Question

Light with a constant frequency shines on a metal surface. Discuss briefly the expectations for the values of the stopping potential and the photoelectric current according to classical physics if the intensity of the light is increased. Explain why Einstein’s interpretation of the measurements was needed, and the subsequent development of our understanding of the nature of light

Answer 1

When light with constant frequency shines on a metal surface it will provide energy to the electron which is utilized in two way

1. some part of it is used to eject the electron which is equal to work function of the metal ($\Phi _{0}$)

2. And rest part of energy will provide the kinetic energy to the electrons which give rise to the photoelectrons.

According to Einstein (who uses Planck's theory of light to explain this phenomenon)

Energy of Photon = Work Function + Kinetic Energy of Electron

$h\nu = \Phi _{0} + \frac{1}{2}mv^{2}$

If frequency of light is just enough to eject the electron i.e. electron gains no kinetic energy

$\Phi _{0} = h\nu_{0}$

Where $\nu_{0}$ is known as threshold frequency. So we can write

$h\nu =h\nu_{0}+ \frac{1}{2}mv^{2}$

$\frac{1}{2}mv^{2}=h\nu -h\nu_{0} = h(\nu -\nu_{0})$

This equation is called Einstein's Photoelectric equation.

Here stopping potential is defined as the potential which make photoelectric current zero i.e.  The stopping potential is defined as the potential necessary to stop any electron (or, in other words, to stop even the electron with the most kinetic energy) from 'reaching the other side'.

Clearly if we increase the intensity of light i.e. more number of photons will shine the surface of the metal so it does not have any impact on stopping potential.