A pure silicon crystal at temperature 300 K has electron and hole concentration ( ni) 10¹⁶ per m ³ each and 10²¹ phosphorus atoms ( ne) are added per cubic metre. The new hole concentration in silicon crystal is (a) 10¹⁹ per m ³ (b) 10²¹ per m ³ (c) 10⁵ per m ³ (d) 10¹¹ per m ³

Answer: (d). Each P atom gives one electron, so ne ≈ 10²¹ m⁻³ (much larger than ni). Mass action law: nh = (ni²)/(ne) = (10¹⁶)²10²¹ nh = 10¹¹ m⁻³ So the answer is (d) 10¹¹ per m ³.

A pure silicon crystal at temperature 300 K has electron and hole… | MHT CET 2026 (13 Apr, Shift 2)

Q10MHT CET 2026 · 13 APR · SHIFT 2Easy

Intrinsic & Extrinsic Semiconductors

A pure silicon crystal at temperature $300$ K has electron and hole concentration ( $n_i$ ) $10^{16}$ per m ${}^{3}$ each and $10^{21}$ phosphorus atoms ( $n_e$ ) are added per cubic metre. The new hole concentration in silicon crystal is

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Answer: (d)

Each P atom gives one electron, so $n_e \approx 10^{21}\ \text{m}^{-3}$ (much larger than $n_i$ ).
Mass action law: $n_h = \dfrac{n_i^2}{n_e} = \dfrac{(10^{16})^2}{10^{21}}$
$n_h = 10^{11}\ \text{m}^{-3}$
So the answer is (d) $10^{11}$ per m $^3$ .

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Intrinsic & Extrinsic Semiconductors question from MHT CET 2026 (13 Apr, Shift 2)

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