The photoelectric effect

Brighter light does not give electrons more energy. Bluer light does. Four small facts about a metal plate that no wave theory can survive — and the work Einstein actually got his Nobel Prize for.

1887 – 192118 min

By the end you should be able to

List the four experimental facts that classical wave theory cannot accommodate
Use E = hν − φ to predict whether a given colour will eject electrons from a given metal
Explain why Einstein’s light quantum was far more radical than Planck’s

The story starts with an annoyance. In 1887 Heinrich Hertz was performing the experiment from Act 1 — generating electromagnetic waves in one spark gap and detecting them in another, confirming Maxwell. The detecting spark was faint and hard to see, so he built a dark enclosure around it. And the spark got weaker. Hertz chased it down carefully and established that ultraviolet light falling on the electrodes made sparking easier. He published a thorough description, stated plainly that he had no explanation, and returned to the waves. He had just discovered, as a nuisance, the effect that would undermine the wave theory he was in the middle of proving.

Philipp Lenard photographed in 1900, in a high collar and dark jacket. — Philipp Lenard in 1900, two years before the measurements that made no sense. He established every one of the four facts this lesson turns on, won the 1905 Nobel Prize for the work — and spent the rest of his life rejecting the explanation, eventually on grounds that had nothing to do with physics.

The effect is easy to state: shine light on a clean metal surface and electrons come off. And it is unusually well suited to measurement, because you can get at both quantities that matter. How many — collect the electrons on a second plate and measure the current. How energetic — apply a reverse voltage that pushes them back. Increase it until the current just stops. At that point the electric potential energy exactly cancels the electrons' kinetic energy, so the stopping voltage gives you the maximum energy directly, in electronvolts. Philipp Lenard, who had been Hertz's assistant, did this systematically in 1902. What he found made no sense at all.

Go redder until emission stops, then turn the brightness to maximum. Then go bluer and turn it right down.

Loading the metal plate…

Sodium has a work function of 2.28 eV, so its threshold is 544 nm — green. The classical delay shown is computed, not asserted: it is how long a wave of that brightness would need to deposit the work function onto a single atom’s cross-section. Compare it with the measured bound of under a nanosecond.

Four facts, and a wave theory that predicts the opposite of each

1. There is a threshold frequency. Below it, no electrons emerge at any intensity, for any length of exposure. A wave says: brightness is energy per second. Enough of it, for long enough, must eventually free an electron. 2. Above threshold, emission is immediate — under a nanosecond, however faint the light. A wave says: dim light delivers energy slowly to each atom, so there must be a measurable delay while it accumulates. For a modest source that delay works out to hours or days. 3. Maximum electron energy depends on frequency, not intensity. A wave says: energy is amplitude. Brighter light must give faster electrons. 4. Intensity controls the number of electrons, not their energy. A wave says: there is no reason for these to separate at all. These are not subtle discrepancies to be argued over. Each one is the reverse of what the theory demands, and the theory in question had just unified electricity, magnetism and light.

In 1905 — the same year as special relativity, E = mc², and the paper on Brownian motion that finally convinced people atoms exist — Einstein published something under a deliberately hedged title: On a Heuristic Viewpoint Concerning the Production and Transformation of Light. Heuristic means: a useful way of looking at it, not necessarily true. He was being careful, and he was right to be. The proposal is that light itself is grainy. Not that oscillators emit in lumps — that was Planck, and Planck thought it was a bookkeeping trick. Einstein's claim is that a beam of light is a hail of localised packets, each carrying energy hν, and that each packet is absorbed whole, by a single electron, in a single event.

Much worse than Planck

It is easy to file this under "Einstein extended Planck's idea". He did not extend it; he went somewhere Planck refused to follow. Planck quantised the oscillators in the cavity wall — matter, not light — and regarded even that as a formal device to be explained away later. The electromagnetic field stayed classical and continuous. Einstein said the field itself is lumpy. That contradicts a century of settled physics. Interference, diffraction, polarisation — Young's double slit, Fresnel's calculations, the whole edifice from Act 1 — all say light is a wave. Maxwell's equations describe a smooth continuous field and had just triumphantly predicted the speed of light. None of it is wrong; all of it is confirmed daily. So Einstein was not repairing a loose end. He was proposing that light is somehow both, without being able to say how. That is why he hedged the title, and why nobody believed him.

The experiment

Lenard’s systematic study of the effect

Philipp Lenard, formerly Hertz’s assistant · 1902 · University of Kiel

The question: When light ejects electrons from a metal, what determines how many come off and how fast they are moving — and does it behave as a wave theory requires?
The apparatus: An evacuated tube with a clean metal cathode illuminated through a quartz window (quartz rather than glass, because glass absorbs ultraviolet). Ejected electrons were collected on an anode and measured as a current. A retarding potential applied between the electrodes was raised until the current fell to zero, giving the maximum electron energy directly. Carbon-arc sources of varying intensity, and filters to select the spectral region.

Theory predicted

On classical wave theory, brighter light carries more energy per second, so it should eject electrons with greater kinetic energy, and light of any colour should work if you wait long enough.

They measured

The stopping potential — and therefore the maximum electron energy — was completely independent of intensity, over a range of about 1000 in brightness. Intensity controlled only the number of electrons. Energy instead depended on the colour of the light, and below a certain frequency no electrons appeared at all.

How sure could they be? Lenard established the intensity independence and the existence of a threshold convincingly. His frequency measurements were much cruder — his sources had broad, poorly characterised spectra — so he could not establish the linear relation K = hν − φ. That took Millikan, and fourteen more years.

Why it mattered

The result that made the photoelectric effect a crisis rather than a curiosity. Lenard received the 1905 Nobel Prize (for cathode rays), and never accepted Einstein’s explanation of his own experiment — he later became an enthusiastic Nazi and a leading figure in the "Deutsche Physik" movement that denounced relativity as Jewish science. Being an excellent experimentalist offers no protection whatever against being a bad judge of theory, or of anything else.

That he may sometimes have missed the target in his speculations, as for example in his hypothesis of light quanta, cannot really be held too much against him.
Max Planck and colleaguesrecommending Einstein for the Prussian Academy of Sciences, 1913

You might think

Einstein won the Nobel Prize for relativity.

Actually

He did not. The 1921 prize citation reads: "for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect." Relativity is not mentioned, and the omission was deliberate — it was still regarded as too speculative and too contested, and there was organised opposition to honouring it, some of it from Lenard and some of it antisemitic. The committee chose the safest of Einstein’s results. There is an irony in this: they picked the light quantum as the uncontroversial option, when it was arguably the more revolutionary idea of the two, and had itself been rejected by nearly everyone for fifteen years. It only became safe to reward once Millikan had spent a decade failing to disprove it.

1887Hertz notices ultraviolet light assisting a spark, while proving Maxwell right. Reports it without explanation.
1888Hallwachs shows a negatively charged zinc plate loses its charge under ultraviolet.
1899J.J. Thomson identifies the emitted particles as electrons.
1902Lenard establishes that electron energy is independent of intensity, and that a threshold exists.
1905Einstein proposes light quanta and K = hν − φ. Almost nobody accepts it.
1916Millikan confirms the equation to within 0.5%, having set out to refute it.
1921Einstein receives the Nobel Prize — for this, not for relativity.
1926Gilbert Lewis coins the word "photon".

Where this leaves us

Light arrives in packets. The evidence is direct, quantitative, and it is not going away. Light also diffracts and interferes. Send it through two slits and you get a pattern that only makes sense if each part of the beam is spread out across both slits at once. That evidence is equally direct, and it is two hundred years old. Particles do not do that. Waves do not arrive in lumps. Both bodies of evidence are overwhelming and they appear to be incompatible. This tension does not get resolved in this act — and it is about to get considerably worse. Within twenty years, someone will demonstrate that electrons diffract too, and electrons are the thing everybody was most confident was a particle. But first: Robert Millikan read Einstein's paper, decided it was obviously wrong, and set out to prove it.