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

Explanation

The 4 bonding electrons of C, Si or Ge lie, respectively, in the second, third and fourth orbit. Hence, energy required to take out an electron from these atoms (i.e., "ionisation energy" `E_(g)`) will be least for Ge, followed by Si and highest for C. Hence, number of free electrons for conduction in Ge and Si are significant but negligibly small for C.