Concept:At \( 0\text{ K} \), the valence band is completely filled and the conduction band is completely empty. As temperature rises to \( 300\text{ K} \), thermal energy breaks some covalent bonds, exciting electrons across the band gap \( E_g \) into the conduction band and leaving behind holes in the valence band.
Formula:$$n_i = p_i = \sqrt{N_c N_v} \exp\left(-\frac{E_g}{2 k T}\right) > 0 \quad (\text{at } T = 300\text{ K})$$
Solution:- Thermal energy (\( k T \approx 0.026\text{ eV} \)) excites a fraction of valence electrons across the band gap into the conduction band.
- This creates equal concentrations of mobile conduction electrons and valence holes (\( n = p = n_i \)), enabling intrinsic electrical conduction.
Why other options are incorrect:- Option A: This describes the ground state at 0 K, not room temperature.
- Option B: Total electrons are conserved; they do not vanish from the crystal.
- Option D: The energy band gap narrows slightly with temperature, but it does not disappear.
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