Arrange the three common unit cells in order from least dense to most dense packing. a. face-centered cubic < body-centered cubic < primitive cubic b. primitive cubic < body-centered cubic < face-centered cubic c. primitive cubic < face-centered cubic < body-centered cubic d. body-centered cubic < primitive cubic < face-centered cubic e. body-centered cubic < face-centered cubic < primitive cubic

b. primitive cubic < body-centered cubic < face-centered cubic

Explanation:

The coordination number is defined as the number of atoms (or ions) surrounding an atom (or ion) in a crystal lattice. Its value gives us a measure of how tightly the spheres are packed together. The larger the coordination number, the closer the spheres are to each other.

In the primitive cubic, each sphere is in contact with 6 spheres, so its coordination number is 6. In the body-centered cubic, each sphere is in contact with 8 spheres, so its coordination number is 12. In the face-centered cubic, each sphere is in contact with 12 spheres, so its coordination number is 12.

Therefore, the increasing order in density is the primitive cubic first, then the body-centered cubic, and finally the face-centered cubic.