Concept:LEDs emit light via spontaneous emission over a narrow range of energy states around the band edge (typically \( \Delta E \approx 2\text{–}3\, k T \)), producing a quasi-monochromatic spectral linewidth of roughly \( 20\text{ to } 50\text{ nm} \).
Formula:$$\Delta E \approx 3 k T \approx 0.075\text{ eV} \implies \Delta \lambda \approx \frac{\lambda_0^2}{h c} \Delta E \approx 20\text{–}50\text{ nm}$$
Solution:- Because carriers occupy a thermal distribution of states near the band edges (spanning \( \approx 3kT \)), emitted photons have a small spread in wavelength.
- This produces a narrow-band, quasi-monochromatic spectrum with a typical full-width at half-maximum (FWHM) of \( 20\text{ to } 50\text{ nm} \).
Why other options are incorrect:- Option A: Linewidths on the order of \( 0.001\text{ nm} \) are characteristic of stimulated emission in laser diodes, not LEDs.
- Option B: Broad continuous spectra across \( 1000\text{ nm} \) are produced by thermal incandescent sources.
- Option D: Quantum thermal broadening prevents zero linewidth in spontaneous emission.
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