Question

In diamond, coordination number of carbon atoms is 4 and its unit cell has 8 carbon atoms.
State whether the given statement is true or false.
(A) True
(B) False

Answer 1

Hint: It is known to us that diamond exists in a crystalline form. However, we need to identify its lattice type. By this we can identify the number of carbon atoms surrounding each carbon atom thus giving us the coordination number. Out of the lattice we can take a cube out and then identify the number of atoms present in one cubic cell.

Complete step-by-step answer:
Diamond is a solid form of carbon element with its atoms arranged in a crystal lattice called diamond cubic. At room temperature and pressure, carbon exists in another solid form called graphite which is the stable form chemically.
Although graphite is the stable form, diamond almost never converts to graphite form. Diamond has the highest hardest and characteristic thermal conductivity of any material. This property is used for cutting and polishing tools.
Diamond crystallises in a face centred cubic cell. The carbon atoms are mainly present at the corners and at every face centre.
Hence the coordination number of carbon atoms in diamond is 4.
The contribution of the corner carbon atom is one eight, the face centre is half of the atom and the contribution of the carbon atom in the tetrahedral void becomes 1. Thus, the number of atoms per unit cell becomes,
$\Rightarrow \text{ 8 x }\dfrac{1}{8}\text{ + 6 x }\dfrac{1}{2}\text{ + 4 = 1+3+4 = 8}$
Therefore, the given statement is true and the correct answer is option (A).

Note: Diamond is a covalent solid and yet has a high melting point mainly due to its interlinked structure. Diamond crystallises in a lattice structure, indicating the presence of strong covalent bonds.
Diamond has a characteristic 3D network in which one carbon is bonded to 4 carbon atoms i.e. having $\text{s}{{\text{p}}^{\text{3}}}$ hybridisation. This network between carbon atoms is the reason why diamond has a high melting point unlike other covalent solids.