Which of the following principles explains why electrons occupy different orbitals with the same energy before pairing up?

The principle that explains why electrons occupy different orbitals with the same energy before pairing up is Hund's Rule. This rule is based on the idea that electrons will fill degenerate orbitals—those at the same energy level—individually and with parallel spins to minimize repulsion between them. By doing so, they occupy separate orbitals first, which maximizes their spatial distribution and reduces electron-electron repulsion. This helps to achieve a more stable electron configuration.

In contrast, the Pauli Exclusion Principle states that no two electrons in an atom can have the same set of quantum numbers. While this principle is important for understanding electron configurations, it does not directly address the filling order of orbitals at the same energy level. The Aufbau Principle, meanwhile, describes the overall order of orbital filling, stating that electrons fill lower energy orbitals first before moving to higher energy ones. Finally, the Quantum Mechanical Model provides the framework for understanding atomic structure and electron behavior, but it does not specify the order in which electrons occupy orbitals. Thus, Hund's Rule is the key principle that properly describes the behavior in question.