The electrical conductivity of a semiconductor increases when electromagnetic radiation of wavelength shorter than 2480 nm is incident on it. The band gap for the semiconductor is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 0.5 eV
A photon can lift an electron from the valence band to the conduction band, and so increase the conductivity, only if its energy is at least the band gap. The longest wavelength that works, 2480 nm, therefore corresponds to the photon energy equal to the gap.
\( \displaystyle E_g = \frac{hc}{\lambda} = \frac{6.63\times10^{-34}\times3\times10^{8}}{2480\times10^{-9}}\,\mathrm{J} = 8.0\times10^{-20}\,\mathrm{J} \)
\( \displaystyle E_g = \frac{8.0\times10^{-20}}{1.6\times10^{-19}}\,\mathrm{eV} = 0.5\,\mathrm{eV} \)
Shortcut: With \( hc \approx 1240\,\mathrm{eV\,nm} \), \( E_g = 1240/2480 = 0.5\,\mathrm{eV} \) in one step.