Why does dim blue light knock electrons out of a metal when bright red light cannot?
In 1887 Heinrich Hertz noticed that light falling on a metal can make it give off electric charge. Later experiments showed what happens: the light knocks electrons out of the metal. This is the photoelectric effect, and it is how solar panels and light sensors work today.
If light is a wave, the explanation seems easy. A wave carries energy, and a brighter wave carries more. Shine bright enough light of any colour and the electrons should eventually shake loose.
Red light frees no electrons from sodium. What happens if you make the red light a hundred times brighter? Still none. Below a certain frequency (for sodium, wavelengths longer than about 540 nm) no electron comes out, however bright the light is. Above it, even very dim light frees electrons at once.
This is what the experiments found, and the wave picture cannot explain it. Whether electrons come out depends on the colour of the light, not on its brightness. Brightness only changes how many electrons come out, never how fast they fly.
Something about light comes in fixed amounts that depend on its colour. The next lesson tells the story of the young physicist who saw what it was.
Each metal needs a minimum energy to free one electron: its work function W. For sodium W ≈ 2.3 eV (an electronvolt, eV, is the energy an electron gains across one volt).
Light frees electrons only if its wavelength is shorter than hc / W: about 540 nm for sodium, which is green light.
The fastest electrons then carry the energy left over: Emax = hf − W. Violet light at 400 nm (3.1 eV) gives electrons of up to 0.8 eV.
Light frees electrons only above a certain frequency, however bright it is: light delivers its energy in fixed amounts set by its colour.