Question

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

Answer 1

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

Step-by-step explanation:

primitive holds 1 atom total, BCC holds 2, FCC holds 4

Answer 2

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

Step-by-step 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.