E_g (energy band-gap) for silicon is greater than that for germanium.…

The correct answer is Option (2) → less number of electron hole pairs will be generated in silicon than in germanium at room temperature

In an intrinsic semiconductor, an electron-hole pair is created when thermal energy lifts an electron from the valence band across the energy band-gap into the conduction band. The larger the gap, the fewer electrons can cross it at a given temperature.

Silicon has \( E_g \approx 1.1\,\mathrm{eV} \) and germanium \( E_g \approx 0.7\,\mathrm{eV} \), so at room temperature far fewer electron-hole pairs are generated in silicon.

NCERT (2026-27):
Classification of Metals, Conductors and Semiconductors – “… Case III: This situation is shown in Fig. 14.2(c). Here a finite but small band gap (E_g < 3 eV) exists. Because of the small band gap, at room temperature some electrons from valence band can acquire enough energy to cross the energy gap and enter the conduction band. These electrons (though small in numbers) can move in the conduction band. Hence, the resistance of semiconductors is not as high as that of the insulators.”