What is forbidden energy gap?

Answer

### Step-by-Step Solution:

1. **Understanding Energy Bands**: In solid-state physics, materials are characterized by energy bands. The two most important bands are the valence band and the conduction band. The valence band is the highest energy band that is fully occupied by electrons, while the conduction band is the band above it that is typically empty or only partially filled.

2. **Definition of Forbidden Energy Gap**: The forbidden energy gap, also known as the band gap, is defined as the energy difference between the top of the valence band and the bottom of the conduction band in a material.

3. **Visual Representation**: If we visualize this, we can represent the conduction band and the valence band on an energy scale. The conduction band is at a higher energy level than the valence band. The gap between these two bands is what we refer to as the forbidden energy gap.

4. **Mathematical Representation**: Mathematically, if we denote the energy of the top of the valence band as \(E_v\) and the energy of the bottom of the conduction band as \(E_c\), then the forbidden energy gap \(E_g\) can be expressed as:
\[ E_g = E_c - E_v \]

5. **Material Dependence**: The value of the forbidden energy gap varies with different materials. For example, in conductors, the gap is negligible, while in insulators, the gap is large. Semiconductors have a moderate gap that allows them to conduct electricity under certain conditions.

6. **Significance**: The size of the forbidden energy gap is crucial as it determines the electrical conductivity of the material. A smaller gap means that electrons can be excited to the conduction band more easily, leading to better conductivity.