In the energy-band diagram of pure silicon at T = 0 K, the valence ba…

The correct answer is Option (2) → a few electrons move into the conduction band and leave an equal number of holes in the valence band

At \(T = 0\) K a pure semiconductor behaves like an insulator. Above 0 K, thermal energy lifts some electrons across the gap into the conduction band. Each electron that leaves the valence band leaves an empty level there, which is a hole.

Option (1) all the electrons of the valence band move into the conduction band — Incorrect. Thermal energy frees only a few electrons. The conduction band is only partly occupied.

Option (2) a few electrons move into the conduction band and leave an equal number of holes in the valence band — Correct. Every electron that crosses the gap leaves one hole behind. So the numbers of free electrons and holes stay equal.

Option (3) a few electrons move into the conduction band and leave a larger number of holes in the valence band — Incorrect. More holes than free electrons is the case of a p-type semiconductor, where acceptor atoms add extra holes. Pure silicon has no such atoms.

Option (4) the energy gap disappears and the two bands overlap — Incorrect. The gap of silicon (about 1.1 eV) stays. Overlapping bands are found in metals.

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. These thermally excited electrons at T > 0 K, partially occupy the conduction band. Therefore, the energy-band diagram of an intrinsic semiconductor will be as shown in Fig. 14.6(b). Here, some electrons are shown in the conduction band. These have come from the valence band leaving equal number of holes there.”