Question

Read the following statements carefully:
Y: The resistivity of a semiconductor decreases with the increase of temperature.
Z: In a conduction solid, the rate of collision between free electrons and ions increases with the increase of temperature.
Select the correct statement(s) from the following.
(This question has multiple correct options)
A) Y is true but Z is false
B) Y is false but Z is true
C) Both Y and Z are true
D) Y is true and Z is the correct reason for Y

Answer 1

Hint: The resistivity of a substance is inversely proportional to temperature. Resistivity is directly proportional to resistance. If the resistivity of a substance increases then the resistance also increases. Rate of collision increases if resistance is low.

Complete step by step solution:
Note that the question is multiple correct options. Let us examine each option.
The resistivity of a semiconductor is inversely proportional to temperature; mathematically it is denoted as:
$\rho$ $\propto$ $\dfrac{1}{T}$ where $\rho $ is the resistivity and $T$ denotes the temperature;
This implies that, with increase in temperature the resistivity will decrease and with decrease in temperature the resistivity will decrease.
Therefore, statement Y is true.

In a conduction solid, when the temperature of a semiconductor is increased the energy of electrons and ions also increases. As a result, the electrons jump from the valence band to the conduction band. Due to this, there are more vibrations of the electrons and hence more collision.
Therefore, statement Z is also true.
Band theory describes the states of electrons in solid materials that have energy only within certain specific ranges. The behaviour of an electron in a solid is related to the behaviour of all other particles around it. Since, both the statements are true and Z is the correct explanation of statement Y.

Option C and D are correct.

Note: Valence bands and conduction bands are different bands given by band theory. When electrons jump from valence band to conduction band, it creates current. Remember that resistivity is inversely proportional to temperature. With increase in temperature in semiconductor, the conductivity increases.