Concept:The forbidden energy bandgap (\(E_g\)) is the energy difference between the top of the valence band and the bottom of the conduction band. In semiconductors, this gap is relatively narrow—on the order of \(1\text{ eV}\) (e.g., \(1.12\text{ eV}\) for Si and \(0.67\text{ eV}\) for Ge at room temperature).
Formula:$$E_g(\text{Si}) \approx 1.1\text{ eV}, \quad E_g(\text{Ge}) \approx 0.7\text{ eV}$$
Solution:- In insulators, \(E_g > 3\text{ to }6\text{ eV}\).
- In semiconductors, \(E_g \approx 1\text{ eV}\).
- In conductors (metals), the valence and conduction bands overlap (\(E_g = 0\)).
Why other options are incorrect:- Option A: \(10\text{ MeV}\) is in the realm of nuclear binding energies, many orders of magnitude too high.
- Option B: \(1\text{ MeV}\) is typical of gamma-ray photons and nuclear transitions.
- Option D: \(100\text{ eV}\) falls in the soft X-ray range, far exceeding solid-state bandgaps.
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