In an intrinsic semiconductor at room temperature:

The correct answer is Option (3) → the number of free electrons and the number of holes are equal and non-zero

In a pure (intrinsic) semiconductor, thermal energy at room temperature breaks some covalent bonds. Each broken bond frees one electron and leaves one hole, so electrons and holes are created in pairs.

    \( \displaystyle n_e = n_h = n_i \)

Option (1) the number of free electrons are much larger than the number of holes — Incorrect. Electrons far outnumber holes only in an n-type (doped) semiconductor.

Option (2) the number of holes are much larger than the number of free electrons — Incorrect. Holes far outnumber electrons only in a p-type (doped) semiconductor.

Option (3) the number of free electrons and the number of holes are equal and non-zero — Correct. Pair generation makes the two numbers equal, and the thermal energy at room temperature makes them non-zero.

Option (4) the number of free electrons and the number of holes are zero — Incorrect. Both would be zero only at absolute zero, where no bond is broken.

NCERT (2026-27):
Intrinsic Semiconductor – “… As the temperature increases, more thermal energy becomes available to these electrons and some of these electrons may break–away (becoming free electrons contributing to conduction).”

Intrinsic Semiconductor – “… In intrinsic semiconductors, the number of free electrons, n_e is equal to the number of holes, n_h. That is

    \( \displaystyle n_e = n_h = n_i \qquad (14.1) \)”