The forbidden energy band gap in conductors, semiconductors and insulators are `EG_(1), EG_(2)` and `EG_(3)` respectively. The relation among them is

Options

A. `EG_(1)=EG_(2)=EG_(3)`
B. `EG_(1)ltEG_(2)ltEG_(3)`
C. `EG_(1)gtEG_(2)gtEG_(3)`
D. `EG_(1)ltEG_(2)gtEG_(3)`

Explanation

To solve the question regarding the forbidden energy band gaps in conductors, semiconductors, and insulators, we can follow these steps:

### Step 1: Understand the Concept of Energy Band Gaps
The energy band gap (EG) is the energy difference between the valence band and the conduction band in a material. It determines how easily electrons can move from the valence band to the conduction band, which in turn affects the electrical conductivity of the material.

### Step 2: Analyze the Band Structure of Conductors, Semiconductors, and Insulators
- **Conductors**: In conductors, the conduction band and the valence band overlap. This means that there is no energy gap (EG1 ≈ 0). Electrons can easily flow, allowing conductors to conduct electricity efficiently.

- **Semiconductors**: In semiconductors, there is a small energy gap (EG2). This gap allows some electrons to jump from the valence band to the conduction band at room temperature, enabling semiconductors to conduct electricity, but not as freely as conductors.

- **Insulators**: In insulators, the energy gap (EG3) is large. This means that at room temperature, it is very difficult for electrons to jump from the valence band to the conduction band, resulting in very poor conductivity.

### Step 3: Establish the Relationship Among the Energy Band Gaps
From the analysis:
- **EG1 (Conductor)** is the smallest, as there is effectively no gap.
- **EG2 (Semiconductor)** is larger than EG1 but smaller than EG3.
- **EG3 (Insulator)** is the largest, as it represents a significant barrier for electron movement.

Thus, the relationship among the energy band gaps is:
\[ EG_1 < EG_2 < EG_3 \]

### Final Answer
The relation among the forbidden energy band gaps in conductors, semiconductors, and insulators is:
\[ EG_1 < EG_2 < EG_3 \]

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