The partition function of the given system is given by, Z = 1 + e(-ε/kT)
So in the '0' energy state, number of particles, n1 = [1/(1 + e(-ε/kT))]N
and in the 'ε' energy state, number of particles, n2 = [e(-ε/kT)/(1 + e(-ε/kT))]N
Now according to condition of population inversion, n1 < N/2
Upon...