Question

The manifestation of band structure in solids is due to: (A) Heisenberg's uncertainty principle (B) Pauli's exclusion principle (C) Bohr's correspondence principle (D) Boltzmann's low

Short answer

The manifestation of band structure in solids is due to Pauli's exclusion principle, which states that no two electrons or fermions in a quantum system can have the same set of quantum numbers. This principle is crucial to understanding the distribution of electrons in different energy levels (bands) within a solid, giving rise to specific energy ranges for the valence and conduction bands.

Step-by-step solution

Option A Analysis: Heisenberg's Uncertainty Principle

Heisenberg's uncertainty principle states that it is impossible to accurately measure both the position and momentum of a particle simultaneously. While this principle plays a vital role in the understanding of quantum mechanics, it is not directly associated with the manifestation of band structures in solids.

Option B Analysis: Pauli's Exclusion Principle

Pauli's exclusion principle states that no two electrons or fermions in a quantum system can have the same set of quantum numbers. This principle is very important in understanding the distribution of electrons in different energy levels (bands) within a solid. As electrons fill available energy states in a solid, they give rise to a band structure with specific energy ranges for the valence and conduction bands. Therefore, Pauli's exclusion principle is crucial to the manifestation of band structures in solids.

Option C Analysis: Bohr's Correspondence Principle

Bohr's correspondence principle states that as the quantum number of a state becomes very large, the behavior of a quantum system approaches that of a classical system. Although this principle is fundamental to understanding the transition between classical and quantum mechanics, it is not directly associated with the manifestation of band structures in solids.

Option D Analysis: Boltzmann's Law

Boltzmann's law deals with the distribution of particles among different energy levels in a thermodynamic system. It describes the probability of a particle being in a specific energy state at a given temperature. While Boltzmann's law is essential for understanding the behavior of particles in terms of energy distribution, it is not directly related to the manifestation of band structures in solids. Based on the analysis of each option, it is clear that Pauli's exclusion principle (option B) plays the most significant role in the manifestation of the band structure in solids.