Aufbau principle
The Aufbau principle, or Aufbau rule, is used to determine the electron configuration of an atom or ion. The rule states that electrons in an atom fill orbitals "from the bottom," starting at the lowest available energy states before filling higher states.
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History
The principle takes its name from the German Aufbauprinzip, ""building-up principle", rather than being named for a scientist. Infact, it was formulated by the Danish physicist Niels Bohr circa 1920.
It was an early application of quantum mechanics to the properties of electrons, and explained chemical properties in physical terms. Each added electron is subject to the electric field created by the positive charge of atomic nucleus and the negative charge of other electrons that are bound to the nucleus.
Applying the principle
The building-up denoted by the name of the principle is a hypothetical process in which the electrons are regarded as entering, one by one, this electric field and assuming their most stable conditions with respect to it.
Therefore, the orbital with the lowest available energy is filled first (e.g. 1s before 2s). The number of electrons that can occupy each orbital is limited by the Pauli exclusion principle. If multiple orbitals of the same energy are available, Hund's rule says that unoccupied orbitals will be filled before occupied orbitals are reused (by electrons having different spins).
The order of occupied orbitals
In general, electrons are added to orbitals in order of increasing Principal quantum number (n, the numeric part of the orbital), and are added in the order s, p, d, f, g for a given n. However, in atoms with multiple electrons, this order is not so straightforward due to electron-electron interactions.
The table below depicts the order in which electrons generally occupy orbitals.
| <math>s<math> | <math>p<math> | <math>d<math> | <math>f<math> | <math>g<math> | |
|---|---|---|---|---|---|
| 1 | 1 | ||||
| 2 | 2 | 3 | |||
| 3 | 4 | 5 | 7 | ||
| 4 | 6 | 8 | 10 | 13 | |
| 5 | 9 | 11 | 14 | 17 | 21 |
| 6 | 12 | 15 | 18 | 22 | |
| 7 | 16 | 19 | 23 | ||
| 8 | 20 | 24 |
The periodic table is the best tool for remembering this order, by utilizing the s-block, p-block, d-block, and f-block, and counting up from hydrogen (1s1) to the desired element, placing electrons along the way. For example, the electron configuration of scandium can be found by counting up from hydrogen and helium (1s1, 1s2), through the s-block elements lithium and beryllium (2s1, 2s2), through the p-block elements boron, carbon, nitrogen, oxygen, fluorine, and neon (2p1 through 2p6), back to the s-block for sodium and magnesium (3s1, 3s2), back to the p-block for aluminum through argon (3p1 through 3p6), back to the s-block again for potassium and calcium (4s1, 4s2), and finally to the d-block for scandium (4d1). Adding all of that together provides the electron configuration of scandium, 1s22s22p63s23p64s23d1.
Building up the nucleus
A version of the aufbau principle can also be used to predict the arrangement of protons and neutrons in an atomic nucleus.