Final answer:
Electron configurations are determined using the Aufbau Principle, the Pauli exclusion principle, and Hund's rule, all of which dictate the unique placement of electrons in an atom's orbitals.
Step-by-step explanation:
Electron configurations can be written by using the Aufbau Principle, the Pauli exclusion principle, and Hund's rule. The Aufbau Principle is the method we use to determine the order in which electron sublevels are filled. The Pauli exclusion principle, a concept proposed by Wolfgang Pauli in 1925, states that no two electrons can have the same set of quantum numbers, effectively limiting the number of electrons in shells and subshells. This principle is a fundamental rule in quantum mechanics, applying to all particles with half-integer spin, which includes electrons. Hund's rule states that electrons must occupy every orbital singly before any orbital is doubly occupied, and all electrons in singly occupied orbitals must have the same spin.
Together, these principles dictate that when filling sublevels with electrons, each electron maintains a unique set of four quantum numbers, explaining why certain configurations are possible while others are not. For example, a maximum of two electrons can occupy the n = 1 level, and they must have opposite spins. Utilizing the Pauli exclusion principle, along with the Aufbau Principle and Hund's rule allows for the prediction of electron configurations, including exceptions that may occur with larger atoms.