If \( n_i \) is the concentration of intrinsic charge carriers in a pure semiconductor and \( n_e \) and \( n_h \) be the concentrations of electrons and holes, respectively after the semiconductor is doped, then at thermal equilibrium.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( n_e\,n_h = n_i^{2} \)
At thermal equilibrium the law of mass action holds: doping raises one carrier concentration, and the other falls by the same factor, so the product of the electron and hole concentrations stays equal to its value in the pure semiconductor.
\( \displaystyle n_e\,n_h = n_i^{2} \)
In the pure semiconductor \( n_e = n_h = n_i \), which gives \( n_i^{2} \) for the product.
NCERT (2026-27):
Extrinsic Semiconductor – “… The electron and hole concentration in a semiconductor in thermal equilibrium is given by
\( \displaystyle n_e n_h = n_i^2 \qquad (14.5) \)”