Question

Question #c2c4a

Answer 1

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

Explanation:

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.