$Sn,C,$ and $Si,Ge$ are all group $XIV$ elements. Yet, $Sn$ is a conductor, $C$ is an insulator while $Si$ and $Ge$ are semiconductors. Why?

We know that the atomic size of elements increases as we move down in a group in the period table.

This increase in size is accompanied by a decrease in ionization energy required. Thus, the energy gap between the conduction band and valence band decreases down the group.

A material will conduct current if there is no energy gap between conduction and valence band in energy band diagram of atom. This energy gap decreases from insulator to semiconductor and from semiconductor to conductor.

For $Sn$ it is $0eV$, for $C$ its $5.4eV$ and for $Si$ and $Ge$ its $1.1eV$ and $0.7eV$ respectively, thus $Sn$ is a conductor, $C$ is an insulator while $Si$ and $Ge$ are semiconductor.

$\text{Final Answer}:$

The energy gap for $Sn$ is $0eV$, for $C$ is $5.4eV$, for $Si$ is $1.1eV$ and for $Ge$ is $0.7eV$, related to their atomic size.