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.
Which of the following energy-band pictures fits sample X?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → The conduction band is partly filled, or it overlaps the valence band.
X has by far the lowest resistivity of the three samples. A value of this order is shown only by metals.
Option (1) The conduction band is partly filled, or it overlaps the valence band. — Correct. This is the band picture of a metal. Many electrons can move freely into empty levels, so the resistance is low.
Option (2) The two bands are separated by a gap of more than 3 eV, and the conduction band is empty. — Incorrect. This is the picture of an insulator. No electron is free to conduct, so the resistivity is very high, as for Z.
Option (3) The two bands are separated by a small gap of about 1 eV. — Incorrect. This is the picture of a semiconductor. Only a few electrons cross such a gap at room temperature, so the resistivity is in between, as for Y.
Option (4) The conduction band is completely filled and the valence band is empty. — Incorrect. The valence band has the lower energies, and its levels are always filled first. No solid has a full conduction band above an empty valence band.
NCERT (2026-27):
Classification of Metals, Conductors and Semiconductors – “(i) Metals: They possess very low resistivity (or high conductivity).”
Classification of Metals, Conductors and Semiconductors – “… One can have a metal either when the conduction band is partially filled and the balanced band is partially empty or when the conduction and valance bands overlap.”