By considering the hybridization of orbitals in diamond, explain why it is (a) an electrical insulator at room temperature and (b) extremely hard.

the sp³ orbital, is a very directional orbital that forms the bonds called covalent.  the material is an electrical Insulator.  hardness of the material comes from the energy needed to break the covalent bonds (sp³)

Explanation:

Carbon has several structures, for its different ways of bonding, in all these the orbital s is excited and mixed with the orbitals p, creating hybrid orbitals sp³, sp² and sp, there are some π orbitals around the latter.

 Each type of hybrid orbital is linked differently, the sp³ orbital, is a very directional orbital that forms the bonds called covalent, where when it binds to another atom they share an electron, therefore the 4 sp³ orbitals form a stable molecule with full orbitals (8 electrons).

 As the electrons are in the direction of the links, they cannot be easily moved, so the material is an electrical Insulator.

The hardness of the material comes from the energy needed to break the covalent bonds (sp³), there are only a few directions in which the links can be separated