The behavior of electrons in atoms and their distribution into orbitals is described by quantum mechanics. According to the Pauli exclusion principle, no two electrons in an atom can have the same set of quantum numbers. This principle is the basis for understanding why two electrons can exist in the same orbital despite their mutual repulsion.
In an atom, electrons occupy specific energy levels known as orbitals. Each orbital can hold a maximum of two electrons with opposite spins. The term "spin" in this context is not a literal spinning motion but rather an intrinsic property of electrons.
The Pauli exclusion principle states that no two electrons within an atom can have the same set of quantum numbers, which includes their spin. This means that in a given orbital, one electron has one spin orientation (e.g., "spin up"), while the other electron has the opposite spin orientation (e.g., "spin down"). By having opposite spins, the two electrons effectively have different quantum states and can occupy the same orbital without violating the exclusion principle.
It is important to note that electrons do repel each other due to their electric charge. However, the repulsion between electrons within the same orbital is balanced by other forces, particularly the attractive force of the positively charged atomic nucleus. The combined effect of these forces determines the overall distribution of electrons within an atom, allowing them to occupy the same orbital while maintaining a stable and energetically favorable configuration.
This behavior is explained by the principles and mathematical formalism of quantum mechanics, which considers the wave-like nature of particles and describes their behavior in terms of probability distributions and energy levels. It is a complex topic that requires a deeper understanding of quantum mechanics to fully appreciate the intricacies of electron behavior in atoms.