Question

A system with just two energy levels in thermal equilibrium with a heat reservior at temp. 600°k .The energy gap between the level is 0.1 eV. Find the probability that the system is in higher energy level.

Answer 1

$$P(1)=\frac{\exp{(-\frac{E}{kT})}}{1+\exp{(-\frac{E}{kT})}}$$

$$P(1)=\frac{\exp{(-\frac{0.1(1.6\cdot10^{-19})}{(1.38\cdot10^{-23})(600)})}}{1+\exp{(-\frac{0.1(1.6\cdot10^{-19})}{(1.38\cdot10^{-23})(600)})}}$$

$$P(1)=0.1265$$