The intrinsic conductivity of germanium at `27^(@)` is 2.13 mho `m^(-1)` and mobilities of electrons and holes are 0.38 and `0.18 m^(2) V^(-1) s^(-1)` respectively. The density of charge carriers is

Options

A. `2.37 xx 10^19 m^(-3)`
B. `3.28 xx 10^19 m^(-3) `
C. `7.83 xx 10^(-19) m^(-3) `
D. ` 8.47 xx 10^19 m^(-3)`

Answer

A

Explanation

Conductivity, `sigma = 1/rho = e(n_emu_e + n_hmu_h)`
ie, `2.13 = 1.6 xx 10^(-19) (0.38 + 0.18)n_i`
(Since in intrinsic semi-conductor, `n_e= n_h = n_i`)
`:. ` density of charge carriers, `n_i`
` = 2.13/(1.6 xx 10^(-19) xx 0.56) = 2.37 xx 10^(19) m^(-3)`