Question

Mobilities of electrons and holes in a sample of intrinsic germanium at room temperature are $0.54\, m^2\, V^{-1} \,s^{-1}$ and $0.18 \,m^2 \,V^{-1} s^{-1}$ respectively. If the electron and hole densities are equal to $3.6 \times 10^{19}\, m^{-3}$ the germanium conductivity is

• A. $4.14 \,S\, m^{-1}$
• B. $2.12 \,S \,m^{- 1}$
• C. $1.13\, S\,m^{-1}$
• D. $5.6\, S \,m^{-1}$

Answer 1

Answer: (B)

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 \left(\mu_{ e } n _{ e }+\mu_{ n } n _{ n }\right) $ $\left.=1.6 \times 10^{-19}\left[0.36 \times 2.5 \times 10^{19}+0.17 \times 2.5 \times 10^{19}\right)\right] $
$=2.12 Sm ^{-1}$ So the electrical conductivies of germanium is $2.12 Sm ^{-1}$