Question

how photoelectric effect can be explained on the basis of plank's quantum theory?

Answer 1

Explanation of photoelectric effect using Quantum Theory:
According to Einstein, when a photon strikes a metal surface, some of its energy is used up to eject the electron from the metal atom (equal to the energy binding the electron with the nucleus) and the remaining energy is given to eject electron in the form of kinetic energy. That is,
Energy of striking photon = Binding energy + Kinetic energy of ejected electron
This means that a certain minimum amount of energy corresponding to the binding energy is necessary to remove the electron from the metal. Thus, when a photon of energy $h\nu$, strikes a metal surface, some of its energy, called threshold energy, $h{\nu }_o$ is used up to remove the electron from the surface and the remaining energy is imparted to the ejected electron as kinetic energy $\frac{1}{2}m{v}^2$.
Therefore,
$h\nu$ = $h{\nu }_o$ + $\frac{1}{2}m{v}^2$

or Kinetic energy of ejected electron ($\frac{1}{2}m{v}^2$) = h ($\nu -{\nu }_o$)

where $\mathrm{h}=6.63\times {10}^{-34}\mathrm{Js}$ , called as Planck's constant.