Einstein's Explanation: The Photon

In 1905, Einstein proposed a radical idea: light does not arrive as a continuous flow, but as grains of energy, photons. The energy of a photon depends only on the frequency:

   E = h·ν        (h = Planck constant = 6.63 x 10^-34 J·s)

An electron in the metal absorbs one photon, all at once, and receives its energy hν. But to escape from the metal, it must first pay a "toll": the work function W₀ (the energy that binds it to the metal). The balance is a simple subtraction:

   E_c,max = h·ν − W₀      (maximum kinetic energy of the ejected electron)

Everything becomes clear. If hν < W₀, the photon does not have enough energy: the electron does not get out, whatever the intensity. Hence the threshold frequency:

   ν₀ = W₀ / h        (below it: no emission)

Increasing the intensity means sending more photons: so more electrons are ejected, but each one still receives hν — their energy does not change. And since the absorption of a photon is a single event, emission is instantaneous.

   photon hν  ->  |--- W₀ (toll) ---|--- E_c,max ---|

This explanation, precisely confirmed by Millikan, won Einstein the Nobel Prize in 1921. It sealed a revolution: light is both wave and particle.