What is electron configuration? Describe the roles that the Pauli exclusion principle and Hund's rule play in writing the electron configuration of elements.

Electron configuration refers to the distribution of electrons of an atom or molecule in atomic or molecular orbitals. For atoms, it is the representation of how electrons are arranged in shells, subshells, and orbitals. This configuration is usually written as a series of numbers and letters, where numbers represent the energy level and letters represent the type of orbital. Each letter is then followed by a superscript indicating the number of electrons in that orbital. For example, the oxygen atom has an electron configuration of 1s² 2s² 2p⁴, indicating 2 electrons in the s orbital of the first energy level, 2 electrons in the s orbital of the second energy level, and 4 electrons in the p orbital of the second energy level.

The Pauli Exclusion Principle is a principle of quantum mechanics, named after physicist Wolfgang Pauli, which states that two or more identical fermions (particles with half-integer spin) cannot occupy the same quantum state within a quantum system simultaneously. For electron configuration, this principle means that each electron in an atom must have a unique set of quantum numbers (values that describe the characteristics of the electron), hence no two electrons can reside in the same orbital with the same spin.

Hund's Rule states that electrons will occupy separate orbitals of the same energy level one at a time before pairing up in a single orbital. This is because electrons are fermions that also carry a charge, with single electrons in an orbital creating less electron-electron repulsion, thus a more stable arrangement than paired electrons sharing the same orbital. In electron configuration, this rule guides the 'filling order' of electrons.