Question

Find the maximum wavelength of electromagnetic radiation which can create a hole - electron pair in germanium. The band gap in germanium is $0.65\text{eV}$.
$(hc=1242\text{eV nm})$

• A. $1.9\times {10}^{-6}\text{m}$
• B. $2.5\times {10}^{-4}\text{m}$
• C. $1.9\times {10}^{-4}\text{m}$
• D. $2.5\times {10}^{-6}\text{m}$

Answer 1

The correct option is A $1.9\times {10}^{-6}\text{m}$

Given, $E=0.65\text{eV}$

For the electron-hole pair creation, the energy of the radiation should be at least equal to the band gap of the material.

$\Rightarrow E=\frac{hc}{\lambda }$

$\Rightarrow \lambda =\frac{hc}{E}=\frac{1242\text{eV nm}}{0.65\text{eV}}$

$\Rightarrow \lambda =1910.7\text{nm}=1910.7\times {10}^{-9}\text{m}$

$\Rightarrow \lambda =1.9\times {10}^{-6}\text{m}$

Hence, option $\left(A\right)$ is correct.