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With applications in chemistry and quantum mechanics, the Pauli exclusion principle deals with the placement of electrons in an atom. The principle states that every electron in an atom must have unique quantum numbers. Quantum numbers indicate the subshell and the size, placement, and energy level of orbitals in which the electrons can be found, as well as the spin of each electron.
In an atom, electrons orbit the nucleus. The areas in which specific electrons occupy space are called the orbitals, and orbitals are grouped together in subshells. The number of electrons in a given orbital or subshell is dictated by the precepts of the Pauli exclusion principle which says no two electrons can have identical quantum numbers. There are four quantum numbers for electrons which, together, state the electron's general location in a given atom. The quantum numbers are called principal, azimuthal, magnetic, and spin.
The principle quantum number indicates the energy level and size of a given orbital. Energy increases as the electron orbitals move father away from the nucleus. This quantum number is indicated by an integer. When scientist notate the position of an electron in an atom, the principle quantum number is the first thing written.
The azimuthal and magnetic quantum numbers give information about the subshell of an orbital. Indicating the actual subshell, the azimuthal dictates information about that subshell. The magnetic determines how many orbitals are in a given subshell and indicates in which of those orbitals the electron resides. Although the azimuthal number can be indicated by a numeral, the scientific notation for it is written as a letter: s, p, d, or f. The magnetic quantum number is indicated by a superscript numeral in scientific notation, but is listed as either zero, or a positive or negative number otherwise.
The spin of an electron can either be clockwise or counterclockwise. The Pauli exclusion principle dictates that each electron in an orbital must spin in a different direction. Since there are only two options, only two electrons can occupy the same orbital and remain unique. Spins are denoted by a positive or negative "1/2" or by arrows pointing up or down.
The Pauli exclusion principle serves as the basis for explaining bonding between atoms, as well as scientific rules and phenomena. It has applications in Hund's Rule and Band Theory. Additionally, it helps determine when and how stars collapse into the white dwarf and neutron star stages of their existences.