Mostly known as the phenomenon of emission or ejection of electrons from a metal when light shines on it. In a wider sense, it is ejection of electrons or ions from any solid, liquid or gas, caused by radiation of energy in the region of visible or ultraviolet light, X rays, or gamma rays. The effect is widely used to convert a light signal into an electric current.

This was one of the mysteries with the classical Newtonian physics that lead to the quantum theory. Albert Einstein was awarded the Nobel Prize for explanation of the Photoelectric Effect in 1921.

At the beginning of the century, the photoelectric effect was known in the form of a current generated by light shining on a metal.  Before Einstein came with the solution, no one could figure out why below a certain frequency of light rays on the metal, there was no electric current at all. This meant that electrons could not be pulled away from the atoms at these radiation frequencies. Above this frequency an electric current emerged and the energy of the electrons seemed to be proportional to the frequency of the incident light

Both 1)the lack of current at low frequencies and the 2)proportionality of kinetic energy of emitted electrons to frequency and not intensity was against the theory at that time.

Einstein realized that electromagnetic radiation exchanges energy with electrons in portions, quanta, contrary to the expectations of classical radiation theory where light was thought of as waves. With the concept of quantified energy portions of light - later denoted photons, Einstein was able to show that the exchanged energy portion was proportional to the frequency of incident radiation. 

The proportionality factor for the photoelectric effect turned out to be the same that was obtained by Max Planck to explain the spectral distribution of black body radiation, which is also heavily dependent of the concept of quantified energy.

When electromagnetic radiation is incident on the surface of certain metals electrons may be ejected. A photon of energy hf penetrates the material and is absorbed by an electron. If enough energy is available, the electron will be raised to the surface and ejected with some kinetic energy, ½mv2. Depending on how deep in the material they are, electrons have a range of valuesof KE will be emitted. Let φ be the energy required for an electron to break free of the surface, the so-called work function. For electrons up near the surface to begin with, an amount of energy (hf - φ) will be available and this is the maximum kinetic energy that can be imparted to any electron.
Accordingly, Einstein's photoelectric equation is

½mv2max = hf - φ

The energy of the ejected electron may be found by determining what potential difference must be applied to stop its motion; then ½mv2 = Vse. For the most energetic electron,

hf - φ = Vse

where Vsis called the stopping potential.

For any surface, the radiation must be of short enough wavelength so that the photon energy hf is large enough to eject the electron. At the threshold wavelength (or the well-known frequency), the photon's energy just equals the work function. For ordinary metals the treshhold wavelength lies in the visible or ultraviolet range. X-rays will eject photoelectrons readily; far-infrared photons will not.

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