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Assertion: The resistivity of a semiconductor increases with temperature.
Reason: The atoms of semiconductor vibrate with larger amplitudes at higher temperatures thereby increasing its resistivity.
A. Both assertion and reason are correct and reason is the correct explanation for assertion.
B. Both assertion and reason are correct but reason is not the correct explanation for assertion.
C. Assertion is correct but reason is incorrect.
D. Both assertion and reason are incorrect.

Last updated date: 23rd May 2024
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Hint: You can start by explaining conductor, insulators in brief. Then explain semiconductors in a little more detail. Then explain what conduction band in a semiconductor is. Then finally write how the number of free electrons increase with temperature and how it will affect resistivity.

Complete step by step answer:
Conductors – They are materials that have a lot of free electrons and as the flow of current is essentially the flow of electrons in a material, thus, we say that conductors have very less resistance and can conduct more current. Example – Metals, tap water, etc.

Insulators - They are materials that have no free electrons, thus, we say that insulators have very high resistance and do not conduct electricity. Example - Wood, plastic, etc.

Semiconductors – Semiconductors lie somewhere in between conductors and insulators. They have few free electrons that can lead to the flow of current. Semiconductors are essentially a crystal lattice in which the atoms are grouped close together. Example – Silicon, Gallium, etc.

Semiconductors are very unique, their ability of conducting electricity can change when impurities are introduced in the crystal lattice (generally a small percentage of another element is added to the semiconductor).
The free electrons that can conduct electricity are said to be in conduction band, basically all the electrons in the conduction band have enough energy to move away from their atoms and conduct electricity.
Now, increasing the temperature will increase the energy of more electrons, increasing the total number of free electrons in the conduction band, this will result in increase in conductivity and a decrease in resistivity.
Thus, both the assertion and the reasons are false as increase in temperature leads to a decrease in resistivity.

Hence, option D is the correct choice.

We mentioned above that conductivity of semiconductors can change because of the presence of impurities. You may also know that diluted water does not conduct electricity, but we mentioned above that tap water is a conductor. This is because pure water does not conduct electricity but tap water has some impurities which like in the case of semiconductors changes its conductivity, hence, make it a conductor.
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