The photoelectric effect

An experiment that defeats classical physics

By the end of the 19th century, light is firmly described as a wave (interference, diffraction). But one experiment resists: when you shine light on a metal plate, it can eject electrons. This is the photoelectric effect.

     incident light
        \  \  \  \
         \  \  \  \        e-  (ejected electron)
          v  v  v  v      /
     ====================
     |||||  METAL  |||||   <- metal plate
     ====================

What wave theory predicts... and gets wrong

If light were a simple wave, its energy would depend on its intensity (its brightness). We would therefore expect that:

• a more intense light would tear off more energetic electrons;
• any colour would eventually work, if you wait long enough or shine brightly enough.

The experiment says exactly the opposite:

   Observation                          Wave prediction
   -----------------------------------  ----------------------------
   Below a threshold frequency,         "Enough intensity always
   NO electron, however intense         ends up working"        -> FALSE

   Above threshold, the energy of the   "Intensity sets
   electrons depends on FREQUENCY,      the electrons' energy"  -> FALSE
   not on intensity

   Ejection is INSTANTANEOUS            "A charge-up time is needed" -> FALSE

There is a threshold frequency below which nothing happens, whatever the intensity. A very powerful red light tears off nothing, whereas a faint ultraviolet light does so immediately.

Einstein's explanation (1905): light is grainy

Einstein puts forward a radical idea: light does not arrive continuously, but in indivisible grains of energy, the photons. A photon's energy depends only on the frequency f of the light:

   E = h × f

where h is the Planck constant (h ≈ 6,63 × 10^-34 J·s), one of the fundamental constants of the universe.

An electron is ejected when a single photon gives it all its energy at once. It's all or nothing:

   photon (E = hf)                   e- ejected if  hf > W
        \                           /              (W = work function)
         v                         /
      --- e- ---  (bound to the metal)

• If hf is less than the work function W (the energy holding the electron), the photon does not have enough energy: nothing happens, even with billions of photons. That is the threshold frequency.
• If hf exceeds W, the electron leaves, and its kinetic energy equals the surplus:

   E_kinetic = hf - W

Increasing the intensity means sending more photons: so more electrons ejected, but not more energetic. Increasing the frequency means making each photon more energetic: so faster electrons. Everything finally fits.

In summary

The photoelectric effect cannot be explained if light is a continuous wave. Einstein solved it by postulating that light is made of photons, grains of energy E = hf. An electron is ejected only if a photon brings it, all at once, more than the work function. This is the first proof that light has a particle nature.