Q83 / 120 · VITEEE 2013 · Physics

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

  • A
    $4.24 \mathrm{Sm}^{-1}$
  • Correct answer
    B
    $2.12 \mathrm{Sm}^{-1}$
  • C
    $1.09 \mathrm{Sm}^{-1}$
  • D
    $0.47 \mathrm{Sm}^{-1}$

Solution

As we know, conductivity, $\begin{array}{l} \sigma=\frac{1}{\rho}=\rho\left(\mu_{\mathrm{e}} \mathrm{n}_{\mathrm{e}}+\mu_{\mathrm{n}} \mathrm{n}_{\mathrm{n}}\right) \\ \left.=1.6 \times 10^{-19}[0.36+0.17]\left(2.5 \times 10^{19}\right)\right] \\ =2.12 \mathrm{Sm}^{-1} \end{array}$

Hence, the correct answer is option: 'B'.

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