Derive an expression for the entropy of a pure atomic crystal of $N$ nuclei, given its partition proposed by Einstein is given by: $)$

$(u\frac{?}{2},$ where $U_0$ is the sublimation energy at $0K.$ Recall that $S=k_{B}T(\frac{dellnQ}{\text{d}\text{e}\text{l}\text{T}}{)}_{N,V}+k_{B}lnQ.$