Q158 / 160 · TS EAMCET 2021 (06 Aug Shift 2) · Physics
What is the maximum wavelength of electromagnetic radiation that create a electron-hole pair in material with band gap $0.7 \mathrm{eV}$ ? Planck's constant $=4.136 \times 10^{15} \mathrm{eV}-\mathrm{s}$, velocity of light $=3 \times 10^8 \mathrm{~m} / \mathrm{s}$.
- A$1773 \times 10^{-8} \mathrm{~m}$
- Correct answerB$1773 \times 10^{-9} \mathrm{~m}$
- C$1873 \times 10^{-9} \mathrm{~m}$
- D$1873 \times 10^{-8} \mathrm{~m}$
Solution
The band gap energy, $E_g=0.7 \mathrm{eV}$
Let the maximum wavelength of the electromagnetic radiation be $\lambda$.
$$
\begin{aligned}
& \therefore \text { We can write, } \frac{h c}{\lambda}=E_g \\
& \Rightarrow \quad \lambda=\frac{h c}{E_g}=\frac{4.136 \times 10^{-15} \times 3 \times 10^8}{0.7} \\
& \Rightarrow \quad \lambda=17.73 \times 10^{-7} \mathrm{~m} \\
& =1773 \times 10^{-9} \mathrm{~m} \\
&
\end{aligned}
$$
Hence, the correct answer is option: 'B'.