Question

The forbidden energy band gap in semi-conductor, conductor and insulator are \(E_{1}, E_{2}\) and \(E_{3}\) respectively. The relation among then is: (A) \(E_{1}E_{3}\) (B) \(\mathrm{E}_{1}>\mathrm{E}_{2}>\mathrm{E}_{3}\) (C) \(E_{1}\mathrm{E}_{2}<\mathrm{E}_{3}\)

Short answer

The correct relation among the forbidden energy band gaps in semiconductors, conductors, and insulators (E1, E2, and E3) is: (C) \(E_{1}<E_{2}<E_{3}\)

Step-by-step solution

Understand the energy bands in solids

In solids, there are two important energy bands: valence band and conduction band. The valence band consists of electrons that are bound to atoms, while the conduction band is formed of free electrons. The forbidden energy band gap is the energy range between the valence and conduction bands where no electron states can exist.

Energy bands in semiconductors

In semiconductors, the forbidden energy band gap is small, which allows some electrons from the valence band to jump into the conduction band when external energy like heat or light is supplied. This small band gap allows semiconductors to have moderate conductivity. Hence, E1 represents the energy band gap in semiconductors.

Energy bands in conductors

In conductors, the valence and conduction bands overlap, meaning there's virtually no forbidden energy band gap. As a result, electrons can easily move from the valence band to the conduction band, making conductors highly conductive. In this case, E2 represents the energy band gap in conductors.

Energy bands in insulators

In insulators, the forbidden energy band gap is very large. Due to this significant gap, electrons cannot jump from the valence band to the conduction band, even when external energy is supplied. This results in insulators having very low or negligible conductivity. E3 represents the energy band gap in insulators.

Compare the energy band gaps

Now, we can compare the energy band gaps in semiconductors (E1), conductors (E2), and insulators (E3): - Since conductors have virtually no forbidden energy band gap (E2 ≈ 0), - Semiconductors have a small band gap (E1), - And insulators have a large band gap (E3), We can conclude that the relation among the forbidden energy band gaps should be E2<E1<E3.

Identify the correct answer

Comparing the given options with our result (E2<E1<E3), we find that the correct answer is: (C) \(E_{1}<E_{2}<E_{3}\)