Question

In a cubic close packing of a sphere in three dimensions, the coordination number of each sphere?
$A.$ $6$
$B.$ $9$
$C.$ $3$
$D.$ $12$

Answer 1

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

Complete step by step 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.
- The unit cell is the smallest group of atoms that 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.
- Now let us discuss cubic close packing in three dimensions to find the coordination number,
- Cubic close packing: In cubic close packing when the third layer is placed above the second layer in such a manner that its sphere covers the octahedral voids and the sphere of the third layer is not aligned with the first or the second layer, This arrangement is known as type.
- Cubic close packing has $ABCABC...$ arrangement. In cubic close packing. In cubic close packing, the atoms are present at the corner and face center of the unit cell. As the atoms present at faces, four in its plane and eight outside the plane.
Hence, the coordination number is $12$.

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