How many atoms are contained in a face-centered cubic unit cell?

How many atoms are contained in a face-centered cubic unit cell?

• A. 2
• B. 4
• C. 3
• D. 6

Answer: (B)

In a face-centered cubic unit cell, atoms are at the corners and at the centers of each face. Corner atoms are shared by eight neighboring cells, so each corner contributes 1/8 of an atom. With eight corners, that adds up to 8 × 1/8 = 1 atom. Face-centered atoms are shared by two unit cells, so each contributes 1/2 of an atom. There are six faces, giving 6 × 1/2 = 3 atoms. Total atoms in the unit cell = 1 + 3 = 4. So there are four atoms per FCC unit cell.

In a face-centered cubic unit cell, atoms are at the corners and at the centers of each face. Corner atoms are shared by eight neighboring cells, so each corner contributes 1/8 of an atom. With eight corners, that adds up to 8 × 1/8 = 1 atom. Face-centered atoms are shared by two unit cells, so each contributes 1/2 of an atom. There are six faces, giving 6 × 1/2 = 3 atoms. Total atoms in the unit cell = 1 + 3 = 4. So there are four atoms per FCC unit cell.