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Mobilities of electrons and holes in a sample of intrinsic germanium at room temperature are $0.36 \mathrm{~m}^{2} \mathrm{~V}^{-1} \mathrm{~s}^{-1}$ and $0.17 \mathrm{~m}^{2} \mathrm{~V}^{-1} \mathrm{~s}^{-1}$. The electron and hole densities are each equal to $2.5 \times 10^{19}$ $\mathrm{m}^{3}$. The electrical conductivity of germanium is
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The correct answer is:
$2.12 \mathrm{Sm}^{-1}$
As we know, conductivity,
$\begin{array}{l}
\sigma=\frac{1}{\rho}=\rho\left(\mu_{\mathrm{e}} \mathrm{n}_{\mathrm{e}}+\mu_{\mathrm{n}} \mathrm{n}_{\mathrm{n}}\right) \\
\left.=1.6 \times 10^{-19}[0.36+0.17]\left(2.5 \times 10^{19}\right)\right] \\
=2.12 \mathrm{Sm}^{-1}
\end{array}$
$\begin{array}{l}
\sigma=\frac{1}{\rho}=\rho\left(\mu_{\mathrm{e}} \mathrm{n}_{\mathrm{e}}+\mu_{\mathrm{n}} \mathrm{n}_{\mathrm{n}}\right) \\
\left.=1.6 \times 10^{-19}[0.36+0.17]\left(2.5 \times 10^{19}\right)\right] \\
=2.12 \mathrm{Sm}^{-1}
\end{array}$
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