Question

Calculate the number of atoms per unit cell in each type of cubic unit cell. Enter three integers separated by commas (e.g., 1,2,3) in the following order: primitive cubic, body-centered cubic, and face-centered cubic.

Answer 1

Answer:

1, 2, 4

Explanation:

The primitive cubic unit cell has eight corners, and each corner is shared with 8 cubic unit cells. Therefore since we have one atom at each corner, we will have:

8 corner x  1 atom/8 corner = 1 atom

There is then the equivalent of one atom per unit cell in the primitive cubic cell.

For the body-centered cubic unit cell, we have 8 corners again shared each by 8 lattices as in the simple cubic plus we have one atom  in the center of the cubic lattice. Therefore, the number of atoms in the body -centerd unit cell is two:

8 corner x 1 atom/8 corner = 1 atom

                      +

1 atom in the center

= 2 atoms/ unit cel

For the face-centerd cubic again we have 8 atoms in the corners shared by 8 lattices, plus 1 atom in each of the faces shared by two unit cells:

8 corner x 1/8 atom/corner + 6 faces x 1 atom/face = 4 atoms/unit cell