Question

The number of atoms in the hcp unit cell is

• A. $4$
• B. $6$
• C. $12$
• D. $13$

Answer 1

The correct option is B

$6$

The explanation for the correct option

(B)$6$

Hexagonal close-packing

• The second row can be stacked on top of the first in a staggered pattern such that its spheres fit in the depressions of the first row.
• If the first row's arrangement of spheres is referred to as 'A-type, the second row's arrangement may be referred to as 'B' type.

Number of atoms in hcp unit cell

• In HCP, there are 6 corner atoms in the top layer and 6 corner atoms in the bottom layer, so 12 atoms in the unit cell. The contribution of each atom in the unit cell is one-sixth.
• Two atoms are present at two face centers. The contribution of each atom in the unit cell is one-half.
• Three atoms are placed within the volume of the unit cell and the contribution of each atom is 1.
• So, the number of atoms in the hcp unit cell is =$12\times \frac{1}{6}+2\times \frac{1}{2}+3=6$

The explanation for the incorrect option

The number of atoms in the hcp unit cell is $6$. So, options (A), (C), and (D) are incorrect.

Hence, the number of atoms in the hcp unit cell is $6$. Hence, option (B) is correct.