Choose the only false statement form the following

Options

A. Substances with energy gap of the order of `10eV` are insulators
B. The conductivity of a semiconductor increases with increases in temperature
C. In conductors the valence and conduction bands may overlap
D. The resistivity of a semiconductor increases with increase in temperature

Answer

To solve the question of identifying the only false statement from the provided options, we will analyze each statement regarding their truthfulness based on our understanding of solid-state physics, particularly focusing on conductors, semiconductors, and insulators.

### Step-by-Step Solution:

1. **Analyze Statement A**: "A substance with energy gap of order of 10 electron volts are insulators."
- **Explanation**: Insulators typically have a large energy gap (greater than 6 eV), which prevents electrons from moving to the conduction band at room temperature. An energy gap of 10 eV is indeed characteristic of insulators.
- **Conclusion**: This statement is **true**.

2. **Analyze Statement B**: "The conductivity of semiconductor increases with increase in temperature."
- **Explanation**: In semiconductors, as temperature increases, more electrons gain enough energy to jump from the valence band to the conduction band, resulting in increased conductivity.
- **Conclusion**: This statement is **true**.

3. **Analyze Statement C**: "The conductors in the valence and conduction band may overlap."
- **Explanation**: In conductors, the valence band and conduction band can overlap, allowing electrons to flow freely without a band gap. This is a characteristic feature of metals.
- **Conclusion**: This statement is **true**.

4. **Analyze Statement D**: "The resistivity of a semiconductor increases with increasing temperature."
- **Explanation**: This statement is incorrect because, in semiconductors, as temperature increases, the resistivity actually decreases due to the increased number of charge carriers (electrons) that can move to the conduction band.
- **Conclusion**: This statement is **false**.

### Final Answer:
The only false statement is **D**: "The resistivity of a semiconductor increases with increasing temperature."

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