absorption of radiationif an atom is initially in

Question

Absorption of radiation

If an atom is initially in a lower state 1, it can rise to a higher stare 2 by absorbing a quantum of radiation. Photon of frequency v where E₁ and E₂ are the atom in the states 1 and 2 respectively. The process is known as absorption of radiation. The probable rate of this transition 1of 2 depends on the properties of stares 1 and 2 and is proportional to the energy density of the radiation of frequency v incident on the atoms. Thus P₁₂ = B₁₂ u (v) where B₁₂ is proportionality constant and is known as Einstein coefficient of absorption of radiation.

Spontaneous emission Let rs now consider an atom initially in the higher state 2. Excited state with higher energy is inherently unstable, and atom in excited stste does not stay for longer time and jumps to the lower energy state 1 emitting a photon of frequency   v. This is spontaneous emission of radiation. If there is an assembly of atoms, the radiation emitted spontaneously by each atom has a random direction and a random phase and is therefore incoherent from one atom to another. The probability of spontaneous emission is determined only by the properties of states 2 and 1. This is denoted by A₂₁ which is known as Einstein coefficient of spontaneous emission of radiation. In this case the probability of spontaneous emission is independent of it.

Stimulated Emission According to Einstein, an atom in an excited energy state may, under the influence of the electromagnetic field of a photon of frequency v incident upon it jumps to a lower energy state, emiting an additional photon of same-frequency (v) (fig). Hence tow photons, one original and the other emitted move together. This is stimulated emission of radiation. The direction of propagation, phase, energy and state of polarization of the emitted photon is exactly same as that of the incident stimulating photon, so the result is an enhanced beam of coherent light. The probability of stimulated emission transition 2 - 1 is proportiaonl to the energy density of the stimulating radiation and is given by B­₂₁ u (v) where B₂₁ is the Einstein coefficient of stimulated emission of radiation. The total probability for an atom in state 2 to drop to the lower state 1 is therefore P₂₁ = A­₂₁ + B₂₁ u (v).                                                         

Relation between Einstein's coefficient   When a steady state is reached, there should be a balance between the absorption and emission processes. Hence under this situation, number of atoms absorbing radiation per unit time must be equal to the number of atoms emitting radiation per unit time so that the number of atoms in any energy level does not change with time.