Question

For identical particles in quantum mechanics, the Pauli exclusion principle states that:

• A. No two particles can occupy the same quantum state
• B. Particles can share quantum states if they have different spins
• C. Identical particles do not interact
• D. All particles must occupy distinct energy levels

Hint:

The Pauli exclusion principle is exclusive to fermions. It restricts them from sharing the same quantum state and is essential in understanding atomic structure and stability of matter.

Answer 1

The Correct Option is A

Step 1: The Pauli exclusion principle states that no two identical fermions (particles like electrons, protons, or neutrons with half-integer spin) can occupy the same quantum state simultaneously.
Step 2: This principle is a cornerstone of quantum mechanics and is responsible for the structure of atoms, where electrons occupy discrete orbitals. It ensures that each electron in an atom has a unique set of quantum numbers.
Step 3: In atomic physics, this principle explains the arrangement of electrons in shells and subshells, leading to the periodic table's structure.
Why other options are incorrect:

• (B) This is misleading. Fermions cannot share the same quantum state even if they differ in spin, unless other quantum numbers also differ. Bosons, not fermions, can occupy the same state.
• (C) Identical particles can interact through fundamental forces like the electromagnetic or strong force.
• (D) Particles may share the same energy level if other quantum numbers (like spin or angular momentum) are different. It is the complete quantum state that must be unique for fermions.