This problem concerns a two$-$level system, labeled A and $B.$ The equation for the

partition function in this case reads:

$q(T)=e^{-\frac{lo{n}_A}{k_{B}T}}+e^{-\frac{lo{n}_B}{k_{B}T}}$

Around room temperature the product $k_{B}T$ is approximately $26$meV $($milli$-$electron$-$volts$).$

Using such value for $k_{B}T,$ and the values of the energy levels, which are $lo{n}_A=90$meV,

$lo{n}_B=105$meV, compute: a$),$ the partition function $q,b),$ the probability for each level $(A$

and $B,$ and the average energy. Recall that the probability is computed as: $p_i=$

exp$\frac{-lo\frac{n_i}{k_B}T}{q}(T).$