Q158 / 160 · AP EAMCET 2024 (21 May Shift 2) · Physics
Pure silicon at 300 K has equal electron and hole concentration of $1.5 \times 10^{16} \mathrm{~m}^{-3}$. If the hole concentration increases to $3 \times 10^{22} \mathrm{~m}^{-3}$, then electron concentration in the silicon is
- A$0.75 \times 10^9 \mathrm{~m}^{-3}$
- B$750 \mathrm{~m}^{-3}$
- C$75 \mathrm{~m}^{-3}$
- Correct answerD$7.5 \times 10^9 \mathrm{~m}^{-3}$
Solution
$\mathrm{n}_{\mathrm{e}}=\mathrm{n}_{\mathrm{h}}=1.5 \times 10^{16} \mathrm{~m}^{-3}$
$\therefore \quad$ Number of intrinsic charge carriers,
$\mathrm{n}_{\mathrm{i}}^2=\mathrm{n}_{\mathrm{e}} \mathrm{n}_{\mathrm{h}}=\left(1.5 \times 10^{16}\right)^2$
Again, $\begin{aligned} & \left(1.5 \times 10^{16}\right)^2=\mathrm{n}_{\mathrm{e}}\left(3 \times 10^{22}\right) \\ & \therefore \quad \mathrm{n}_{\mathrm{e}}=7.5 \times 10^9 \mathrm{~m}^{-3} \end{aligned}$
Again, $\begin{aligned} & \left(1.5 \times 10^{16}\right)^2=\mathrm{n}_{\mathrm{e}}\left(3 \times 10^{22}\right) \\ & \therefore \quad \mathrm{n}_{\mathrm{e}}=7.5 \times 10^9 \mathrm{~m}^{-3} \end{aligned}$
Hence, the correct answer is option: 'D'.