Question

The coordination number of the cation in the Face centered cubic (FCC) lattice is:
(A) $4$
(B) $8$
(C) $3$
(D) $12$

Answer 1

Hint : Analyse the structural diagrams of face centered cubic lattice from solid state and then find the number of atoms adjacent neighbouring a single atom. Face centered cubic lattice has overall four atoms combining its all the contributing atoms.

Complete step by step solution
First let us see what coordination number is. Coordination numbers come into picture when we discuss the solid state of matter.
When we discuss crystals of solid there is a central atom and surrounding atoms. The number of atoms or ions which surround the central atom is called coordination number of that crystal. It is also called ligancy of the compound.
Now let us analyse the structure of a face centered cubic lattice. Atoms are present in all corners of an FCC unit cell as well as at centres of all faces of the cube. The face centered atom is shared between two adjacent unit cells and only half of a single atom belongs to one unit cell. Only $12$ atoms belong to a unit cell in FCC. So whether it is a cation or an anion in an FCC lattice its coordination number is $12$ .
So option D is the correct answer.

Note
Number of atoms per unit cell and coordination number of a compound are two different things. For example in BCC there are a total eight atoms in a unit cell. So the number of atoms per unit cell of BCC is $1/8$ .
For reference the coordination number of different structures are:
Coordination number of BCC is $8$
Coordination number of FCC is $12$
Coordination number of CCP is $12$
Coordination number of HCP is $12$ .