(Solved): A 2D mono-atomic layer has N1022 atoms positioned either in " O " or " X " potential well sites ...

A 2D mono-atomic layer has $$N?10^{22}$$ atoms positioned either in " $$O$$ " or " $$X$$ " potential well sites in mutually embedded cubic lattice arrangement, as shown in the figure on the right. The energy of an atom in " $$\mathrm{O}$$ " site is lower than that of an atom in " $$\mathrm{X}$$ site by the amount $$?$$. a) Determine the entropy for states with $$n$$ atoms in " $$X$$ " sites if $$1?n?N$$, assuming that any atom situated on an " $$O$$ " site will "jump" to one of its four nearest " $$X$$ " sites. b) Calculate the entropy as in part (a), assuming that the $$n$$ unoc no relationship with the $$n$$ occupied " $$X$$ " sites. c) Determine the fraction of " $$X$$ " sites that at filled at low tempe Assume that there is no interaction between atoms positione