Question

The number of atoms in the hcp unit cell is ……..

Answer 1

Hint: The hcp is referred to as Hexagonal Closest Packing. It consists of three layers of atoms. The hcp structure is a common structure for the elemental metals such as magnesium, zinc, beryllium, zinc, cadmium and zirconium.

Complete step-by-step answer:
The arrangement in hcp follows the order ABAB. The structure of hcp is given below.
                                               

We can calculate the number of atoms in hcp unit cell as follows:
1. 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.
2. 2 atoms are present at two face centres. The contribution of each atom in the unit cell is one-half.
3. 3 atoms are placed within the volume of the unit cell and contribution of each atom is 1.
Adding all these:
The number of atoms in hcp unit cell is $=12\times {\displaystyle \frac{1}{6}}+2\times {\displaystyle \frac{1}{2}}+3=6$

Therefore, the number of atoms in the hcp unit cell is 6.

Note: Students may get confused between the various crystal systems. The hexagonal close packing is shortly written as hcp. The hcp structure is a right rhombic prism unit cell. It has two equal edges say a and height say c which is perpendicular to the two base axes and has an angle of ${120}^{\circ }$.