The band gap of an insulator, conductor and semiconductor are respectively `E_(g1)` and `E_(g2)` and `E_(g3).` The relationship between them is given as______.

Options

A. `E_(g_1)gtE_(g_2)ltE_(g_3)`
B. `E_(g_1)gtE_(g_2)gtE_(g_3)`
C. `E_(g_1)ltE_(g_2)gtE_(g_3)`
D. `E_(g_1)ltE_(g_2)ltE_(g_3)`

Answer

To solve the problem regarding the relationship between the band gaps of an insulator, conductor, and semiconductor, we can follow these steps:

### Step 1: Understand the definitions
- **Band Gap**: The energy difference between the conduction band and the valence band in a material. It determines the electrical conductivity of the material.
- **Insulator**: Has a large band gap, making it difficult for electrons to move from the valence band to the conduction band.
- **Semiconductor**: Has a smaller band gap compared to insulators, allowing some electrons to jump to the conduction band at room temperature.
- **Conductor**: Has a negligible or zero band gap, allowing electrons to flow freely.

### Step 2: Identify the band gaps
Let’s denote the band gaps as follows:
- \( E_{g1} \): Band gap of the insulator
- \( E_{g2} \): Band gap of the conductor
- \( E_{g3} \): Band gap of the semiconductor

### Step 3: Compare the band gaps
From the definitions:
- The band gap of an insulator (\( E_{g1} \)) is the largest because it requires a significant amount of energy to move electrons to the conduction band.
- The band gap of a semiconductor (\( E_{g3} \)) is smaller than that of an insulator but larger than that of a conductor.
- The band gap of a conductor (\( E_{g2} \)) is negligible or close to zero, meaning electrons can easily flow.

### Step 4: Establish the relationship
From the above comparisons, we can establish the following relationship:
\[ E_{g1} > E_{g3} > E_{g2} \]

### Conclusion
Thus, the relationship between the band gaps of an insulator, conductor, and semiconductor is:
\[ E_{g1} > E_{g3} > E_{g2} \]