Absorption:

At a given temperature different species (atoms and molecules) are distributed amongst the allowed energy levels in accordance with the Boltzmann distribution. According to the Boltzmann statistical distribution, a population of the ground state that is the number of species within the ground state is highest and it keeps on decreasing as we go to higher energy levels. A population of any excited state associative to that of the ground state is given through the following formula.

N_i/N₀ = e ^-?E/kT

Where N_i and N₀ are the populations of the i^th level and the ground state respectively; ?E is the difference in the energies of the ground and excited state, k is called the Boltzmann constant and T is the absolute temperature. Let us calculate the population of an energy level, having energy of 2 kJ mol^-1 associative to the energy at ground state at 300 K.

?E = E_f - E_i = 2 × 10³ J mol ^-1/6.022 × 10²³ mol ^-1= 3.32 × 10^-21 J

Ni/ N0   = e ^{-?E/ kT} = e -3.32×10^-21 J/1.38×10^-23     JK-1   ×300K = e^-0.802 = 0.4484

This implies that for every 10000 species at the ground state there are 4484 species at the level that has energy of 2 kJ mol^-1 relative to it.