Hexagonal emit-packed structure Consider first Brillouin zone of a crystal with a simple hexagonal lattice in three dimensions with lattice constants a and c. Let G_c denote the shortest reciprocal lattice vector parallel to the c axis of the crystal lattice. 

(a) Show that for a hexagonal-close-packed crystal structure the Fourier component U(G_c) of the crystal potential U(r) is zero. 

(b) Is U (2G_c) also zero? 

(c) Why is it possible in principle to obtain an insulator made up of divalent atoms at tile lattice points of a simple hexagonal lattice? 

(d) Why is it nut possible to obtain an insulator made up of monovalent atoms in a hexagonal-close-packed structure?