many photons arrive. Each electron needs one photon with enough energy to cross the barrier. Brightness adds more photons, but each photon still carries too little energy. This explains why no current flows below the threshold frequency.

The threshold frequency is f0 = φ / h. The corresponding threshold wavelength is λ0 = c / f0. Light with a longer wavelength than λ0 cannot eject electrons from that metal.

Working with electronvolts

Physicists often express photon energy in electronvolts, the energy an electron gains when it moves through one volt. One electronvolt is about 1.60 × 10^-19 joules. In these units, Planck's constant becomes h = 4.14 × 10^-15 electronvolt seconds, and a useful shortcut appears: photon energy in electronvolts is about 1240 divided by wavelength in nanometres.

A blue photon at 500 nanometres therefore carries about 2.5 electronvolts. A red photon at 700 nanometres carries about 1.8 electronvolts. A violet photon at 400 nanometres carries about 3.1 electronvolts.

Threshold values for common metals

The table gives approximate work functions and the threshold wavelengths they imply. Real values depend on surface cleanliness, crystal orientation and temperature, so the numbers are guides rather than exact constants.

Metal	Work function (eV, approx.)	Threshold wavelength (approx.)
Caesium	2.1	590 nm (yellow-orange)
Sodium	2.3	540 nm (green)
Zinc	4.3	290 nm (ultraviolet)
Platinum	5.6	220 nm (deep ultraviolet)

Caesium responds to visible light, which is why early photocells used it. Zinc and platinum need ultraviolet light, so ordinary room light cannot eject their electrons. The same physics explains why a sunburn comes from ultraviolet rays and not from visible light, although the sunburn involves more than just the photoelectric effect.

A worked calculation

Suppose blue light at 450 nanometres shines on sodium with a work function of 2.3 electronvolts. The photon energy is about 1240 / 450 = 2.76 electronvolts. The maximum kinetic energy of the ejected electrons is 2.76 − 2.3 = 0.46 electronvolts. The stopping potential would be about 0.46 volts. Increasing the light intensity to ten times brighter would release ten times as many electrons, each still carrying 0.46 electronvolts of energy.

If the wavelength is changed to 600 nanometres, the photon energy drops to 2.07 electronvolts, which is below the 2.3 electronvolt work function. No electrons are ejected, however bright the source.

Why the result mattered

Einstein's explanation was one of the three landmark papers he published in 1905. It showed that light has particle-like behaviour in some experiments, while interference and diffraction show wave-like behaviour in others. This dual nature became one of the foundations of quantum mechanics. Einstein received the Nobel Prize in Physics for his work on the photoelectric effect, and the citation honoured the law it revealed rather than the wider theory of relativity.

Robert Millikan confirmed the linear relation between kinetic energy and frequency with careful experiments in 1916, and he measured Planck's constant from the slope of the line. Millikan had doubted the photon idea, yet his measurements supported Einstein's equation.

Modern uses

The photoelectric effect is the working principle of many devices. Photomultiplier tubes in scientific instruments use a photocathode to convert faint light into measurable electrical pulses. Digital image sensors use the internal photoelectric effect in semiconductors, where photons create electron-hole pairs that are collected as charge. Solar cells rely on the same process to generate current from sunlight.

Modern photoelectron spectroscopy uses the effect to probe the electronic structure of materials. By measuring the kinetic energy of the ejected electrons, scientists determine the binding energies of electrons in a sample, which reveals its chemistry.

Common misunderstandings

A frequent error is to think that brighter light gives faster electrons. The correct statement is that brighter light gives more electrons, and each electron's maximum energy depends on frequency alone. Another error is to think that light must be quantized in every experiment. Interference and diffraction still require the wave description, so the modern view is that light has both properties, and each experiment reveals one aspect more clearly than the other.

Some people also assume that the electron absorbs energy slowly over time. In the photoelectric effect, the energy transfer is effectively instant, which is why the emission is immediate.

Key takeaways

The photoelectric effect is the ejection of electrons from a metal when light shines on it. The rules of the effect cannot be explained by a purely wave model of light.

Einstein proposed that light arrives in photons with energy E = hf. An electron needs enough energy to overcome the work function, so the maximum kinetic energy is K_max = hf − φ.

Frequency sets the threshold and the energy of each electron. Brightness sets only how many electrons leave. Caesium responds to visible light, while platinum requires deep ultraviolet.

The effect launched quantum theory and still powers image sensors, solar cells and photomultiplier tubes. It remains one of the clearest demonstrations that energy in light comes in discrete packets.