4. The Boltzmann equation for a two-level system is shown below:

equitation 2. n2/n1= e−ΔE/kBT

where n1 is the number of molecules in the lower state, n2 is the

number of molecules in the upper state, and ΔE is the energy

difference between them. kB is Boltzmann’s constant and T is

the temperature. The total number of molecules, n is given

equitation 3. n = n1 + n2

By rearranging Equations 2 and 3, show that the fraction of

molecules in the lower state, n1/n, is given by the following

expression:

n1/n= (eΔE/kBT/1 + eΔE/kBT )