E = hf · KEmax = hf − φ · and the end of light as only a wave
Shine red light on caesium as brightly as you like and not one electron leaves. Shine the faintest violet and they come off at once. No wave theory can produce that result, and the experiment that showed it is where the quantum century begins.
This page covers the four observations a wave picture cannot explain, the photon that explains all four at once, the work function of a metal, and the straight line whose gradient is Planck's constant. By the end you'll be able to:
Not relativity — this. It is also the operating principle of every solar panel, camera sensor and automatic door in the world:
Searched as: photoelectric effect explanation, work function, threshold frequency, stopping potential, einstein photoelectric equation, why wave theory fails.
Predict the stopping voltage, lock it, then drag the brightness from one end to the other and watch what refuses to move. 🟢 real KE = hf − φ engine
Guess, then lock — the bench waits until you commit.
Set a wavelength and a metal, then drag the brightness across its whole range and watch what does not move.
Six results from the laboratory. For each one, decide whether the frequency, the brightness or the metal is responsible — that is the whole argument.
Bright red light shone on caesium, and nothing at all comes off. What decides this?
Ask whether the change is about how much energy each photon carries, or simply how many of them arrive.
A wave picture gets three of these six exactly backwards, which is why the experiment mattered.
A caesium photocell, and a target stopping voltage. Choose a wavelength that delivers it — 3 attempts.
Set the wavelength, then shine it. eVₛ = hf − φ.
Each claim breaks something the experiment actually shows. Tap the broken idea.
An electron absorbs one photon or none. If a single red photon carries less than the work function, no number of them will help, and the threshold is absolute rather than gradual.
Speed comes from the energy of the single photon each electron absorbs, and brightness does not change what one photon carries. Doubling it doubles the NUMBER of electrons and leaves the stopping voltage exactly where it was.
The measured delay is under a nanosecond however dim the light is. A wave picture predicts minutes of accumulation for a faint source, and that delay has never been observed — emission is immediate or it does not happen.
Thinking beats memorising. Sort every claim about the photoelectric effect into three boxes.
One change is made to the experiment. Say whether the current goes up, the maximum kinetic energy goes up, or neither does.
Ask whether the change alters the energy of each photon or only how many arrive.
A photocell answers to everything shorter than its own cut-off wavelength. Pick a job, then pick a work function that matches it.
λ₀ = hc/φ — a bigger work function means a shorter cut-off.
Read the scene. All three are the same threshold, wearing ordinary clothes.
Silicon has a threshold around 1.1 eV, so every infrared photon below it passes through without freeing anything, and every photon well above it wastes the surplus as heat. Those two losses together cap a simple silicon cell at about a third, before any manufacturing issue is considered.
It is a threshold, exactly like the photoelectric one. Breaking a chemical bond in skin needs a photon above a certain energy, and visible photons fall short however many arrive. The ultraviolet in sunlight clears it, which is why a lamp a hundred times brighter still cannot burn you.
Each pixel counts the electrons freed by arriving photons. When only a handful arrive, the count naturally varies between neighbouring pixels, and that variation is the grain. You are looking at the discreteness of light itself.
In plain terms: light does not deliver its energy smoothly. It arrives in countable packets, one electron takes one packet, and everything strange about this experiment follows from that.
A photon carries E = hf, and an electron absorbs one of them entirely or not at all. It cannot save up two half-payments. That single rule explains why a threshold exists: if one photon is short of the escape cost, a billion of them are still each short of it, and the metal stays quiet however bright the lamp.
Getting out of a metal costs a minimum amount of energy called the work function, φ, which differs from metal to metal — 2.1 eV for caesium, 5.65 for platinum. Whatever the photon brought beyond that becomes kinetic energy, so KEmax = hf − φ. It says maximum because electrons starting deeper in the metal lose more on the way out.
A wave spreads its energy smoothly, so a faint wave should free electrons slowly rather than not at all, and a brighter wave should free them faster. The experiment says the opposite on both counts: emission is instant or absent, and brightness changes only the number. Four separate results, and the photon explains all four with one line of arithmetic.
The stopping voltage measures the fastest electrons, not the average, which is why the formula carries the word maximum. A graph of KE against frequency is a straight line of gradient h for every metal, with only the intercept changing — which is how Millikan measured Planck's constant. And light still diffracts and interferes, so this experiment did not replace the wave picture; it proved one picture was never going to be enough.
Exams reward the method. Work it one step at a time — read the thought, predict the line, then reveal it.
Three small labs. The middle one is the one that ended the argument.
Six wrong ideas, most of them borrowed from the wave picture it overturned. Tap a card to bust the myth.
While proving radio waves exist, Hertz found that ultraviolet light made a spark gap fire more easily. He reported it and moved on; nobody could explain it.
Planck found that treating energy as coming in small fixed amounts fixed the equations for radiation from hot objects. He regarded it as a mathematical device.
He proposed that light itself really does arrive as packets of energy hf, and wrote down KE = hf − φ. The idea was rejected by almost everyone, including Planck.
Ten years of precise measurement intended to refute Einstein produced a perfect straight line of gradient h. Millikan published the result and said plainly that the equation held.
Einstein received it for this, not for relativity. The committee wanted something experimentally settled, and by then this was.
Photons above the threshold free charge carriers; the rest pass through or waste their surplus as heat, which is why efficiency has a ceiling.
Each pixel counts freed electrons. In very low light the grain you see is the random arrival of individual photons.
A beam keeps a photocell current flowing. Break the beam and the current stops, which is the signal to open.
One sentence each: what is being counted, and what it is counted for.
Drag the slider. Six photon energies, and what a single one of each can and cannot do.
Twelve orders of magnitude of photon energy, and a threshold sitting somewhere in every material.
Each one is a build and a measurement — the measuring is what turns a demo into a project.
Build: a freshly cleaned zinc plate on a charged electroscope, lit first by a bright lamp and then by an ultraviolet source.
Measure: the time for the leaf to fall in each case. The lamp does nothing at all; the ultraviolet source discharges it in seconds.
Build: a small solar cell, a lamp, and coloured filters that pass roughly equal amounts of light.
Measure: the voltage for each colour at matched brightness, and see how it tracks the wavelength.
Build: several LEDs of known wavelength, each on a variable supply with a meter.
Measure: the turn-on voltage of each, plot it against 1/λ, and the gradient gives hc/e to within a few per cent.
Build: a school photocell with a variable retarding voltage and four narrow-band filters.
Measure: the stopping voltage for each filter, plot against frequency, and read h off the gradient and φ off the intercept.
Build: a camera on manual, photographing an almost dark scene at rising ISO settings.
Measure: the pixel-to-pixel variation in a flat patch. It should grow as the square root of the count, which is what a countable arrival predicts.
Build: a photocell and a simple grating or prism spreading a lamp's light across it.
Measure: the longest wavelength that still gives a reading, then work backwards to φ = hc/λ₀ and identify the metal.
Straight answers, each one complete on its own:
Because an electron absorbs one photon or none, and cannot combine several. A red photon carries less energy than the metal's work function, so it cannot pay the escape cost no matter how many of its companions arrive. A violet photon carries more than the cost, so every one that is absorbed frees an electron, even if only a handful arrive each second.
It is the minimum energy an electron needs to escape from the surface of a particular metal, and it is a property of that metal alone. Caesium's is about 2.1 electronvolts and platinum's about 5.65, which is why caesium responds to visible light and platinum needs deep ultraviolet. It is the amount subtracted in Einstein's equation.
Because only electrons right at the surface escape having paid exactly the work function. Electrons starting deeper inside lose additional energy on the way out through collisions, so they emerge more slowly. The result is a spread of speeds from zero up to a maximum, and it is that maximum which hf minus φ predicts and which the stopping voltage measures.
It is the reverse voltage just large enough to turn back even the fastest electron, so the current falls to zero. Since an electron crossing a potential difference V loses energy eV, the stopping voltage multiplied by the electron charge equals the maximum kinetic energy. In electronvolts the two are numerically the same, which is why the unit is so convenient here.
No. Light diffracts round edges and produces interference fringes, and only waves do that. It also arrives in countable packets with a hard energy threshold, and only particles do that. Both sets of experiments are reliable, so physics accepted that neither picture on its own is complete. That acceptance is what wave–particle duality means.
A wave spreads its energy over the whole surface, so a very faint wave would need a long time — minutes, on the arithmetic — for any one electron to accumulate enough to escape. Measurements found emission beginning within about a nanosecond however faint the source. That rules out accumulation entirely and points straight at a single concentrated packet doing the whole job at once.
Because it belongs to light rather than to the metal. Plot maximum kinetic energy against frequency for caesium, sodium and zinc and you get three parallel lines: the intercept shifts, because that is the work function, but the gradient is identical because it is h. Millikan used precisely that to measure h to within about half a per cent.
Two losses, both from this chapter. Photons with less than the threshold energy pass straight through and contribute nothing, which throws away much of the infrared in sunlight. Photons with far more than the threshold free one carrier each and waste the surplus as heat. Together these cap a single-junction silicon cell at about a third even in theory, before any practical losses.
Spot these before the exam does.
Seven question formats, the way LLOS.ai serves them — multiple choice, multiple-correct, fill-in-the-blank, match, sequence, read-think-connect, and write-your-own. Every question has layered hints: a quick nudge, the reasoning, then a deeper connection — so a wrong answer opens a door, never a dead end. 🟢 received from a board-tagged question bank · seed toward 2,000
Pick your board — the set re-tunes to its wording and emphasis. Competitive draws the JEE / NEET / Olympiad lane.
Four setups, four different lamps and metals. Tap them in order, fastest electrons first. Then read the arithmetic — one of them produces nothing at all.
650 nm red, turned up as bright as the supply allows, on caesium.
410 nm violet, barely visible in a dark room, on caesium.
250 nm ultraviolet at moderate brightness, on zinc.
532 nm green, bright and steady, on caesium.
Tap the four in the order you believe, fastest electrons first.
Millikan spent ten years trying to prove Einstein wrong about this and measured Planck's constant instead. That is what a good experiment does to a good argument.