Question

The forbidden energy gap can be overcome on thermal agitation by light. The substance is
(A) An insulator
(B) A conductor
(C) A semiconductor
(D) A superconductor

Answer 1

Hint: In conductors and superconductors, the conduction and valence bands are overlapped, so there is already no forbidden energy gap. In insulators, the forbidden energy gap is too large to be overcome by thermal excitation. In semiconductors, the forbidden energy gap is moderate and can be overcome.

Complete step by step solution:
First of all, we need to have a clear idea of what the forbidden energy gap is.


The forbidden energy band gap is the energy difference between valence band and conduction band of a substance. As the name suggests, this energy region is forbidden, that is, no electron occupies this state. This gap between valence band and conduction band, also determines the classification on the basis of electrical conductivity of a material. On the basis of electrical conductivity, materials are categorized into three main types:
Insulators: Forbidden energy gap > 9eV
Semiconductors: Forbidden energy gap ≈ 1eV
Conductors: Forbidden energy gap < 1eV
The forbidden energy band gap for all three types is shown:


Therefore, in semiconductors, the forbidden energy gap is small and can be overcome by thermal agitation, that is, by increasing temperature, unlike insulators. So, as the temperature of the semiconductor is increased, the forbidden energy gap tends to decrease.

Option (C) is correct.

Note: There is also an explicit temperature dependence of the forbidden energy gap which can be mathematically expressed from the following relation: \[{E_g}(T) = {E_g}(0) - \dfrac{{\alpha {T^2}}}{{T + \beta }}\]
where, \[{E_g}(T)\] is the forbidden energy gap at absolute temperature T
\[{E_g}(0)\] is the intrinsic forbidden energy gap
\[\alpha \] and \[\beta \] are constants.
So, we can see the decrease in the forbidden energy gap on increasing temperature mathematically as well as theoretically. Hence, the forbidden energy gap can be overcome by thermal agitation in semiconductors but not in insulators.