Consider a face-centered cubic lattice. Assume the atoms are hard spheres with the surfaces of the nearest neighbors touching. Assume the effective radius of the atom is 2.37 Å. (a) Determine the volume density of atoms in the crystal. (b) Calculate the surface density of atoms in the (110) plane. (c) Determine the distance between near-est (110) planes. (d) Repeat parts (b) and (c) for the (111) plane.