Assertion (A) : The conductivity of a semiconductor has some finite value at absolute zero.
Reason (R) : The conductivity of a semiconductor decreases with rise in temperature.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Both (A) and (R) are false.
Assertion (A) The conductivity of a semiconductor has some finite value at absolute zero. — False. At \( T=0\,\mathrm{K} \) every electron stays in the filled valence band and the conduction band is empty, so there are no free electrons or holes. The semiconductor behaves like an insulator and its conductivity is zero.
Reason (R) The conductivity of a semiconductor decreases with rise in temperature. — False. As the temperature rises, thermal energy excites more electrons from the valence band to the conduction band, each leaving a hole behind. The number of charge carriers grows, so the conductivity increases (the resistivity decreases), unlike in metals.
NCERT (2026-27):
Intrinsic Semiconductor – “An intrinsic semiconductor will behave like an insulator at T = 0 K … It is the thermal energy at higher temperatures (T > 0K), which excites some electrons from the valence band to the conduction band.”
Temperature Dependence of Resistivity – “Unlike metals, the resistivities of semiconductors decrease with increasing temperatures.”