Concept:To excite an electron from the valence band to the conduction band, an incident photon must deliver energy at least equal to the bandgap \( E_g \).
Formula:$$E_{\text{photon}} = h f = \frac{h c}{\lambda} \ge E_g$$
Solution:- If \( h f < E_g \), the photon cannot excite an electron across the forbidden gap, and the material is transparent to that wavelength.
- If \( h f \ge E_g \), the photon is absorbed, exciting a valence electron into the conduction band and creating a free electron-hole pair.
Why other options are incorrect:- Option A: Sub-bandgap photons lack the energy needed to bridge the forbidden gap.
- Option B: \( E_g / 2 \) is insufficient for single-photon band-to-band excitation.
- Option C: The required wavelength depends on the specific material's bandgap \( E_g \).
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