Resistivity of a Semiconductor Increases with Increase in Temperature

Explanation:

Conductors, Insulators, and Semiconductors:
- In solid materials, the behavior of electrons determines their classification as conductors, insulators, or semiconductors.
- Conductors have a high density of free electrons in their valence band, which allows for easy flow of electric current.
- Insulators have a large energy gap between their valence and conduction bands, which makes it difficult for electrons to move from the valence to the conduction band.
- Semiconductors have a smaller energy gap compared to insulators, which allows for some electrons to move from the valence to the conduction band, resulting in partial conductivity.

Valence and Conduction Bands:
- In conductors and semiconductors, there are two energy bands that are of significance: the valence band and the conduction band.
- The valence band is the highest energy band occupied by electrons at absolute zero temperature.
- The conduction band is the energy band immediately above the valence band, and it is empty at absolute zero temperature.

Statement a) In conductors, the valence and conduction bands may overlap:
- This statement is true. In conductors, the valence and conduction bands overlap, allowing electrons to move freely from the valence band to the conduction band, resulting in high conductivity.

Statement b) Substances with energy gap of the order of 10 eV are insulators:
- This statement is true. Insulators have a large energy gap between their valence and conduction bands, typically greater than 3 eV. Substances with an energy gap of the order of 10 eV have a very large energy gap, making it extremely difficult for electrons to move from the valence to the conduction band, thus behaving as insulators.

Statement c) The resistivity of a semiconductor increases with an increase in temperature:
- This statement is false. The resistivity of a semiconductor actually decreases with an increase in temperature.
- As the temperature increases, the thermal energy of the semiconductor increases, allowing more electrons to move from the valence band to the conduction band, resulting in increased conductivity and decreased resistivity.

Statement d) The conductivity of a semiconductor increases with an increase in temperature:
- This statement is true. The conductivity of a semiconductor increases with an increase in temperature.
- As the temperature increases, more electrons acquire sufficient energy to move from the valence band to the conduction band, increasing the number of charge carriers and thus the conductivity.

In conclusion:
- The only false statement from the options provided is statement c) "The resistivity of a semiconductor increases with an increase in temperature." The resistivity of a semiconductor actually decreases with an increase in temperature due to increased conductivity.