Rami Arieli: "The Laser Adventure" Chapter 2.5 page 4
Question 2.3:The difference between population numbers

Prove that the difference in population numbers (N1, N2) between two energy levels E2 and E1 is given by:

N1-N2 = N1*(1-exp(-hn/kT)

n = n2-n1is the frequency which corresponds to the energy difference between the two levels E2 and E1.

In the equation in question 2.2, the second term inside the parenthesis is always less than 1. So, the parenthesis are always less than 1. Thus the very important conclusions:

  1. In a thermodynamic equilibrium, the population number of higher energy level is always less than the population number of a lower energy level.
  2. The lower the energy difference between the energy levels, the less is the difference between the population numbers of these two levels.
Physically, the electrons inside the atom prefer to be at the lowest energy level possible. Even when they are excited to a higher level, they return back to the lowest energy level after a short time.