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.
Consider the following statements about the energy bands of solids:
(A) \(E_C\) is the lowest energy level of the conduction band and \(E_V\) is the highest energy level of the valence band.
(B) At 0 K, the conduction band of pure silicon is completely filled.
(C) In a silicon crystal of \(N\) atoms, the conduction band has \(4N\) energy states.
(D) In silicon, the outermost orbit of each atom is the third orbit (\(n = 3\)).
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A), (C) and (D) only
In a crystal of silicon, the \( 8N \) energy states of the outer electrons split into two bands. A gap \( E_g \) separates them.
(A) \( E_C \) is the lowest energy level of the conduction band and \( E_V \) is the highest energy level of the valence band. — True. These two levels mark the edges of the gap, so \( E_g=E_C-E_V \).
(B) At 0 K, the conduction band of pure silicon is completely filled. — False. At 0 K, the valence electrons fill the valence band completely. The conduction band is then completely empty.
(C) In a silicon crystal of \( N \) atoms, the conduction band has \( 4N \) energy states. — True. The \( 8N \) states split into two bands of \( 4N \) states each. The \( 4N \) valence electrons fill the lower band, and the upper band has the other \( 4N \) states.
(D) In silicon, the outermost orbit of each atom is the third orbit (\( n = 3 \)). — True. Each silicon atom has four outer electrons in its third orbit. For germanium, the outermost orbit is the fourth orbit.
NCERT (2026-27):
Classification of Metals, Conductors and Semiconductors – “The lowest energy level in the conduction band is shown as EC and highest energy level in the valence band is shown as EV. …”
Classification of Metals, Conductors and Semiconductors – “… The lower band which is completely occupied by the 4N valence electrons at temperature of absolute zero is the valence band. The other band consisting of 4N energy states, called the conduction band, is completely empty at absolute zero.”
Classification of Metals, Conductors and Semiconductors – “… For Si, the outermost orbit is the third orbit (n = 3), while for Ge it is the fourth orbit (n = 4). …”