The photoelectric effect

Shine a light on a piece of metal and something invisible can happen: the light can knock tiny particles called electrons right out of the surface. This is the photoelectric effect, and at first it sounds dull. The strange part is how it behaves, because it broke the rules everyone thought light obeyed.

Here is what scientists expected. Light was thought to be a wave, like ripples on a pond. A brighter light is a bigger wave carrying more energy, so a bright light should knock electrons out harder and faster, and a dim light should knock them out gently. And any colour of light should work eventually, as long as you wait long enough for the energy to build up.

None of that is what happens. The colour of the light is what matters, not the brightness. Red light can be blindingly bright and still knock out nothing at all, while a faint blue or ultraviolet light knocks electrons out instantly. Make the light bluer and the electrons come flying out faster. Make it brighter without changing the colour and you just get more electrons, all moving at the same speed as before. And there is no waiting: the moment the right colour of light lands, electrons leap out straight away.

In 1905 Albert Einstein worked out why, and the answer changed physics forever. Light is not a smooth wave after all, or at least not only a wave. It comes in tiny packets of energy, like a stream of bullets, and each packet is called a photon. A bluer photon carries more energy than a redder one. One photon hits one electron and hands over all its energy at once. If the photon carries enough energy, the electron escapes; if it does not, nothing happens, no matter how many weak photons you throw at it. That simple idea, that light comes in lumps, was the beginning of the strange new science we call quantum physics. And it is the discovery that won Einstein his Nobel Prize, not his famous theory of relativity.

Shine light on a clean metal surface and it can eject electrons from it. The effect was first noticed by Heinrich Hertz in 1887 and studied carefully by Philipp Lenard around 1902, and what they found refused to fit the physics of the day.

By 1900 light was understood as an electromagnetic wave, and that picture made clear predictions. The energy of a wave depends on its brightness, so a brighter light should give the ejected electrons more energy, and a faint light should give them less. Any colour should work if you make it bright enough or wait long enough, since the electron could slowly soak up energy from the wave until it had enough to break free. Dim light, in particular, should eject electrons only after a noticeable delay.

Every one of those predictions was wrong. The energy of the ejected electrons does not depend on the brightness of the light at all. It depends on the colour, which is to say the frequency. Below a certain threshold frequency, no electrons come out no matter how intense the light or how long you wait. Above it, electrons appear instantly, with no delay even for very faint light. Turning up the brightness produces more electrons, but each one carries exactly the same energy as before. And the bluer the light, the faster the electrons fly.

In 1905, the same year as his work on relativity, Albert Einstein explained all of this with one bold idea, building on a suggestion Max Planck had made five years earlier. Light is not delivered continuously but in discrete packets of energy, later called photons. The energy of a single photon is set entirely by its frequency, through the relation \(E = hf\), where \(f\) is the frequency and \(h\) is a tiny number now called Planck's constant. Blue and ultraviolet photons are more energetic than red ones.

This one assumption resolves every puzzle. The photoelectric effect is a one-on-one collision: a single photon strikes a single electron and gives it all of its energy at once. To escape the metal, an electron must be handed a minimum amount of energy called the work function, written as the Greek letter \(\varphi\). Whatever energy is left over becomes the electron's motion. So the maximum kinetic energy of an ejected electron is the photon's energy minus the work function: \(KE_\text{max} = hf - \varphi\).

Now everything fits. If a photon's energy \(hf\) is smaller than the work function, it cannot free an electron, and throwing more such photons at the metal does nothing, which is the threshold. Brighter light simply means more photons per second, so it ejects more electrons but cannot make any single one more energetic. There is no delay because the energy arrives in one lump rather than building up slowly. And because \(KE_\text{max}\) grows directly with frequency, bluer light makes faster electrons.

The story has a fitting end. The American physicist Robert Millikan disliked Einstein's photon idea and spent a decade trying to prove it wrong. His careful experiments, finished around 1916, did the opposite: they confirmed Einstein's equation precisely and even measured the value of Planck's constant. Einstein received the 1921 Nobel Prize specifically for explaining the photoelectric effect, not for relativity. The humble sight of light knocking electrons off a metal plate had cracked classical physics open and helped begin the quantum age.

State the experiment carefully and the conflict with classical physics is unavoidable. Monochromatic light incident on a clean metal cathode ejects electrons, and four features of those electrons resist any wave description: there is a sharp threshold frequency, the electron energy depends on frequency and not intensity, emission is effectively instantaneous, and intensity controls only the number of electrons, never their energy.

The wave theory makes the wrong predictions, quantitatively. In Maxwell's electromagnetism the energy carried by a light wave is proportional to its intensity and accumulates continuously at the surface. Three consequences follow, all contradicted by experiment. First, the kinetic energy of the photoelectrons should rise with intensity, since a stronger field does more work on each electron; instead it is wholly independent of intensity. Second, there should be no threshold, because any frequency, given enough intensity or time, should eventually free electrons; instead emission ceases entirely below a critical frequency. Third, under faint illumination there should be a measurable lag while an electron absorbs enough energy, on the order of seconds for very dim light; instead emission begins within nanoseconds. Philipp Lenard's 1902 measurements established the intensity independence, and that is precisely the feature classical physics cannot accommodate.

Einstein quantized the field, going beyond Planck. In 1905 Einstein proposed that electromagnetic energy is not merely emitted and absorbed in quanta, as Planck had assumed in 1900 to fit the blackbody spectrum, but that the radiation field itself is granular, composed of localized quanta each carrying energy \(E = hf\). Planck had treated quantization as a property of his material oscillators and regarded the continuous field as intact. Einstein took the more radical step of attributing the discreteness to light itself. This is the "heuristic viewpoint" announced in his paper's title, and it is the conceptual core of the photon.

The photoelectric equation and its experimental signature. A single quantum is absorbed by a single electron, transferring its entire energy \(hf\). Liberating the electron costs at least the work function \(\varphi\), the minimum energy needed to remove an electron from the metal into the vacuum, so the maximum kinetic energy of the emitted electron is \(KE_\text{max} = hf - \varphi\). Emission requires \(hf \ge \varphi\), which defines the threshold frequency \(f_0 = \varphi/h\), below which no current flows regardless of intensity. The cleanest test uses a retarding potential: a reverse bias is increased until even the most energetic electrons are turned back, and at that stopping potential \(V_s\) one has \(eV_s = hf - \varphi\). Plotting \(V_s\) against \(f\) yields a straight line whose slope is \(h/e\), the same for every metal, with a frequency intercept fixed by \(\varphi\). The choice of metal enters only through \(\varphi\), shifting the line while leaving the slope universal.

Millikan's confirmation, against his own expectation. Robert Millikan, deeply skeptical of the photon, undertook a meticulous program through 1916 to test the linear relation. His results verified \(KE_\text{max} = hf - \varphi\) across several alkali metals and returned a value of \(h\), from the slope, in agreement with Planck's blackbody value. The convergence of two utterly different phenomena, thermal radiation and photoemission, on the same constant was powerful evidence that \(h\) is fundamental rather than a fitting trick. Einstein was awarded the 1921 Nobel Prize for the discovery of the law of the photoelectric effect.

Intensity is photon flux, and the statistics are quantum. In the quantum picture, intensity is the number of quanta arriving per unit time, not the energy per quantum, and this dissolves the paradoxes at once. More intensity means more independent one-photon absorption events, hence more photoelectrons of unchanged energy, while the energy per event, and therefore \(KE_\text{max}\), is fixed by frequency alone. The absence of any delay follows because no accumulation is needed; a single absorption suffices. Photoemission is therefore intrinsically probabilistic, each photon either ejecting an electron or not, a foreshadowing of the quantum mechanics still to come.

And here is what the metal plate was really showing. Light that produces flawless interference fringes, the unmistakable signature of a wave, also arrives in indivisible lumps that strike one electron at a time, the unmistakable signature of a particle. The photoelectric effect did not overturn the wave theory; it forced both descriptions to be true at once, and that refusal to choose is the heart of quantum mechanics. The Compton effect in 1923, giving photons momentum as well as energy, sealed the case. The deepest surprise is not that Einstein won his only Nobel for this rather than for relativity, but that the whole quantum revolution can be traced to one stubborn fact: the colour of light, not its brightness, decides whether an electron flies free.