Shine light on a metal and electrons fly off — but only above a threshold colour, and no amount of dim red light will do what a whisper of violet does instantly. Classical waves say brighter should mean faster; the metal disagrees. Einstein's cure: light arrives in lumps of energy hf, and one lump frees one electron. Down the centre: frequency and metal go in, the engine computes the maximum kinetic energy, the verdict comes out. Blue builds it; red tries to break it.
source Einstein, Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt, Ann. Phys. 17, 132–148 (1905) — ui.adsabs.harvard.edu/abs/1905AnP...322..132E. Rendered, not quoted.
An electron in the metal sits in a well of depth φ (the work function). A single quantum of light carries hf. If it frees the electron, whatever is left is kinetic energy:
KEmax = hf − φ
A line in frequency: slope h, intercept −φ. Below f₀ = φ/h the lump is too small — nothing comes out, at any brightness. Live for the current setting:
| quantity | value |
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Planck (1900) split the oven's glow into quanta hf to kill the ultraviolet catastrophe — but called it a bookkeeping trick. Einstein took the lump literally: a real particle of light, the photon.
the-plancks-law's mathematical lump is made a real particle here; that same photon is the quantum the-bohr-model's electron emits when it jumps. Each sphere is the next one's premise.
The blue team's live re-check: recover h from the slope of two frequencies, and confirm KEmax is unmoved by intensity while the threshold holds at every brightness. If red tampers, this badge turns red.
Two inputs decide everything: the light's frequency f (its colour — energy per lump) and the metal's work function φ (how deep the electron sits). A third dial, intensity, is the honest trap: classically it should matter, and it does not — it only sets how many lumps arrive per second.
Frequency is shown in units of 1014 Hz; energies in eV. Constants are exact SI: h = 6.62607015×10−34 J·s, e = 1.602176634×10−19 C, c = 2.99792458×108 m/s. Work functions are AMBER literature values (surface- and temperature-sensitive).
Slide below the threshold and the beam can be blinding — still nothing leaves. Cross it by a hair and electrons fly at once.
Every number is computed live from KE = hf − φ — never looked up. The line's slope is h; the intercept is −φ.
What the machine proves, live: KEmax is linear in frequency with slope h (recovered from two points), there is a hard threshold f₀=φ/h below which no electron leaves at any intensity, and doubling the brightness changes the electron count but never their maximum energy. The stopping voltage Vstop=KEmax/e is the same line.
The blue witness (left) confirms these live; the red team (right) tries to make them false.
And φ is not a clean number: it depends on crystal face, adsorbates, and temperature (Fowler's law smears the threshold near it). The values in the panel are AMBER approximations — the shape of the law is what is LIT, not the third decimal of any metal.
"Brighter light ejects faster electrons." Cut. Intensity raises only the number of electrons; KEmax depends on f alone. This is the exact fact the tamper (below) breaks.
"Any colour works if it's bright enough." Cut. Below f₀=φ/h, zero electrons at any intensity — the threshold is a wall, not a slope.
"Einstein discovered the effect." Kept, corrected. Hertz (1887) and Lenard saw it; Einstein explained it (1905); Millikan measured h from it (1916) while trying to disprove the photon — and confirmed it.
The red team's move: rewire the engine so KEmax feeds on intensity — exactly what classical wave theory wrongly predicted. The threshold and the energy–independent–of–intensity facts both collapse; the blue witness (7) recomputes and turns red.
Feed intensity into the energy and dim below-threshold light starts ejecting electrons, and brighter light "speeds them up" — the witness disagrees with the known law and turns red. Nothing is faked; the attack is real and it is caught.