Latice of Spin States Consider a system of N objects on a lattice. Each object has a $$spin$$ which can have two states that have corresponding energies of $+$ and $.$ The number of objects with energy $+$ is given by n$.$ We are taking this system to be isolated. i$.$ Show that the total energy of the system is given by E $=(2$n $$ N$),$ Calculate the number of microstates that yield a particular E value $$ that is$,$ calculate $($E$).$ ii$.$ Express the result in terms of only N$,$ E$,$ and $.$ Be sure to derive$/$explain your answer. iii. Calculate the entropy of the system. To simplify this expression, assume that N$,$ N $+$ E$/,$ and N $$ E$/$ are all very large.