Allotropes are two or more forms of the same elements that exist in the same physical state (solid, liquid, or gas) but have physical and chemical properties that differ from one another.
Carbon exhibits many allotropic forms. Diamond and graphite are two well-known crystalline forms of carbon.
Each carbon atom in a diamond undergoes hybridization and is bonded to four other carbon atoms in a tetrahedral fashion.
Diamond is the hardest substance on the Earth because it is extremely difficult to break extended covalent bonding.
Graphite
In a hexagonal ring, the hybridization of each carbon atom is .
bond is formed by the fourth electron. The electrons are delocalized over the whole sheet.
So, Graphite conducts electricity along the sheet.
Graphite is extremely slippery and soft because it cleaves easily between layers.
Hence, graphite, an allotrope of carbon conducts electricity.