A sample of pure germanium is warmed from 300 K to 350 K. What happens to its electrical resistance?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → It decreases, because more covalent bonds break and more electron-hole pairs are formed.
In a pure semiconductor, the charge carriers come from covalent bonds broken by thermal energy. A higher temperature gives more energy, so more bonds break.
Option (1) It increases, because the atoms vibrate more and scatter the electrons more. — Incorrect. A resistance that rises on heating is the behaviour of a metal. In germanium the growth in the number of carriers is much larger than the effect of extra scattering.
Option (2) It stays the same, because the number of atoms in the sample does not change. — Incorrect. The number of atoms is fixed, but the number of free electrons and holes grows with temperature.
Option (3) It decreases, because more covalent bonds break and more electron-hole pairs are formed. — Correct. More broken bonds give more free electrons and holes. The conductivity rises and the resistance falls.
Option (4) It decreases, because the energy gap of germanium becomes zero at 350 K. — Incorrect. The energy gap of germanium stays at about 0.7 eV. A zero gap is the case of tin, which is a metal.
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). …”
Temperature Dependence of Resistivity – “For insulators and semiconductors, however, n increases with temperature. This increase more than compensates any decrease in τ … so that for such materials, ρ decreases with temperature.”