In a p type semiconductor the acceptor level is situated 50 meV above the valence band. The maximum wavelength of light required to produce a hole will be :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 2.48 \times 10^{-5}\,\mathrm{m} \)
A hole is produced when an electron from the valence band is lifted to the acceptor level. The photon must carry at least this energy gap, so the maximum wavelength corresponds to a photon energy exactly equal to the gap.
\( \displaystyle \lambda_{\max} = \frac{hc}{E} \)
\( E = 50\,\mathrm{meV} = 0.05\,\mathrm{eV} \)
\( hc = 1240\,\mathrm{eV\,nm} \)
\( \displaystyle \lambda_{\max} = \frac{1240\,\mathrm{eV\,nm}}{0.05\,\mathrm{eV}} = 24800\,\mathrm{nm} \)
\( \displaystyle \lambda_{\max} = 24800\times10^{-9}\,\mathrm{m} = 2.48\times10^{-5}\,\mathrm{m} \)