Rami Arieli: "The
Laser Adventure" Chapter 2.5 page 1

From thermodynamics we know that a collection of atoms, at a temperature
T [^{0}K], in thermodynamic equilibrium with its surrounding, is
distributed so that at each energy level there is on the average a certain
number of atoms.

The number of atoms (N_{i}) at specific energy level (E_{i})
is called **Population Number**.

The **Boltzmann equation**
determines the relation between the population number of a specific energy
level and the temperature:

N=_{i}Population Number= number of atoms per unit volume at certain energy level E_{i}.

k = Boltzmann constant: k = 1.38*10^{23}[Joule/^{0}K].

E. We assume that E_{i}= Energy of level i_{i}> E_{i-1}.

Const= proportionality constant. It is not important when we consider population of one level compared to the population of another level as we shall see shortly.

T = Temperature in degrees Kelvin[^{0}K] (Absolute Temperature).

The Boltzmann equation shows the dependence of the population number
(N_{i}) on the energy level (E_{i}) at a temperature T.

From this equation we see that:

2. **The higher the energy level, the lower the
population number**.