What is the ratio of the populations of two energy states wh

What is the ratio of the populations of two energy states whose energies differ by 500J at:

a) 200K

b) 500K

c) 1000K

Solution

We know that, the ratio of populations of energy is given by

n_upper / n_lower = exp[-E / RT]

E=energy,R = 8.31 J*mol-1,Temperature in Kelvin

1. When T=200k

n_upper / n_lower = exp[-500 / 8.314*200]

This gives us,

n_upper /n_{lower = 0.74}

_{2. when t=500k}

n_upper / n_lower = exp[-500 / 8.314*500]

= 0.8866

3. When T=1000k

n_upper / n_lower = exp[-500 / 8.314*1000]

= 0.94