1.13 Treating atoms as rigid spheres with radii equal to one-half the distance between nearest neighbors, show that the ratio of the volume occupied by the atoms to the total available volume in the various crystal structures is (a) 7/6 or 52% for the simple cubic lattice. (b) V34/8 or 68% for the body centered cubic lattice. (c) V21/6 or 74% for the face centered cubic lattice. (d) V37/16 or 34% for the diamond lattice