The density of an electron-hole pair in a pure germanium is 3 × 1016 m-3 at room temperature. On doping with aluminium, the hole density increases to 4.5 × 1022 m-3. Now the electron density (in m-3) in doped germanium will be

Question

The density of an electron-hole pair in a pure germanium is 3 × 1016 m-3 at room temperature. On doping with aluminium, the hole density increases to 4.5 × 1022 m-3. Now the electron density (in m-3) in doped germanium will be (A) 1 × 1010 (B) 2 × 1010 (C) 0.5 × 1010 (D) 4 × 1010

Tardigrade Admin · Accepted Answer

n21 = nhne ⇒ ne = ((3× 1016)2/4.5 × 1022)= (9 × 1032/4.5× 1022) = 2 × 1010 m -3

Q. The density of an electron-hole pair in a pure germanium is $3 \times 1 0^{16} m^{- 3}$ at room temperature. On doping with aluminium, the hole density increases to $4.5 \times 1 0^{22} m^{- 3}$ . Now the electron density (in $m^{- 3}$ ) in doped germanium will be

$1 \times 1 0^{10}$

$2 \times 1 0^{10}$

$0.5 \times 1 0^{10}$

$4 \times 1 0^{10}$

$n_{1}^{2} = n_{h} n_{e}$
$\Rightarrow n_{e} = \frac{( 3 \times 1 0 ^{16} ) ^{2}}{4.5 \times 1 0 ^{22}} = \frac{9 \times 1 0 ^{32}}{4.5 \times 1 0 ^{22}}$
$= 2 \times 1 0^{10} m^{- 3}$

Q. The density of an electron-hole pair in a pure germanium is 3×1016m−3 at room temperature. On doping with aluminium, the hole density increases to 4.5×1022m−3. Now the electron density (in m−3) in doped germanium will be

1×1010

2×1010

0.5×1010

4×1010