Question

Write Einstein’s photoelectric equation and explain the terms in it.

Answer 1

Hint: In photoelectric effect, when the energy of the incident radiation exceeds the work function of the metal, the electrons are emitted from the surface of the metal and kinetic energy of the electrons is equal to the difference between energy of radiation and the work function of metal.

Complete step-by-step answer:
In photoelectric effect, we have a radiation of certain wavelength or frequency incident on a metal surface. When the energy of the radiation is greater than the work function of metal, it is observed that electrons are emitted from the metal surface and their kinetic energy is equal to the difference between energy of photon and the work function of metal.
$\therefore \dfrac{1}{2}m{{\text{v}}^2} = h\nu - W{\text{ }}...{\text{(i)}}$
This equation is known as Einstein's photoelectric equation. Here the first term is the kinetic energy of the emitted photoelectrons, the second term is the energy of photons incident on the metal surface while the third term is the work function of the metal. The consequences of this equation are given as follows:
1. Photoelectric current in a photocell increases with the increase in the intensity of the incident radiation.
Explanation: When the intensity of light is increased then it means that the number of photons incident on the metal surface increases which leads to greater production of photoelectrons which means that the photo current is increasing due to increase in intensity of incident radiation.
2. The stopping potential (\[{V_0}\]) varies linearly with the frequency ($\nu $) of the incident radiation for a given photosensitive surface with the slope remaining the same for different surfaces.
Explanation: The stopping potential signifies the amount of energy required to stop a photo-electron. Greater the kinetic energy of the electrons, greater is the stopping potential required to stop them. In equation (i), we notice that if we increase the frequency of light then kinetic energy of the photoelectrons increases which means we need greater stopping potential to stop the photoelectrons.
3. Maximum kinetic energy of the photo-electrons is independent of the intensity of incident radiation.
Explanation: The kinetic energy of the photoelectrons is decided by the frequency of the incident light as can be seen in equation (i) while increasing intensity of light only increases the flux of photons on the surface, not their energy.

Note: 1. Photoelectric effect shows the particle nature of light photons transmitting energy to the metal in chunks called quanta. Photons are the quanta of electromagnetic radiation.
2. Work function of a metal is defined as the minimum amount of energy required to pull out an electron from that metal.