Concept:The forbidden energy band gap (\( E_g \)) is the energy difference between the top of the valence band and the bottom of the conduction band.
Formula:$$E_{g,\text{insulator}} (> 3\text{ to } 6\text{ eV}) > E_{g,\text{semiconductor}} (\approx 0.7\text{–}1.1\text{ eV}) > E_{g,\text{conductor}} (\approx 0\text{ eV})$$
Solution:- In insulators (e.g., diamond, quartz), \( E_g \ge 6\text{ eV} \), meaning thermal energy at room temperature cannot excite electrons across the gap.
- Semiconductors have a moderate gap (\( \approx 1.1\text{ eV} \) for Si, \( 0.7\text{ eV} \) for Ge).
- Conductors have overlapping bands with zero forbidden gap.
Why other options are incorrect:- Option A: Conductors have zero energy gap because valence and conduction bands overlap.
- Option B: Semiconductors have a narrow gap (\( \sim 1\text{ eV} \)), significantly smaller than that of insulators.
- Option D: Superconductors are metallic conductors at low temperatures with overlapping bands.
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