# Explain the photoelectric effect. Photoelectric effect commonly refers to the behavior of electrons that are ejected from the surface of a metal due to the light shining on the metal. Photoelectric effect was first noticed by Hertz at the end of the 19th century in the course of his experiments involving electromagnetic waves. The unusual characteristics of the current (stream of electrons) emitted from the metal were later (in the beginning of the 20th century) explained by Einstein.

In order for an electron to be ejected from the surface of the metal, it needs to posses a certain amount of energy in order to overcome the electric forces binding it to the metal. This amount of energy is called work-function and it depends on the type of metal.

According to the laws of classical physics, it would be expected that the kinetic energy with which electrons leave metal would depend on the intensity of incident light, because more intense light would impart more energy to the electrons. However, this is not what was observed. The kinetic energy was measured to be dependent not on intensity, but instead, on the frequency of the incident light. Again, this was surprising because the energy carried by light, thought of as electromagnetic wave, depends only on the wave's amplitude, but not frequency. Moreover, it was found that if the frequency of the incident light was too low, no electrons were emitted at all, no matter how intense the light was.

Einstein explained these results by using the Planck hypothesis that the light can be thought of as composed of quanta ("pieces") of energy proportional to its frequency:

`E = hnu`

Here, h is the Planck's constant and

`nu`

is the frequency.

The photoelectric equation, obtain experimentally, is

`K= hnu - phi` , where

`K = mv^2/2` is the kinetic energy of electrons (proportional to the square of the speed) and

`phi` is the work-function of the metal. From here, it can be seen that if the frequency `nu` is too low, there is no sufficient energy for the electrons to leave the metal. The threshold frequency is determined by setting K = 0, corresponding to the electrons leaving the metal with no extra energy. Then,

the threshold frequency equals

`nu = phi/h`

No electrons is emitted if the light incident on the metal has the frequency below this value.

These results were significant because they supported the understanding of the dual nature of light: light can behave either as an electromagnetic wave, or as a stream of massless particles called photons.