Question

The manifestation of the band structure in solids is due to which of the following?

• A. Heisenberg’s uncertainty principle
• B. Pauli’s exclusion principle
• C. Bohr’s correspondence principle
• D. Boltzmann’s law

Hint:

Pauli’s exclusion principle states that no two electrons in a solid can occupy the same quantum state simultaneously, which helps form the band structure in solids.

Answer 1

The Correct Option is B

Step 1: Understanding Band Structure 
The band structure in solids arises due to the quantum mechanical properties of electrons.
It is a result of the collective interaction of many electrons in a solid.
The Pauli exclusion principle plays a key role in the formation of energy bands by limiting the number of electrons that can occupy each energy state. 
Step 2: Explanation of Other Options 
Option (a) is incorrect because Heisenberg’s uncertainty principle deals with the limitation in the precision of simultaneous measurements of position and momentum, not directly with the formation of band structures.
Option (c) is incorrect because Bohr’s correspondence principle relates to the transition between quantum and classical descriptions of atomic systems and does not apply to band theory.
Option (d) is incorrect because Boltzmann’s law deals with statistical distributions and energy states in a system at equilibrium but is not directly related to the formation of the band structure.

Step 3: Conclusion 
Thus, the manifestation of the band structure in solids is due to Pauli’s exclusion principle, which governs the arrangement of electrons in energy bands.