PHOTOELECTRIC
E = hf − φ — below threshold, a floodlight ejects nothing; above it, a glimmer.
Use the simulation above to change the variables and play through the guided stages. The explanation below describes the default starting values; the simulation updates its explanation as you experiment.
Setup
One color of light falls on a metal plate in a vacuum tube, with a brightness dial on the lamp. The wave story says brightness is energy — crank the dial and electrons must eventually boil off, whatever the color. The plate disagrees.
The quantum ledger
Einstein’s 1905 wager: light arrives in packets of E = hf, and one electron absorbs one packet. The exit fee is the work function φ; whatever remains — hf minus φ — leaves as the electron’s kinetic energy. One line of arithmetic, and it carries the whole quantum.
What intensity cannot buy
Intensity sets how many packets arrive per second, never their energy. Below f₀ no electron leaves; exactly at f₀ electrons can just emerge with zero maximum kinetic energy; above it the excess becomes kinetic energy.
The stream
The stream runs: packet arrivals at a rate proportional to intensity — the spacing is presentational and says so — while every energy on screen stays exact. Turn the dial and watch the count change while the stopping voltage refuses to move.
Audit
Audited: both stopping-voltage routes agree; the Millikan slope is h; the exact-threshold branch reports emitted electrons with KE_max = V_s = 0 rather than misclassifying equality; and intensity leaves every energy unchanged.