What principle states that two electrons in the same orbital must have opposing spins?

The principle stating that two electrons in the same orbital must have opposing spins is the Pauli exclusion principle. This fundamental concept in quantum mechanics highlights that no two electrons in an atom can have the same set of four quantum numbers, which inherently includes their spin. In any given orbital, which can hold a maximum of two electrons, the spins of these electrons must differ; one will have a spin value of +1/2 and the other -1/2. This requirement arises from the fermionic nature of electrons, which are classified as fermions, meaning they obey the Pauli exclusion principle and cannot occupy the same quantum state.

In contrast, Hund's rule states that electrons will fill degenerate orbitals (orbitals of the same energy) singly, with the same spin, before pairing up. The Aufbau principle concerns the order in which electrons fill orbitals based on increasing energy levels. The Heisenberg uncertainty principle addresses the limits of measuring the position and momentum of particles, stating that they cannot be precisely determined simultaneously. These concepts, while significant in the framework of quantum mechanics and atomic structure, do not pertain specifically to the requirement of opposing spins in a single orbital.