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

In 1900, Max Planck fixed a broken formula by assuming energy came in discrete chunks. He called it a mathematical trick — a convenient fiction to make the numbers behave. He expected someone to come along and explain it away properly.

Someone did come along, five years later. But instead of explaining it away, he took Planck's idea and pushed it further than anyone had dared.

His name was Albert Einstein. He was twenty-six, working as a patent clerk in Bern, Switzerland. And he asked a question that changed physics forever: what if Planck's quanta aren't just a calculation trick — what if they're real?

A Strange Spark

The story starts in 1887, with a physicist named Heinrich Hertz who wasn't looking for anything unusual.

Hertz was experimenting with electromagnetic waves when he noticed something odd: ultraviolet light shining on a metal surface made the metal produce sparks more easily. Light was knocking something loose. Later experiments identified what it was — electrons, the negatively charged particles that make up the outer layers of atoms.

Shine light on a metal, and under the right conditions, electrons fly off the surface. This phenomenon got a name: the photoelectric effect.
The effect was repeatable and well-documented. The problem was that nobody could explain why it behaved the way it did.

What the Wave Theory Got Wrong

By the late 1800s, light was one of the best-understood things in physics. Maxwell's equations had proved, decisively, that light is an electromagnetic wave.

The theory explained reflection, refraction, and interference with extraordinary precision. Nobody doubted it.

So physicists applied wave theory to the photoelectric effect and made two perfectly reasonable predictions:

1. Brightness should be what matters. A brighter light beam carries more energy. Crank up the brightness enough and you should always be able to eject electrons — regardless of the light's color or frequency.

2. There should be a delay with dim light. Waves spread energy continuously across the metal surface. A weak light source would need time to "charge up" enough energy in the surface electrons before any of them could escape.

Both predictions made complete sense from a wave perspective. Both turned out to be completely wrong.

What Actually Happened

Philipp Lenard — a meticulous German experimentalist — studied the photoelectric effect carefully in the early 1900s. His results were baffling.

There is a threshold frequency. Below a certain frequency (specific to each metal), no electrons are ejected — ever. Not a trickle. None. You can flood the surface with the most intense low-frequency beam imaginable and nothing happens. But a faint high-frequency source ejects electrons immediately.

Brightness controls quantity, not energy. When electrons *are* ejected, a brighter light produces more of them — but each individual electron's energy depends only on the frequency, not the brightness. Double the brightness and you get twice as many electrons, each moving at exactly the same speed as before.

There is no delay. Even with an extremely dim light source, if the frequency is above the threshold, electrons are ejected the instant the light turns on. No accumulation, no waiting. Instantaneous.

The wave theory had no explanation for any of this. Why would frequency — rather than intensity — determine whether ejection happens at all? Waves don't work that way.

Einstein's Answer: Light Is Made of Particles

In 1905 — the same year he published special relativity — Einstein published a paper on the photoelectric effect. Its central claim was audacious.

He proposed that light is not a continuous wave. It is a stream of discrete particles, each carrying a fixed packet of energy. He called these particles light quanta. We call them photons.

The energy of each photon is determined entirely by its frequency:
> E = hf

This is Planck's equation — same formula, same constant h — but the interpretation is completely different. Planck said energy exchange between light and matter was quantized. Einstein said light itself is quantized, always, even in empty space.

With that single idea, every anomaly in the photoelectric effect has a clean explanation.

How It Works: The Work Function

Think of the electrons inside a metal as sitting at the bottom of a shallow pit. To escape, each electron needs a minimum amount of energy to climb out. This minimum is called the work function of the metal — a fixed threshold that differs from one material to another.

> For example: Cesium has a low work function, which makes it very sensitive to light — it's used in photodetectors and digital camera sensors. Gold has a high work function, which is part of why its surface electrons are tightly bound and resistant to chemical reactions.

When a photon arrives, it doesn't wash over the whole surface like a wave. It collides with a single electron and hands over all of its energy at once. What happens next depends on how much energy that photon carried:

- If the photon's energy is less than the work function, the electron can't escape. It doesn't matter how many such photons arrive — each one interacts with one electron, and none of them have enough energy to get out.

- If the photon's energy is greater than the work function, the electron escapes. Whatever energy is left over after clearing the threshold becomes the electron's kinetic energy — the speed it flies off with.

This gives a direct equation for the ejected electron's energy:

> KE = hf − φ

where φ (phi) is the work function of the metal.

Now Lenard's results make perfect sense. The threshold frequency exists because below it, no single photon carries enough energy to meet the work function. Brightness doesn't help because more brightness just means more photons arriving — not more energetic ones. And there's no delay because the interaction is instantaneous: one photon, one electron, right now or not at all.