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Assertion: The probability of electrons ...

Assertion: The probability of electrons to be found in the conduction band of an intrinsic semiconductor at a finite temperature decrease exponentially with increasing band gap.
Reason: It will be more difficult for the electron to cross over the large band gap while going from valence band to conduction band.

A

If both assertion and reason are true and reason is the correct explanation of assertion.

B

If both assertion and reason are true not but reason is not the correct explanation of assertion.

C

If assertion is true but reason is false

D

If both assertion and reason are false.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we need to analyze both the assertion and the reason provided. ### Step 1: Understanding the Assertion The assertion states that "the probability of electrons to be found in the conduction band of an intrinsic semiconductor at a finite temperature decreases exponentially with increasing band gap." - In intrinsic semiconductors, at absolute zero, all electrons are in the valence band. As the temperature increases, some electrons gain enough thermal energy to jump into the conduction band. - The probability of this happening is influenced by the band gap energy (Eg). As Eg increases, fewer electrons have enough energy to jump from the valence band to the conduction band, leading to a decrease in the probability of finding electrons in the conduction band. ### Step 2: Understanding the Reason The reason states that "it will be more difficult for the electron to cross over the large band gap while going from valence band to conduction band." - This is a direct explanation of the assertion. If the band gap is larger, the energy required for an electron to jump from the valence band to the conduction band is also larger. Therefore, fewer electrons will have sufficient energy to make this transition, which aligns with the assertion that the probability decreases. ### Step 3: Conclusion Both the assertion and the reason are true, and the reason provides a correct explanation for the assertion. Thus, we conclude that: - Assertion: True - Reason: True - The reason is a correct explanation of the assertion. ### Final Answer Both the assertion and the reason are true, and the reason correctly explains the assertion. ---
To solve the question, we need to analyze both the assertion and the reason provided. ### Step 1: Understanding the Assertion The assertion states that "the probability of electrons to be found in the conduction band of an intrinsic semiconductor at a finite temperature decreases exponentially with increasing band gap." - In intrinsic semiconductors, at absolute zero, all electrons are in the valence band. As the temperature increases, some electrons gain enough thermal energy to jump into the conduction band. - The probability of this happening is influenced by the band gap energy (Eg). As Eg increases, fewer electrons have enough energy to jump from the valence band to the conduction band, leading to a decrease in the probability of finding electrons in the conduction band. ...
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