The intrinsic germanium conductivity at $27^{0}$ is $2.13 \frac{m h o_{}}{m}$ and mobility of electron and holes are 0.38 and $0.18 m^{2} v^{- 1} s^{- 1}$ respectively. The density of charge carriers is

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$3.7 \times 10^{19} / m^{3}$

$8.9 \times 10^{13} / m^{3}$

$2.37 \times 10^{19} / m^{3}$

$2.5 \times 10^{19} / m^{3}$

answer is C.

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Detailed Solution

$\begin{array}{l} I n i n t r i n s i c s e m i c o n d u c t o r, n_{e} = n_{h} = n_{i} \\ C o n d u c t i v i t y, σ = n_{i} e (μ_{e} + μ_{n}) \\ \Rightarrow n_{i} = \frac{σ}{e (μ_{e} + μ_{h})} = \frac{2.13}{1.6 \times 10^{- 19} (0.38 + 0.18)} \\ \Rightarrow n_{i} = \frac{2.13 \times 10^{19}}{1.6 \times 0.56} = 2.37 \times 10^{19} / m^{3} \end{array}$