A silicon crystal has \(N\) atoms. Each Si atom has 4 electrons in its outermost orbit, and this orbit can hold at most 8 electrons. At the spacing between the atoms of the crystal, the outer energy states split into a valence band and a conduction band. The numbers of energy states in the valence band and in the conduction band are, respectively,
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(4N\) and \(4N\)
The \(N\) atoms give \(4N\) outer electrons in all. Each atom has room for 8 outer electrons, so the crystal has \(8N\) available energy states. At the Si spacing these \(8N\) states split into two bands separated by the energy gap \(E_g\).
The lower band, the valence band, is the one that the \(4N\) valence electrons fill completely at absolute zero. So it has \(4N\) states. The other \(8N - 4N = 4N\) states form the conduction band.
From the above, each band has \(4N\) states. Hence, the valence band and the conduction band have \(4N\) and \(4N\) states.
NCERT (2026-27):
On the basis of energy bands – “At the distance between the atoms in the crystal lattices of Si and Ge, the energy band of these 8N states is split apart into two which are separated by an energy gap Eg … 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.”