In a semiconductor, the number density of intrinsic charge carries at 27 ^\circ C is 1.5 \times 1016/m3. If the semiconductor is doped with impurity atom, the hole density increases to 4.5 \times 1022/m3. The electron density in the doped semiconductor is \underline\hspace2cm \times 109/m3.

Electronic Devices PYQ — JEE Main 2021 · 25 Jul · Shift 2 · Q71 with Solution

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Correct answer: 5

For any semiconductor in thermal equilibrium,

$np = n_i^2$

where:

$n_i = 1.5 \times 10^{16}\, \text{m}^{-3}$

$p = 4.5 \times 10^{22}\, \text{m}^{-3}$

We need to find $n$ .

$n = \frac{n_i^2}{p}$

First compute $n_i^2$ :

$n_i^2 = (1.5 \times 10^{16})^2 = 2.25 \times 10^{32}$

Now,

$n = \frac{2.25 \times 10^{32}}{4.5 \times 10^{22}}$

$n = \frac{2.25}{4.5} \times 10^{32-22}$

$n = 0.5 \times 10^{10}$

$n = 5 \times 10^9\, \text{m}^{-3}$

The question asks for:

$\underline{\hspace{2cm}} \times 10^9/\text{m}^3$

So the blank is:

$5$

Stored correct answer = $5$

This matches our derived answer.