Assertion (A): The resistivity of a semiconductor decreases with temperature.
Reason (R ): The atoms of a semiconductor vibrate with larger amplitude at higher temperature there by increasing it's resistivity.

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

To solve the given question, we will analyze both the assertion and the reason provided.

### Step 1: Understand the Assertion
The assertion states that "The resistivity of a semiconductor decreases with temperature."

- **Explanation**: In semiconductors, as the temperature increases, more charge carriers (electrons and holes) are generated due to the breaking of covalent bonds. This increase in charge carriers enhances the conductivity of the semiconductor. Since resistivity (ρ) is inversely related to conductivity (σ), we can conclude that as conductivity increases, resistivity decreases.

### Step 2: Understand the Reason
The reason states that "The atoms of a semiconductor vibrate with larger amplitude at higher temperature thereby increasing its resistivity."

- **Explanation**: While it is true that atoms in a semiconductor vibrate more at higher temperatures, this does not lead to an increase in resistivity. Instead, the increased vibration can lead to more collisions among charge carriers, but the primary effect at higher temperatures is the generation of more charge carriers. Therefore, this reasoning is incorrect because it contradicts the assertion.

### Step 3: Conclusion
Based on the analysis:
- The assertion (A) is **true**: The resistivity of a semiconductor does decrease with temperature.
- The reason (R) is **false**: The increased amplitude of atomic vibrations does not increase resistivity; rather, it is the increase in charge carriers that decreases resistivity.

Thus, the correct answer is that the assertion is true, but the reason is false.

### Final Answer
- Assertion (A) is true.
- Reason (R) is false.