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Question
Find the maximum wavelength of electromagnetic radiation which can create a hole-electron pair in germanium. The band gap in germanium is 0.65 eV.
(Use Planck constant h = 4.14 × 10-15 eV-s, Boltzmann constant k = 8·62 × 10-5 eV/K.)
Solution
Given:
Band gap of germanium, E = 0.65 eV
Wavelength of the incident radiation, λ = ?
For the electron‒hole pair creation, the energy of the incident radiation should be at least equal to the band gap of the material.
So,
\[E = \frac{hc}{\lambda}\]
\[ \Rightarrow \lambda = \frac{hc}{E} = \frac{1242 eV - \text{ nm }}{0 . 65 eV}\]
\[ \Rightarrow \lambda = 1910 . 7 \times {10}^{- 9} \text{m}\]
\[ \Rightarrow \lambda \approx 1 . 9 \times {10}^{- 6} \text{m}\]
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