What is the photoelectric effect and how does it provide evidence for the quantisation of light?

During the experiment that shows this effect, light is shone on a metal plate. This causes electrons to be emitted from the surface of the metal, but only if the frequency of the light is above a threshold frequency. For example, UV light may cause electrons to be emitted, but red light might not, no matter how high the intensity or how long the light is shone for. Above this threshold, increasing the frequency increases the kinetic energy of the electrons, and increasing the intensity of the light increases the rate at which electrons are emitted.Electrons require a certain amount of energy to escape from the surface of the metal, known as the work function, so if the energy transferred is less than this, the electron will not be emitted. According to the classical wave theory of light, the energy is continuous and spread over the whole surface. Therefore, it should be the intensity, not the frequency of the light that determines whether or not electrons are emitted, but this isn't the case experimentally. This instead provides evidence for the existence of photons, as quantised packets of energy. Each electron absorbs one photon, so each photon must have enough energy to cause one electron to be emitted, and any additional energy above the work function is transferred to kinetic energy of the electron. The energy of the photon is related to the frequency by E=hf, with h being the Planck constant. As higher intensity light would mean more photons, this also provides an explanation for the intensity of light increasing the rate of photons being released, rather than the energy of the photons.