The Photoelectric Effect
Turn the lamp up as far as you like. Below a certain colour, not one electron comes out.
The Photoelectric Effect visualization
Each dot in the beam is one photon. Blue dots are electrons that got across; rose ones are electrons the retarding field turned back before they reached the collector.
What to try first
Start on sodium with the beam at half power. Drag the frequency slider down towards the red end and watch the current fall to nothing at 5.51×10¹⁴ Hz — 544 nm, a yellow-green. Now turn the intensity to 100%. Nothing comes back. Not a trickle, not a delayed trickle: nothing.
Then push the frequency back up and raise the retarding voltage until the current dies again. Note the voltage. Double the intensity and find it again. It has not moved.
Read Planck’s constant off the slope
Stopping voltage against frequency, for all four metals. Four parallel lines: changing the metal slides the line sideways without ever tilting it.
The slope figure is a least-squares fit to the plotted points, not a constant typed in — but be clear about what that proves. These points were generated from Einstein’s equation, so recovering h from them is a check on the arithmetic, not on nature. What is remarkable is that Robert Millikan, measuring real photocurrents from real alkali metals between 1912 and 1916 in an effort to disprove the photon, got the same slope to within half a percent — and said so in print while still calling the theory “untenable”.
Why this broke classical physics
Light was a wave, and a wave carries energy in proportion to its amplitude. Shine a brighter beam on a metal and each electron should soak up energy faster, so it should leave sooner and leave faster. Shine a dim beam and the electrons should still come — you would just have to wait while they accumulated enough energy. Frequency should not enter into it at all.
Every one of those predictions is wrong. Brightness changes how many electrons come out and not how fast they move. Frequency changes how fast they move and not how many. And below a threshold frequency the wait is not long, it is infinite: the metal sits there in a blaze of light and emits nothing.
One photon, one electron
Einstein’s 1905 answer was that light arrives in indivisible lumps of energy hf, and that an electron absorbs one whole lump or none. Freeing it from the metal costs a fixed toll — the work function φ, a property of the surface — and whatever is left over becomes kinetic energy:
KE_max = hf − φ
Intensity does not appear in that equation. It sets the number of lumps arriving per second, which sets the number of electrons leaving per second — the current — and nothing else. If one lump is too small to pay the toll, a million of them per second are still each too small, because they cannot pool their energy. That is the threshold, and it is the sentence a wave cannot say.
What the stopping voltage measures
Make the collector negative and it pushes the electrons back. An electron with 1.5 eV of kinetic energy can climb 1.5 volts and no further, so as you raise the retarding voltage you cut off slower and slower electrons until, at exactly V_stop, even the fastest one falls short. The current reaches zero, and eV_stop = KE_max.
That is why the graph above is the experiment’s payoff rather than a decoration. Plot V_stop against f and you get a straight line of slope h/e, the same slope for sodium and for platinum — a constant of nature falling out of a voltmeter reading. The metal you chose changes only where the line crosses the axis, at f₀ = φ/h.
Where you have already used it
The photomultiplier tubes that count individual photons in particle detectors are photoelectric cells with an amplifier bolted on. So is the light meter that decides your phone camera’s exposure, and so are the sensors in the automatic doors you walked through this week.
The same energy accounting explains why ultraviolet light burns skin and radio waves from a transmitter a thousand times more powerful do not. Damage is done one photon at a time, and a photon that cannot pay the ionisation toll cannot pay it in bulk either. Einstein got his Nobel Prize for this paper, not for relativity.