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Asked in GUJCET 2020 · Energy bands and band gap
Idea: the forbidden gap E_g is the energy an electron must gain to cross from the valence band into the conduction band, and its size is what separates the three classes of solid.
Metal: the two bands overlap, so E_g is effectively zero and electrons are free at any temperature.
Semiconductor: E_g is small, near 1 eV, so thermal energy frees a small number of carriers.
Insulator: E_g is large, several eV and about 6 eV in diamond, so practically no electron crosses and no current flows.
The forbidden gap is therefore largest for the insulator.
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