1. Pauli's Exclusion Principle: States that no two electrons in the same atom can have identical values for all four quantum numbers ($n, l, m_l, m_s$). This implies that if two electrons occupy the same orbital (having the same $n, l,$ and $m_l$), they must have opposite spins ($m_s = +1/2$ and $-1/2$).
2. Distinction from other rules:
• Aufbau Principle: Electrons fill lower-energy orbitals first before moving to higher-energy ones.
• Hund's Rule: Orbitals of the same energy (degenerate orbitals) are each occupied by one electron before any orbital is doubly occupied.
Consequently, Pauli's Principle is the rule that limits each orbital to a maximum of two electrons with opposite spins.