In a semiconductor
A. there are no free electrons at any temperature
B. there are no free electrons at 0 K (zero Kelvin)
C. the number of free electrons is less than that in a conductor
D. the number of free electrons increases with temperature
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → B, C and D only
In a semiconductor the valence band is full and the conduction band is empty at 0 K; free electrons appear only when thermal energy lifts electrons across the small energy gap.
(A) There are no free electrons at any temperature — Incorrect. Above 0 K some electrons are thermally excited into the conduction band, leaving holes behind.
(B) There are no free electrons at 0 K (zero Kelvin) — Correct. At 0 K the semiconductor behaves like an insulator.
(C) The number of free electrons is less than that in a conductor — Correct. A conductor has a large number of free electrons, whereas a semiconductor has only the few that are thermally excited (or supplied by dopants).
(D) The number of free electrons increases with temperature — Correct. A higher temperature excites more electrons across the gap.
NCERT (2026-27):
Intrinsic Semiconductor – “… An intrinsic semiconductor will behave like an insulator at T = 0 K as shown in Fig. 14.6(a). It is the thermal energy at higher temperatures (T > 0K), which excites some electrons from the valence band to the conduction band.”
