$C$, $Si$ and $Ge$ have the same lattice structure. Why is $C$ an insulator while $Si$ and $Ge$ are intrinsic semiconductors?

(A) The $4$ bonding electrons of $C$, $Si$, and $Ge$ reside in the second, third, and fourth orbits, respectively.
As the principal quantum number increases, the valence electrons are further from the nucleus and less tightly bound.
Consequently, the energy gap $(E_g)$ required to excite an electron from the valence band to the conduction band is highest for $C$ $(\,5.4 \ eV)$, intermediate for $Si$ $(\,1.1 \ eV)$, and lowest for $Ge$ $(\,0.7 \ eV)$.
For $C$, the energy gap is so large that thermal energy at room temperature is insufficient to excite electrons, making it an insulator.
In $Si$ and $Ge$, the energy gap is small enough that a significant number of electrons can be thermally excited to the conduction band at room temperature, allowing them to act as intrinsic semiconductors.