Assertion: The resistivity of a semiconductor increases with temperature.
Reason: The atoms of a semiconductor vibrate with larger amplitude at higher temperature therby increasing it resistivity.

Options

A. If the both assertion and reason are true and the reason is the correct explanation of the assertion
B. If both assertion and reason are true and the reason is not the correct explanation of the assertion
C. If assertion is true but reason is false
D. If both assertion and reason are false statements.

Explanation

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

**Assertion:** The resistivity of a semiconductor increases with temperature.

1. **Understanding Resistivity and Conductivity:**
- Resistivity (ρ) is a measure of how strongly a material opposes the flow of electric current. It is inversely related to conductivity (σ), which is the ability of a material to conduct electricity.
- The relationship can be expressed as:
\[ \rho = \frac{1}{\sigma} \]

2. **Behavior of Semiconductors with Temperature:**
- In semiconductors, as temperature increases, more electrons gain enough energy to jump from the valence band to the conduction band.
- This results in an increase in the number of charge carriers (electrons) available for conduction.

3. **Effect on Conductivity:**
- Since the number of charge carriers (n) increases, the conductivity (σ) of the semiconductor also increases.
- Therefore, as conductivity increases, resistivity must decrease:
\[ \text{If } \sigma \text{ increases, then } \rho \text{ decreases.} \]

4. **Conclusion on Assertion:**
- The assertion that "the resistivity of a semiconductor increases with temperature" is **incorrect**. In fact, the resistivity decreases with increasing temperature.

**Reason:** The atoms of a semiconductor vibrate with larger amplitude at higher temperature thereby increasing its resistivity.

5. **Understanding Atomic Vibration:**
- It is true that as temperature increases, the atoms in a semiconductor vibrate more vigorously due to increased thermal energy.
- However, this increased vibration does not lead to an increase in resistivity. Instead, the increased thermal energy helps electrons to jump into the conduction band, enhancing conductivity.

6. **Conclusion on Reason:**
- The reason provided is also **incorrect** because while atomic vibrations increase with temperature, they do not increase resistivity; rather, they contribute to the increased conductivity.

**Final Conclusion:**
- Both the assertion and the reason are incorrect. Therefore, the correct answer to the question is that both the assertion and the reason are false statements.

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