Solution:

Einstein's co-efficient of stimulated emission:-

• Einstein found a new process called stimulated emission to increase the number of transition of atoms from higher energy levels to lower energy levels.

• Stimulated emission is the process of photon emissions takes place by an inducement given by another photon incident on the atoms in higher energy levels.

• The energy of the photon emitted is equal to the energy of the photon incident.

• Consider an atom in the higher energy level (E2).

• When an external radiation of photon energy E2 - E1 is incident on the excited atom, the photon stimulates the atom to make transition from higher to lower energy level.

• As a result the same photon energy E2 - E1 is emitted in the form of radiation.

• During this process, the stimulating photon and the photon emitted by the excited atom are emitted simultaneously in the same direction.

• Hence they are identical in phase, direction and frequency and are coherent. This process of stimulated emission is used to produce laser beam.

• 1) the number of atoms in the higher energy level (N2)

• 2) The number of photons in the incident radiation (Q)

$$ie N_{st} ∝ N_2 Q \ (or)\ N_{st} = BN_2 Q$$

• Where B is a constant known as the probability of stimulated transition per unit time. Also it is called Einstein's co-efficient of stimulated emission.

• The stimulated emission can be multiplied through a chain reaction as shown in the figure.

• When a single photon hits an atom in the higher energy level, two photons are emitted by stimulated emission.

• Then these two photons hit on two atoms of higher level, four photons are emitted. This process is continued as a chain reaction and the photons are getting multiplied.

• Finally it leads to the emission of the powerful, coherent, monochromatic and highly directional beam of laser light. This is called Light amplification by stimulated emission of radiation.

• This amplification takes place only if there are more number of atoms in the excited state (higher energy level) than in the ground state (lower energy level).