The intrinsic conductivity of germanium at 27° C 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

Question

The intrinsic conductivity of germanium at 27° C 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 (A) 2.37 × 1019 m -3 (B) 3.28 × 1019 m -3 (C) 7.83 × 1019 m -3 (D) 8.47 × 1019 m -3

Tardigrade Admin · Accepted Answer

Conductivity, σ=(1/ρ)= e ( n e μ e + n h μ h ) i.e., 2.13=1.6 × 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 × 10-19 × 0.56)=2.37 × 1019 m -3

Q. The intrinsic conductivity of germanium at $2 7^{\circ} C$ is $2.13 mh o$ $m^{- 1}$ 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

$2.37 \times 1 0^{19} m^{- 3}$

$3.28 \times 1 0^{19} m^{- 3}$

$7.83 \times 1 0^{19} m^{- 3}$

$8.47 \times 1 0^{19} m^{- 3}$

Q. The intrinsic conductivity of germanium at 27∘C is 2.13mho m−1 and mobilities of electrons and holes are 0.38 and 0.18 m2V−1s−1 respectively. The density of charge carriers is

2.37×1019m−3

3.28×1019m−3

7.83×1019m−3

8.47×1019m−3

Conductivity, σ=ρ1​=e(ne​μe​+nh​μh​) i.e., 2.13=1.6×10−19(0.38+0.18)ni​ (Since in intrinsic semi-conductor, ne​=nh​=ni​ ) ∴ density of charge carriers, ni​ =1.6×10−19×0.562.13​=2.37×1019m−3

Q. The intrinsic conductivity of germanium at $2 7^{\circ} C$ is $2.13 mh o$ $m^{- 1}$ 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

$2.37 \times 1 0^{19} m^{- 3}$

$3.28 \times 1 0^{19} m^{- 3}$

$7.83 \times 1 0^{19} m^{- 3}$

$8.47 \times 1 0^{19} m^{- 3}$