Why does the colour of light matter more than its brightness in the photoelectric effect?

Because light delivers its energy in photons, and each photon carries energy set by its frequency (E = hf, or hc/λ = 1240/λ in eV with λ in nm), not by how many photons there are. One photon ejects at most one electron, giving it KEmax = hf − φ. Turning up the brightness sends more photons, so more electrons come off — a larger current — but each still leaves with the same maximum energy. Only raising the frequency (bluer light) raises that energy. This is the observation classical wave theory could not explain.

What is the threshold, and why does it differ between metals?

Every metal holds its electrons with a characteristic binding energy called the work function φ. A photon must carry at least that much energy to free one, so there is a threshold wavelength λ0 = 1240/φ above which no electrons emerge, however intense the light. Because φ ranges from 2.10 eV for cesium to 6.35 eV for platinum, the thresholds range from 590 nm (cesium responds to visible light) down to 195 nm (platinum needs deep ultraviolet). Cesium, sodium and calcium work under visible light; zinc, copper, silver and platinum require UV.

Can you really measure Planck’s constant this way?

Yes — that is exactly what Millikan did in 1916. Plot the maximum electron energy against light frequency and you get a straight line, KEmax = hf − φ; its slope is Planck’s constant (divided by the electron charge, since we measure energy in eV). Taking two points off the simulator’s numbers gives a slope of 4.136×10⁻¹⁵ eV·s, so h = 6.63×10⁻³⁴ J·s — within 0.01% of the accepted 6.626×10⁻³⁴. The line’s x-intercept is the metal’s threshold frequency.

Quantum

The Photoelectric Effect: Frequency Beats Brightness

By Lucian — builder & engineer, LK Forge

Shine light on a metal and electrons can fly off — but whether they do, and how fast, depends on the light’s colour, not how bright it is. A dim blue lamp works where a blazing red one does nothing. That refusal to behave like a wave is what forced physics to accept the photon, and it is a straight line on a graph whose slope is one of nature’s fundamental constants. We took the numbers from the photoelectric lab and read that constant off.

September 10, 2026 · 6 min read · exact from KEmax = hf − φ

6.63×10⁻³⁴

Planck’s constant, read off the slope (accepted 6.626)

590 nm

cesium’s threshold — plain visible light ejects electrons

195 nm

platinum needs deep UV to emit at all

none

effect of brightness on an electron’s maximum energy

The line that weighs a constant

Plot the maximum electron energy against the light’s frequency and every metal gives the same straight line, just shifted sideways. The slope is universal — it is Planck’s constant h (over the electron charge, since the y-axis is in electron-volts) — and only the point where each line crosses zero, the threshold frequency, tells the metals apart. This is Millikan’s 1916 measurement in one picture: the parallel lines below are cesium, sodium and zinc, sharing a slope of 4.14×10⁻¹⁵ eV·s.

KEmax vs frequency for cesium, sodium and zinc. Same slope (= h), different thresholds (the dots). Below its threshold a metal emits nothing; the slope never changes.

Every metal has its own gate

The threshold wavelength λ0 = 1240/φ is the longest wavelength (lowest energy) that can still free an electron. It sorts the metals into two camps: those cesium, sodium and calcium respond to ordinary visible light, while zinc, copper, silver and platinum stay dark until you reach into the ultraviolet. It is why the first practical photocells used cesium, and why a UV lamp will discharge a zinc plate that sunlight leaves alone.

Threshold wavelength λ0 = 1240/φ. Bars reaching into the green band respond to visible light; the violet ones need ultraviolet.

Why brightness is the wrong knob

A classical wave should pour more energy into the metal as you brighten it, so given enough time even dim red light ought to shake an electron loose, and brighter light ought to make faster electrons. Neither happens. Light arrives in photons, each carrying energy hf; one photon frees at most one electron and hands it KEmax = hf − φ, no more. Double the brightness and you double the number of photons — twice the electrons, twice the current — but each electron still leaves with the identical maximum energy 1.85 eV for 300 nm light on sodium, brightness be damned. Energy comes in grains, and their size is set by colour alone. That single sentence is the quantum revolution in miniature, and it is what Einstein’s 1921 Nobel Prize was for.

Reproduce it yourself

Two lines of physics; the third recovers Planck’s constant from the slope.

const hc = 1240;                     // eV·nm
const photonE = nm => hc / nm;       // eV
const keMax   = (nm, phi) => Math.max(0, photonE(nm) - phi);

// sodium, phi = 2.28 eV
keMax(400, 2.28);   // 0.82 eV      keMax(300, 2.28); // 1.85 eV
const l0 = hc / 2.28;               // 543.9 nm threshold

// Planck's constant from the KEmax-vs-frequency slope:
const c = 2.998e8, e = 1.602e-19;
const f = nm => c / (nm * 1e-9);
const slope = (keMax(250,2.28) - keMax(350,2.28)) / (f(250) - f(350)); // eV·s
const h = slope * e;                // 6.63e-34 J·s  (accepted 6.626e-34)

The photonE and keMax come straight from the photoelectric solver; the metal and slope sweeps are the small script behind this post.

Eject some electrons

Open the lab, switch metals, slide the wavelength past the threshold, and watch the current stop dead — then turn the brightness up and see the energy refuse to move.

Open the photoelectric lab →

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