Which lattice type has the highest number of atoms in its conventional unit cell?

• A. Simple Cubic
• B. Body-Centered Cubic
• C. Hexagonal Close-Packed
• D. Face-Centered Cubic

Answer: (D)

Counting how many atoms sit in a conventional unit cell depends on how atoms are shared among neighboring cells. Atoms at corners are shared by six unit cells, atoms at faces are shared by two, and atoms entirely inside count fully.

In a simple cubic lattice, the eight corner atoms contribute 8 × (1/8) = 1 atom per cell. In a body-centered lattice, you still have that 1 from the corners plus one atom in the center, totaling 2. In a face-centered lattice, the corners contribute 1 (8 × 1/8) and the six face-centered atoms contribute 6 × (1/2), giving 4 atoms per unit cell.

For hexagonal close-packed, the conventional hexagonal cell has 12 corner atoms, each contributing 1/6, which totals 2 atoms from corners. In addition, there are four atoms entirely inside the cell. Altogether, this sums to 6 atoms per conventional unit cell.

Thus, the hexagonal close-packed lattice has the highest number of atoms in its conventional unit cell among the options.