Question

Mobilities of electrons and holes in a sample of intrinsic germanium at room temperature are $0.36m^2{V}^{-1}{s}^{-1}$ and $0.17m^2{V}^{-1}{s}^{-1}$. The electron and hole densities are each equal to $2.5\times {10}^{19}{m}^3$. The electrical conductivity of germanium is

• A. $4.24S{m}^{-1}$
• B. $2.12S{m}^{-1}$
• C. $1.09S{m}^{-1}$
• D. $0.47S{m}^{-1}$

Answer 1

Answer: (B)

$2.12S{m}^{-1}$

Given in question,

Mobilities of electrons${\mu }_e=0.36\times m^2{V}^{-1}{s}^{-1}$

Mobilities o holes${\mu }_h=0.17\times m^2{V}^{-1}{s}^{-1}$

densities of electron$=$ densities of holes$=2.5\times {10}^{19}{m}^{-3}$

As we know, conductivity,
$\sigma =\frac{1}{p}=e({\mu }_e{n}_e+{\mu }_n{n}_n)$
$=1.6\times {10}^{-19}[0.36\times 2.5\times {10}^{19}+0.17\times 2.5\times {10}^{19})]$
$=2.12S{m}^{-1}$

So the electrical conductivies of germanium is$2.12S{m}^{-1}$