How many of the following statements about an intrinsic semiconductor are correct?
(A) The number of free electrons is equal to the number of holes.
(B) Under an applied electric field, the holes move towards the negative potential.
(C) The total current is the sum of the electron current and the hole current.
(D) At equilibrium, the rate of generation of charge carriers is equal to the rate of recombination.
(E) The electron that was set free when the bond broke also takes part in the motion of the hole.
(F) At \(T = 0\ \mathrm{K}\), a few electrons are present in its conduction band.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Four
In a pure semiconductor, each broken covalent bond gives one free electron and one hole. Both of them move and carry current.
The statements that are correct:
(A) \( n_e=n_h \)
(B) holes move towards the negative potential
(C) \( I=I_e+I_h \)
(D) rate of generation = rate of recombination
The statements that are not correct:
(E) — The free electron takes no part in hole motion. An electron from a neighbouring bond jumps into the vacancy, so the hole shifts to that bond.
(F) — At \( T=0\ \mathrm{K} \), all bonds are intact. The conduction band is empty and the semiconductor behaves like an insulator.
Number of correct statements = 4
NCERT (2026-27):
Intrinsic Semiconductor – “In intrinsic semiconductors, the number of free electrons, ne is equal to the number of holes, nh. …”
Intrinsic Semiconductor – “… Note that the electron originally set free … is not involved in this process of hole motion. …”
Intrinsic Semiconductor – “… Under the action of an electric field, these holes move towards negative potential giving the hole current, Ih. The total current, I is thus the sum of the electron current Ie and the hole current Ih: I = Ie + Ih …”
Intrinsic Semiconductor – “… At equilibrium, the rate of generation is equal to the rate of recombination of charge carriers. …”
Intrinsic Semiconductor – “An intrinsic semiconductor will behave like an insulator at T = 0 K …”