Step 1: Understanding the Concept:
In statistical mechanics, large systems of particles are modeled using specific probability distributions. The choice of distribution depends entirely on the quantum properties of the particles, specifically whether they are distinguishable and what their intrinsic angular momentum (spin) is.
Step 2: Key Formula or Approach:
The approach involves matching the particle characteristics to the rules of the three primary statistical distributions in physics: Classical (MB), Bosonic (BE), and Fermionic (FD).
Step 3: Detailed Explanation:
Let's review the statistical distributions:
1. Maxwell-Boltzmann statistics apply to identical but distinguishable particles, such as molecules in an ideal gas at high temperatures. Spin is irrelevant here.
2. Bose-Einstein statistics apply to identical, indistinguishable particles that have integral spin ($0, 1, 2, \ldots$). These particles are called bosons (like photons) and do not obey the Pauli exclusion principle.
3. Fermi-Dirac statistics apply to identical, indistinguishable particles that have half-integral spin ($1/2, 3/2, 5/2, \ldots$). These particles are called fermions (like electrons, protons, and neutrons).
Because fermions possess half-integral spin, they obey the Pauli exclusion principle, meaning no two particles can occupy the exact same quantum state simultaneously. This behavior is perfectly modeled by the Fermi-Dirac distribution.
Step 4: Final Answer:
The correct option is (C).