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The electron configurations of atoms are understood in terms of quantum mechanics and Schrödinger’s equation which have produced the following three principles.
The Aufbau Principle says that, electrons are added first to the lowest energy atomic orbitals available before they fill higher energy orbitals. The name derives from aufbau in German, which means building up. The Aufbau Principle makes sense because it produces the lowest energy or most stable arrangement of the electrons in the atom.
The Pauli Exclusion Principle says that two electrons in an atom cannot have the same set of quantum numbers simultaneously. This principle determines the number of electrons that can occupy each orbital. In addition to the quantum numbers, n, l, and ml, there is a fourth quantum number, ms, or the spin angular momentum. There are two possible values for ms: +1/2 and -1/2. So, two electrons can be in each orbital and have the same values for n, l, and ml, as long as they have different values for ms (one as +1/2 and the other as -1/2). The two different spin angular momentum states for electrons (+1/2 and -1/2) are represented in orbital diagrams by up and down arrows.
Hund’s Rule says that if multiple orbitals with the same energy are available, then the unoccupied orbitals will be filled by electrons with the same spin before electrons with different spins pair up in occupied orbitals. Hund’s Rule makes sense because electrons repel each other. If they are in the same orbital, they will be close together and their energy will by higher than it would be if they are separated in different orbitals.