Einstein's photoelectric equation

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 hν 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

hν = W + ½ mv²    …… (1)

If the electron does not lose energy by internal collisions, as it escapes from the metal, the entire energy (hν-W) will be exhibited as the kinetic energy of the electron. Thus, (hν-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

hν = W + ½ mv_max²    …… (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,

hν_o = W     …………………..(3)

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

hν - hν_o = ½ mv²_max

or

h(v-v₀)= ½ mv²_max

This is another form of Einstein's photoelectric equation.

Experimental verification of Einstein's photoelectric equation

Einstein's photoelectric equation is,

½ mv²_max = h(v-v₀)

½ mv²_max = eV₀

From equations (1) and (2)

eV₀ = h(v-v₀)

V₀= (h/e)v - (h/e)v₀     ………………………(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.