Choose the only false statement from the following :

Options

A. Substances with energy gap of the order of 10 eV are insulators
B. The conductivity of a semiconductor increases with increase 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 determine the only false statement from the given options, we will analyze each statement based on our understanding of semiconductor physics.

### Step-by-step Solution:

1. **Understanding the Energy Gap**:
- The energy gap (ΔE) is the difference in energy between the conduction band and the valence band in a material.
- In insulators, this energy gap is typically greater than 10 eV, making it difficult for electrons to jump from the valence band to the conduction band.

**Hint**: Recall that the energy gap is crucial in determining the electrical properties of materials.

2. **Analyzing Statement 1**:
- Statement: "Substances with energy gap above the order of 10 eV are insulators."
- This statement is true because insulators have a large energy gap, typically greater than 10 eV.

**Hint**: Think about the characteristics of insulators and their energy gaps.

3. **Analyzing Statement 2**:
- Statement: "The conductivity of semiconductor increases with increase in temperature."
- This statement is true. As temperature increases, more electrons gain enough energy to jump into the conduction band, thus increasing conductivity.

**Hint**: Consider how temperature affects the movement of charge carriers in semiconductors.

4. **Analyzing Statement 3**:
- Statement: "In conductors, the valence and conduction band may overlap."
- This statement is true. In conductors, the conduction band and valence band overlap, allowing electrons to flow freely without needing additional energy.

**Hint**: Reflect on the behavior of electrons in conductors compared to semiconductors and insulators.

5. **Analyzing Statement 4**:
- Statement: "The resistivity of a semiconductor increases with increasing temperature."
- This statement is false. In semiconductors, as temperature increases, the resistivity actually decreases because more charge carriers become available for conduction.

**Hint**: Remember the relationship between temperature and resistivity in semiconductors.

### Conclusion:
The only false statement among the options provided is:
**"The resistivity of a semiconductor increases with increasing temperature."**