Einstien photoelectric effect

In the photoelectric effect, electrons are emitted from matter (metals and non-metallic solids, liquids or gases) as a consequence of their absorption of energy from electromagnetic radiation of very short wavelength, such as visible or ultraviolet light. Electrons emitted in this manner may be referred to as "photoelectrons".First observed by Heinrich Hertz in 1887, the phenomenon is also known as the "Hertz effect", although the latter term has fallen out of general use. Hertz observed and then showed that electrodes illuminated with ultraviolet light create electric sparks more easily.

The photoelectric effect requires photons with energies from a few electronvolts to over 1 MeV in high atomic number elements. Study of the photoelectric effect led to important steps in understanding the quantum nature of light and electrons and influenced the formation of the concept of wave–particle duality. Other phenomena where light affects the movement of electric charges include the photoconductive effect (also known as photoconductivity or photoresistivity), the photovoltaic effect, and the photoelectrochemical effect.

The photons of a light beam have a characteristic energy determined by the frequency of the light. In the photoemission process, if an electron within some material absorbs the energy of one photon and thus has more energy than the work function (the electron binding energy) of the material, it is ejected. If the photon energy is too low, the electron is unable to escape the material. Increasing the intensity of the light beam increases the number of photons in the light beam, and thus increases the number of electrons excited, but does not increase the energy that each electron possesses. The energy of the emitted electrons does not depend on the intensity of the incoming light, but only on the energy or frequency of the individual photons. It is an interaction between the incident photon and the outermost electron.

Electrons can absorb energy from photons when irradiated, but they usually follow an "all or nothing" principle. All of the energy from one photon must be absorbed and used to liberate one electron from atomic binding, or else the energy is re-emitted. If the photon energy is absorbed, some of the energy liberates the electron from the atom, and the rest contributes to the electron's kinetic energy as a free particle.[citation needed]
Experimental results of the photoelectric emission
For a given metal and frequency of incident radiation, the rate at which photoelectrons are ejected is directly proportional to the intensity of the incident light.
For a given metal, there exists a certain minimum frequency of incident radiation below which no photoelectrons can be emitted. This frequency is called the threshold frequency.
For a given metal of particular work function, increase in intensity of incident beam increases the magnitude of the photoelectric current, though stoppage voltage remains the same.
For a given metal of particular work function, increase in frequency of incident beam increases the maximum kinetic energy with which the photoelectrons are emitted, but the photoelectric current remains the same, though stoppage voltage increases.
Above the threshold frequency, the maximum kinetic energy of the emitted photoelectron depends on the frequency of the incident light, but is independent of the intensity of the incident light so long as the latter is not too high [5]
The time lag between the incidence of radiation and the emission of a photoelectron is very small, less than 10−9 second.
The direction of distribution of emitted electrons peaks in the direction of polarization (the direction of the electric field) of the incident light, if it is linearly polarized.[citation needed]
Mathematical description

The maximum kinetic energy Kmax of an ejected electron is given by


where h is the Planck constant, f is the frequency of the incident photon, and φ = hf0 is the work function (sometimes denoted W), which is the minimum energy required to remove a delocalised electron from the surface of any given metal. The work function, in turn, can be written as


where f0 is called the threshold frequency for the metal. The maximum kinetic energy of an ejected electron is


Because the kinetic energy of the electron must be positive, it follows that the frequency f of the incident photon must be greater than f0 in order for the photoelectric effect to occur
Stopping potential

The relation between current through an illuminated photoelectric system and applied voltage illustrates the nature of the photoelectric effect. For discussion, a plate P is illuminated by a light source, and any emitted electrons are collected at another plate electrode Q. The potential between P and Q can be varied and the current flowing in the external circuit between P and Q is measured.

If the frequency and the intensity of the incident radiation are kept fixed, it is found that the photoelectric current increases gradually with the increase in positive potential until all the photoelectrons emitted are collected. The photoelectric current attains saturation value and it does not increase further for any increase in the positive potential. The saturation current depends on the intensity of illumination, but not its wavelength.

If we apply negative potential to plate Q with respect to plate P, and increases it gradually we note that photoelectric current decreases rapidly until it is zero, at a certain negative potential on plate Q.The minimum negative potential given to plate Q at which the photoelectric current becomes zero is called stopping potential or cut off potential.[7] i. For the given frequency of incident radiation, the stopping potential is independent of its intensity.

ii. For a given frequency of the incident radiation, the stopping potential V0 if related to the maximum kinetic energy of the photoelectron that is just stopped from reaching plate Q.

If m is the mass and vmax is the maximum velocity of photoelectron emitted, then



If e is the charge on the electron and V0is the stopping potential, then work done by the retarding potential in stopping the electron = eV0.

Therefore, we have, 1/2mv2max = eV0

The above relation shows that the maximum velocity of the emitted photoelectron is independent of the intensity of the incident light.

Hence, we have the next equality:
Kmax = eV0

The stopping voltage varies linearly with frequency of light, but depends on the type of material. For any particular material, there is a threshold frequency that must be exceeded, independent of light intensity, to observe any electron emission.
Three-step model

In the X-ray regime, the photoelectric effect in crystalline material is often decomposed into three steps:[8]
Inner photoelectric effect (see photodiode below). The hole left behind can give rise to auger effect, which is visible even when the electron does not leave the material. In molecular solids phonons are excited in this step and may be visible as lines in the final electron energy. The inner photoeffect has to be dipole allowed. The transition rules for atoms translate via the tight-binding model onto the crystal. They are similar in geometry to plasma oscillations in that they have to be transversal.
Ballistic transport of half of the electrons to the surface. Some electrons are scattered.
Electrons escape from the material at the surface.

In the three-step model, an electron can take multiple paths through these three steps. All paths can interfere in the sense of the path integral formulation. For surface states and molecules the three-step model does still make some sense as even most atoms have multiple electrons which can scatter the one electron leaving.[citation needed]