The maximum wavelength of electromagnetic radiation which can create a hole-electron pair in the semiconductor Ge is: (Given, the band gap of Ge is 0.72 eV)
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → ~1.7 x 10−6 m
A photon can create an electron-hole pair only if its energy is at least the band gap. The longest wavelength corresponds to a photon energy equal to the band gap:
\( \displaystyle \frac{hc}{\lambda_{\max}} = E_g \)
\( \displaystyle \lambda_{\max} = \frac{hc}{E_g} = \frac{6.63\times10^{-34} \times 3\times10^{8}}{0.72 \times 1.6\times10^{-19}}\,\mathrm{m} \)
\( \displaystyle \lambda_{\max} \approx 1.7\times10^{-6}\,\mathrm{m} \)
Shortcut: With \( hc \approx 1240\,\mathrm{eV\,nm} \): \( \lambda_{\max} = 1240/0.72\,\mathrm{nm} \approx 1720\,\mathrm{nm} = 1.7\times10^{-6}\,\mathrm{m} \).