Question

Carbon, silicon and germanium have four valence electrons each. At room temperature the appropriate statement is
(A) The number of free electrons for conduction is significant only in $Si$ and $Ge$ but small in $C$
(B) The number of free conduction electrons is significant in $C$ but small $Si$ and $Ge$
(C) The number of free conduction electrons is negligibly small in all the three.
(D) The number of free conduction electrons is significant in all the three.

Answer 1

The kinetic energy of the electron is inversely proportional to that of the band gap energy. The kinetic energy is required for the electron in an atom and molecule to move inside the atom. The free electrons are responsible for the conduction of the current.

Complete answer:
The atom has the electrons revolving around the nucleus in the orbitals but some of the electrons are far away and the nucleus does not have the influence over electrons. These are free electrons. The band gap energy is the difference in the energy between the valence band and the conduction band. In the valence band, the electrons are not free to move but in the conduction band, the electrons are free to carry the current. In silicon and the germanium at the temperature of about $300\,K$ , the energy band gap is very less and hence the kinetic energy of the electrons will be more to conduct the electric current. Hole is produced in a valence band, so the silicon and the germanium are more significant. But in the carbon, the energy band gap is more and hence it is not significant to conduct the electrons. Hence the number of free electrons for conduction is significant only in the silicon and the germanium but not in the carbon.

Thus the option (A) is correct.

Note: In the above solution, the significance is calculated based on the conduction of the current. This is mainly possible when the atom possesses more and more free electrons. Due to the significance of the silicon and the germanium, they are used as the diodes in the bipolar transistors.