Match List-I with List-II. Assume that the Si intrinsic semiconductor has 5 x 1028 atoms/m3. (Given: the intrinsic concentration of electrons in the semiconductor is 1016 m−3).
| LIST-I | LIST-II | ||
| A. | When it is doped with 2 ppm concentration of a pentavalent atom, ne is | I. | 4.0 x 108 m−3 |
| B. | When it is doped with 2 ppm concentration of a pentavalent atom, nh is | II. | 2.5 x 1023 m−3 |
| C. | When it is doped with 5 ppm concentration of a pentavalent atom, ne is | III. | 109 m−3 |
| D. | When it is doped with 5 ppm concentration of a pentavalent atom, nh is | IV. | 1023 m−3 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → A-IV, B-III, C-II, D-I
Each pentavalent atom donates one electron, so \( n_e \approx N_D \) (the intrinsic electrons are negligible). The hole concentration then follows from the mass-action law \( n_e n_h = n_i^{2} \), with \( n_i^{2} = (10^{16})^{2} = 10^{32}\,\mathrm{m^{-6}} \). One ppm is one part in \( 10^{6} \).
(A) When it is doped with 2 ppm concentration of a pentavalent atom, ne is — this matches (IV) 1023 m−3.
\( \displaystyle n_e = 2\times10^{-6} \times 5\times10^{28}\,\mathrm{m^{-3}} = 10^{23}\,\mathrm{m^{-3}} \)
(B) When it is doped with 2 ppm concentration of a pentavalent atom, nh is — this matches (III) 109 m−3.
\( \displaystyle n_h = \frac{n_i^{2}}{n_e} = \frac{10^{32}}{10^{23}}\,\mathrm{m^{-3}} = 10^{9}\,\mathrm{m^{-3}} \)
(C) When it is doped with 5 ppm concentration of a pentavalent atom, ne is — this matches (II) 2.5 x 1023 m−3.
\( \displaystyle n_e = 5\times10^{-6} \times 5\times10^{28}\,\mathrm{m^{-3}} = 2.5\times10^{23}\,\mathrm{m^{-3}} \)
(D) When it is doped with 5 ppm concentration of a pentavalent atom, nh is — this matches (I) 4.0 x 108 m−3.
\( \displaystyle n_h = \frac{10^{32}}{2.5\times10^{23}}\,\mathrm{m^{-3}} = 4.0\times10^{8}\,\mathrm{m^{-3}} \)
Note: NTA picked this question from an NCERT (2026-27) example and changed the figures. Do not ignore NCERT while practising numericals.
NCERT (2026-27):
Extrinsic Semiconductor – …
