Consider the three types of cubic units cells.
(a) Assuming that the spherical atoms or ions in a primitive cubic unit cell just touch along the cube’s edges, calculate the percentage of occupied space within the unit cell. (Recall that the volume of a sphere is (4/3)πr³, where r is the radius of the sphere.)
(b) Compare the percentage of occupied space in the primitive cell (pc) with the bcc and fcc unit cells. Based on this, will a metal in these three forms have the same or different densities? If different, in which is it most dense? In which is it least dense?