According to Einstein, the emission of photo electron is the result of the interaction between a single photon of the incident radiation and an electron in the metal. When a photon of energy hν is incident on a metal surface, its energy is used up in two ways :

*Einstein's photoelectric equation*

In 1905, Albert Einstein, successfully applied
quantum theory of radiation to photoelectric effect.

According to Einstein, the emission of photo
electron is the result of the interaction between a single photon of the
incident radiation and an electron in the metal. When a photon of energy *h**ν* is incident on a metal surface, its energy is used up in two ways
:

1. A part of the energy of the photon is used in
extracting the electron from the surface of metal, since the electrons in the
metal are bound to the nucleus. This energy W spent in releasing the photo
electron is known as photoelectric work function of the metal. The work
function of a photo metal is defined as the minimum amount of energy required
to liberate an electron from the metal surface.

2. The remaining energy of the photon is used to
impart kinetic energy to the liberated electron.

If *m*
is the mass of an electron and *v*, its
velocity then

Energy of the incident photon = Work function +
Kinetic energy of the electron

*h**ν** = W + ½ mv ^{2} …… (1)*

If the electron does not lose energy by
internal collisions, as it escapes from the metal, the entire energy *(h**ν**-W)* will be exhibited as the kinetic energy of the electron. Thus, *(h**ν**-W)* represents the maximum kinetic energy of the ejected photo
electron. If *v _{max}* is the
maximum velocity with which the photoelectron can be ejected, then

*h**ν** = W + ½ mv _{max}^{2} …… (1)*

This equation is known as Einstein's
photoelectric equation.

When the frequency (ν) of the incident radiation is equal to the threshold frequency (ν_{o}) of the
metal surface, kinetic energy of the electron is zero. Then equation (2)
becomes,

*h**ν*_{o}* = W …………………..(3)*

Substituting the value of *W* in equation (2) we get,

*hν - hν _{o} = ½ mv^{2}_{max} *

*or*

*h(v-v _{0})= ½ mv^{2}_{max}*

This is another form of Einstein's photoelectric
equation.

*Experimental verification of Einstein's
photoelectric equation*

Einstein's photoelectric equation is,

*½ mv ^{2}_{max }= h(v-v_{0})*

*½ mv ^{2}_{max }= eV_{0}*

*From equations (1) and (2)*

*eV _{0 }= h(v-v_{0})*

*V _{0}= (h/e)v - (h/e)v_{0} ………………………(3)*

This is an equation of a straight line.
Millikan verified equation (3) experimentally and found that it is in harmony
with the observed facts.

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11th 12th std standard Class Physics sciense Higher secondary school College Notes : Einstein's photoelectric equation |

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