Question

In a semiconductor,
(a) there are no free electrons at 0 K
(b) there are no free electrons at any temperature
(c) the number of free electrons increases with temperature
(d) the number of free electrons is less than that in a conductor.

Answer 1

(a) there are no free electrons at 0 K
(c) the number of free electrons increases with temperature
(d) the number of free electrons is less than that in a conductor

In semiconductors, the valence band is full at 0 K, but the conduction band is empty. So, no free electron is available for conduction at 0 K.
As the temperature increases, covalent bonds that provide free charge carriers for conduction in a semiconductor break.
As the conduction band in metals is already partially filled at 0 K, many free electrons below the Fermi level acquire energy from an external source or temperature, jump to the conduction band and start behaving like free electrons. Hence, metals contain more free electrons than semiconductors.