Question

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

Answer 1

Hint: Coordination number of an atom is defined as the number of its nearest neighbors. In covalent bonded molecules and polyatomic ions, the coordination number is determined by just counting the number of bonded atoms.

Complete answer:
There are two types of two dimensional packing such as square close packing and hexagonal close packing whereas in three dimensions it is three types namely, hexagonal close packing, Cubic close packing and body-centered cubic close packing.
Face centered cubic: An arrangement of atoms in a crystal in which the atomic centers are disposed in space such that the atom is located at each of the corners of the cube and one at the centre, one at the centre of each face. This structure contains the same particles in the corner of the six faces of the unit cell. In the face centered cubic lattice a centre one unit cell is neighbor by $12$ neighbor atom out of them $4$ is present at the corner of the lattice, $4$ are present above and below of the lattice crystal.
Thus the co-ordination of cation in Face centered cubic $\left( {FCC} \right)$ is $12$ .

So, the correct option is (D).

Additional Information:
Unit cells are the smallest group of atoms which has the overall symmetry of a crystal, and from which the entire lattice can be built up by repetition in three dimensions. When we arrange a unit cell in all dimensions, we obtain a structure of the crystal. The properties of the unit cell can be measured by the length of edges and the angle of joining the edges.

Note:
Close packing in crystals refers to space efficient arrangement of constituent (such as atoms, molecules and ions) particles in a crystal lattice. The unit cell of crystal is defined by the lattice points.