Read the following passage and answer the questions.
A student measures the resistivity of three unlabelled solids, X, Y and Z, at room temperature. Her readings are about \(1.7\times10^{-8}\ \Omega\,\mathrm{m}\) for X, \(2\times10^{3}\ \Omega\,\mathrm{m}\) for Y and \(10^{14}\ \Omega\,\mathrm{m}\) for Z. She plans to warm each sample a little and take the readings again. To explain her results, she will compare the samples with the energy-band pictures of solids. Such a picture shows a valence band and a conduction band. In some solids the two bands are separated by an energy gap, and the size of this gap differs from one solid to another. She also notes four elements of group IV of the periodic table: carbon (as diamond), silicon, germanium and tin. Each of them has four valence electrons, yet they behave very differently in electric circuits.
The student warms samples Y and Z by a small amount and measures their resistivity again. What does she observe?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → The resistivity of Y falls noticeably, while Z stays practically non-conducting.
Warming gives the electrons in the valence band more thermal energy. Whether this helps conduction depends on the size of the energy gap. With a resistivity between those of metals and insulators, Y is a semiconductor with a small gap. With a very high resistivity, Z is an insulator with a large gap.
Option (1) The resistivity of both Y and Z rises noticeably. — Incorrect. A rise in resistivity on warming is how a metal behaves. Neither Y nor Z is a metal.
Option (2) The resistivity of both Y and Z falls by about the same factor. — Incorrect. Thermal energy can lift electrons across the small gap of Y but not across the large gap of Z. So the two samples do not change in the same way.
Option (3) The resistivity of Y falls noticeably, while Z stays practically non-conducting. — Correct. In Y, more electrons cross the small gap into the conduction band, so its resistivity falls. In Z, the gap is too large for thermal excitation, so it still does not conduct.
Option (4) The resistivity of Y rises, while that of Z falls noticeably. — Incorrect. This reverses the real behaviour. The semiconductor Y conducts better when warm, while the insulator Z hardly changes.
NCERT (2026-27):
Classification of Metals, Conductors and Semiconductors – “… 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.”
Classification of Metals, Conductors and Semiconductors – “… Note that the energy gap is so large that electrons cannot be excited from the valence band to the conduction band by thermal excitation. This is the case of insulators.”