In germanium doped with arsenic, the energy needed to set the fifth v…

The correct answer is Option (3) → \( 0.01\,\mathrm{eV} \)

When an arsenic atom takes a germanium site, four of its five valence electrons bond with the four germanium neighbours. The fifth electron sees the four bonding electrons as part of the core of the atom and is only very weakly bound. About \( 0.01\,\mathrm{eV} \) sets it free. This is far less than the energy of about \( 0.72\,\mathrm{eV} \) needed to cross the forbidden band of germanium. So at room temperature these donor electrons are free to move.

NCERT (2026-27):
Extrinsic Semiconductor – “… As a result the ionisation energy required to set this electron free is very small and even at room temperature it will be free to move in the lattice of the semiconductor. For example, the energy required is ~ 0.01 eV for germanium, and 0.05 eV for silicon, to separate this electron from its atom. This is in contrast to the energy required to jump the forbidden band (about 0.72 eV for germanium and about 1.1 eV for silicon) at room temperature in the intrinsic semiconductor.”