ISRO EC 2025 Q.29: solution and answer

Official answer: CSource: ISRO's final answer key of 15 May 2026

1. Mobility is $\mu =\frac{q\tau }{m^{\ast }}$, so it falls whenever the mean scattering time $\tau$ falls.

2. In a non-degenerate semiconductor at ordinary temperatures, the dominant scattering is by lattice vibrations (phonons). This is lattice (phonon) scattering.

3. As $T$ rises, lattice vibrations become stronger, so scattering increases. The mean free time shrinks and ${\mu }_{\text{lattice}}\propto T^{-3/2}$.

4. Ionized-impurity scattering goes the other way (${\mu }_{\text{imp}}\propto T^{3/2}$), but it matters only at low temperature or high doping. Lattice scattering dominates above about room temperature.

5. So $\mu$ decreases with $T$ because lattice scattering increases. This is option (c).

6. Option (a) is wrong because more phonon scattering lowers mobility. Option (b) is wrong because lattice scattering increases with $T$, not decreases. Option (d) is wrong because mobility depends on temperature.