Assertion (A): As the temperature of a semiconductor increases, its resistance decreases.
Reason (R ): The energy gap between conduction band and valence band is small.

Options

A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true but R is NOT the correct explanation of A
C. A is true but R is false
D. A is false and R is true

Explanation

### Step-by-Step Solution:

1. **Understanding the Assertion**: The assertion states that as the temperature of a semiconductor increases, its resistance decreases. This is a known behavior of semiconductors. At higher temperatures, more electrons gain enough energy to jump from the valence band to the conduction band, leading to increased conductivity and decreased resistance.

2. **Analyzing the Reason**: The reason provided states that the energy gap between the conduction band and valence band is small. In semiconductors, the energy gap is indeed smaller compared to insulators, which allows electrons to move more freely between these bands when thermal energy is provided (i.e., when temperature increases).

3. **Connecting Assertion and Reason**: The assertion is true because the increase in temperature leads to more electrons being excited to the conduction band, thus decreasing resistance. The reason is also true because the small energy gap in semiconductors facilitates this process. Therefore, both the assertion and reason support each other.

4. **Conclusion**: Since both the assertion and the reason are true, and the reason correctly explains the assertion, we conclude that the assertion is correct and the reason is valid.

### Final Answer:
Both the assertion (A) and the reason (R) are true, and the reason supports the assertion.

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