Rami Arieli: "The Laser Adventure" Chapter 2.5 page 2
Relative Population (N2/N1)
 The relative population (N2/N1) of two energy levels E2 compared to E1 is:
N2/N1 = const* exp (-E2/kT)/ const* exp (-E1/kT) = exp(-(E2-E1)/kT)

The proportionality constant (const) is canceled by division of the two population numbers.

Conclusions:

  1. The relation between two population numbers (N2/N1) does not depend on the values of the energy levels E1 and E2, but only on the difference between them: E2- E1.
  2. For a certain energy difference, the higher the temperature, the bigger the relative population.
  3. The relative population can be between 0 and 1.