Question

The coordination number of a metal crystallizing in a hexagonal close-packed structure is :
A.12
B. 4
C. 8
D. 6

Answer 1

Hint: The spatial arrangements of atoms within a given lattice can be done in one dimension or two dimensions or even in 3 dimensions. Cubic close packing (ccp), hexagonal close packing (hcp), and body-centered cubic (bcc) are all 3-dimensional spatial arrangements.

Complete step by step answer:
Hexagonal close-packed structure is one kind of crystal lattice. In this unit cell top and down faces of the unit cell contain one atom at its center and one atom in each alternative side face of the hexagon. And contains one atom at the twelve corners of the unit cell.
The coordination number in a lattice is the number of the nearest atoms surrounded by an atom is called the coordination number of that lattice.
The structures of the hexagonal close-packed crystal lattice are,

The coordination number of the hexagonal close-packed structure is 12.

So, the correct option is A.

Note:
 Number of atoms Per hexagonal close-packed Unit Cell is,
Each atom at the corner of the hexagonal face is shared by 6 unit cells i.e. each atom contributes \[{\dfrac{1}{6}^{th}}\]to their mass. There are two such hexagonal faces with a total of 12 such atoms. Thus, the contribution of corner atoms = \[\dfrac{1}{6} \times 12 = 2\]
The atom at the center of the hexagonal faces is shared by two cells each. Therefore, the contribution of face-centered atoms = \[\dfrac{1}{2} \times 2 = 1\]
Three atoms are contained within the unit cell; therefore, their contribution is \[3 \times 1 = 3\].
So, the total number of atoms per unit cell is \[{\text{ }}2{\text{ }} + {\text{ }}1{\text{ }} + {\text{ }}3{\text{ }} = {\text{ }}6\].