Photoelectric Effect -Einstein’s Photoelectric Equation

In 1905, Einstein explained photoelectric effect on the basis of Planck’s quantum theory. According to this theory, light travels in the form of small bundles or packets of energy, called ‘photons”. The energy of each photon is hv, where v is the frequency of light and h is Planck’s universal constant. The intensity of light depends on the number of these photons.

When a photon falls on a metal, it transfers all of its energy hv to one of the electrons present in the metal. A part of this energy is used in ejecting the electron from the metal and the rest is given to the ejected electron as kinetic energy.

All the electrons ejected from the metal are not ejected from the surface only but also from the interior of the metal. The electrons which are ejected from the interior of the metal, expend some of their energy in collisions with the atoms on their way to the surface.

Thus, electrons with different energies are emitted from the metal. The electrons emitted from the surface of the metal have maximum kinetic energy because their energy is not lost by collisions.

Suppose, the (maximum) kinetic energy of photoelectrons emitted from the metal-surface is Ek and W is the energy required to eject a photoelectron from the metal. W is the work-function of the metal. Then, according to the above explanation, we have

hv = W + Ek

Or Ek = hv – W ————-(1)

where hv is the energy of the photon absorbed by the electron in the metal.

If the energy of the photon absorbed by the electron is less than the work function W of the metal, then the electron will not be emitted.

Therefore work function W = hvo.

Substituting this value in (1), we get

Ek = hv – hvo

Ek = h(v – vo)

If the maximum velocity of the emitted photoelectrons is Vmax, then

Ek = (1/2) m vmax^2

Therefore, (1/2) m vmax^2 = h(v – vo)

This equation is called Einstein’s Photoelectric equation.