Question
Find the maximum wavelength of electromagnetic radiation which can create a hole-electron pair in germanium. The band gap in germanium is 0.65eV.
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Answer
Given,
Band gap of germanium, E = 0.65eV
Wavelength of the incident radiation, $\lambda=?$
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,
$\text{E}=\frac{\text{hc}}{\lambda}$
$\Rightarrow\lambda=\frac{\text{hc}}{\text{E}}=\frac{1242\text{eV}-\text{nm}}{0.65\text{eV}}$
$\Rightarrow\lambda=1910.7\times10^{-9}\text{m}$
$\Rightarrow\lambda=1.9\times10^{-5}\text{m}$
Band gap of germanium, E = 0.65eV
Wavelength of the incident radiation, $\lambda=?$
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,
$\text{E}=\frac{\text{hc}}{\lambda}$
$\Rightarrow\lambda=\frac{\text{hc}}{\text{E}}=\frac{1242\text{eV}-\text{nm}}{0.65\text{eV}}$
$\Rightarrow\lambda=1910.7\times10^{-9}\text{m}$
$\Rightarrow\lambda=1.9\times10^{-5}\text{m}$
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