The manifestation of band structure in solids is due to

Options

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

Explanation

To solve the question regarding the manifestation of band structure in solids, we need to analyze the provided options and their relevance to the concept of band structure.

### Step-by-Step Solution:

1. **Understanding Band Structure**:
- Band structure in solids refers to the range of energy levels that electrons can occupy in a solid material. It arises from the quantum mechanical behavior of electrons in a periodic potential created by the lattice of atoms in the solid.

2. **Analyzing the Options**:
- **Option 1: Heisenberg's Uncertainty Principle**:
- This principle states that it is impossible to simultaneously know both the position and momentum of a particle with absolute precision. While this principle is fundamental to quantum mechanics, it does not directly explain the band structure of solids.
- **Conclusion**: Incorrect.

- **Option 2: Pauli's Exclusion Principle**:
- This principle states that no two electrons can occupy the same quantum state simultaneously. This principle is crucial in determining how electrons fill the available energy levels in a solid and thus directly influences the formation of the band structure.
- **Conclusion**: Correct.

- **Option 3: Bohr's Correspondence Principle**:
- This principle relates to the behavior of electrons in atomic orbitals and does not apply to the band structure of solids. It primarily deals with the transition from quantum to classical descriptions of atomic systems.
- **Conclusion**: Incorrect.

- **Option 4: Boltzmann Law**:
- This law describes the statistical distribution of particles over various energy states in thermal equilibrium and is not directly related to the formation of band structures in solids.
- **Conclusion**: Incorrect.

3. **Final Answer**:
- Based on the analysis, the correct answer is **Option 2: Pauli's Exclusion Principle**.