What is the range of energy gap `( E_g )` in insulators , semiconductors and conductors ?

Explanation

To determine the range of the energy gap \( (E_g) \) in insulators, semiconductors, and conductors, we can analyze the properties of these materials based on their electronic structure.

### Step-by-Step Solution:

1. **Understanding Energy Gap**:
- The energy gap \( (E_g) \) is the energy difference between the valence band (where electrons are normally present) and the conduction band (where electrons can move freely and contribute to conduction).
- Electrons need to gain energy equal to the energy gap to jump from the valence band to the conduction band.

2. **Energy Gap in Insulators**:
- Insulators have a large energy gap, which prevents electrons in the valence band from easily jumping to the conduction band.
- The typical range of the energy gap in insulators is \( E_g \geq 3 \, \text{eV} \). This large gap means that at room temperature, very few electrons can gain enough energy to conduct electricity.

3. **Energy Gap in Semiconductors**:
- Semiconductors have a smaller energy gap compared to insulators, allowing some electrons to jump to the conduction band at room temperature or with the addition of energy (e.g., heat or light).
- The energy gap in semiconductors typically ranges from \( 0 \, \text{eV} \) to \( 3 \, \text{eV} \). This range allows for their unique properties, such as being able to conduct electricity under certain conditions.

4. **Energy Gap in Conductors**:
- Conductors, such as metals, have a very small or negligible energy gap. In ideal conductors, the energy gap is effectively \( 0 \, \text{eV} \).
- In non-ideal conductors, there may be a very small energy gap (e.g., around \( 0.1 \, \text{eV} \)), but this is still considered negligible for conduction purposes.

### Summary of Energy Gaps:
- **Insulators**: \( E_g \geq 3 \, \text{eV} \)
- **Semiconductors**: \( 0 \, \text{eV} < E_g < 3 \, \text{eV} \)
- **Conductors**: \( E_g \approx 0 \, \text{eV} \) (or slightly more for non-ideal conductors)