Question #c2c4a

1 Answer
Dec 1, 2017

There is no derivation of photoelectric effect equation. There is just an understanding by interpreting Planck's quanta as light particle.


The energy of a photon is related to its frequency as : #E_{\nu} = h\nu#;

The electron is bound to the surface and some energy is required to pluck this electron. This energy is called work function (#\phi#). This energy corresponds to a photon of frequency #\nu_0#.
#\phi = h\nu_0#

If a photon with frequency less than #\nu_0# is incident on the material, no photo electrons will be produced. However if a photon with frequency greater than #\nu_0# is incident on the surface, an energy of #\phi = h\nu_0# will be utilised in plucking the electron and the remaining will become the kinetic energy of the electron.

#h\nu = \phi + E_k; \qquad h\nu = h\nu_0 + E_k;#
Kinetic energy of the ejected photo electron is:

#E_k = h\nu - h\nu_0 = h(\nu-\nu_0)#

This is the photoelectric equation which was a mystery and could not be explained using classical electrodynamics. Einstein gave a simple explanation by interpreting Planck's photons as light particles.