# Electron configuration

In atomic physics, the electron configuration is the arrangement of electrons in an atom, molecule or other body. Specifically, it is the placement of electrons into atomic, molecular, or other forms of electron orbitals.

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## Why electron configurations occur

The notion of electron configuration is predicated on three facts:

1. In a confined space, such as an atom or molecule, the energy and other properties of an electron are quantized, or restricted to certain possible states. The possible states are determined by electron orbitals. Each state generally has a different energy than any other state.
2. Electrons are fermions and are thus subject to the Pauli exclusion principle, which states that no two fermions can occupy the same quantum state at once. Once a state is occupied by an electron, the next electron must occupy a different state.
3. An electron is not stable if it is not in the state with the lowest possible energy. If a state with lower energy is available, the electron will, given time, switch to that state (and emit its excess energy as a photon).

As a result, any system has only one stable electron configuration. If left in equilibrium, it will always have this configuration, though the electrons may be temporarily "excited" to other configurations.

The electron configuration of a system is determined by its orbitals and by the number of electrons present. If one wishes to deduce the configuration, one must know the orbitals. This is relatively simple for hydrogen, much more difficult for other atoms, and extremely difficult for molecules. As a result, atomic electron configurations are more commonly discussed.

## Electron configuration in atoms

### Summary of the quantum numbers

The state of an electron in an atom is given by four quantum numbers. Three of these are properties of the atomic orbital in which it sits (a more thorough explanation is given at that article).

• The principal quantum number is denoted n, and can take any integer value greater than or equal to 1.
• The azimuthal quantum number is denoted l, and can take any integer value in the range [itex]0 \le l \le n-1[itex]. For instance, if the electron is in an [itex]n=2[itex] state, l can be either 0 or 1.
• The magnetic quantum number is denoted m, and can take any integer value in the range [itex]-l \le m \le l[itex]. For instance, if the electron is in an [itex]n=2,\ l=1[itex] state, m can be either -1, 0, or 1.

The spin quantum number is an intrinsic property of the electron and independent of the other numbers. It is denoted s, and can only take the values 1/2 or -1/2 (sometimes referred to as "up" and "down").

### Shells and subshells

States with the same value of n are related, and said to lie within the same electron shell. States with the same value of l are more closely related, and said to lie within the same electron subshell.

For instance, the n = 1 shell only possesses an s subshell and can only take 2 electrons, the n = 2 shell possesses an s and a p subshell and can take 8 electrons overall, the n = 3 shell possesses s, p and d subshells and has a maximum of 18 electrons, and so on. It can be shown that the total capacity of a shell is [itex]2n^2[itex].

### Aufbau principle

In the ground state of an atom, the states are "filled" in order of increasing energy; i.e., the first electron goes into the lowest energy state, the second into the next lowest, and so on. The fact that the 3d state is higher in energy than the 4s state but lower than the 4p is the reason for the existence of the transition metals. The order in which the states are filled is as follows:

```1s
2s           2p
3s           3p
4s        3d 4p
5s        4d 5p
6s     4f 5d 6p
7s     5f 6d 7p
8s  5g 6f 7d 8p
...
```

This leads directly to the structure of the periodic table. The chemical properties of an atom are largely determined by the arrangement of the electrons in its outermost ("valence") shell (although other factors, such as atomic radius, atomic mass, and increased accessibility of additional electronic states also contribute to the chemistry of the elements as atomic size increases).

Progressing through a group from lightest element to heaviest element, the outer-shell electrons (those most readily accessible for participation in chemical reactions) are all in the same type of orbital, with a similar shape, but with increasingly higher energy and average distance from the nucleus. For instance, the outer-shell (or "valence") electrons of the first group, headed by hydrogen all have one electron in an s orbital. In hydrogen, that s orbital is in the lowest possible energy state of any atom, the first-shell orbital (and represented by hydrogen's position in the first period of the table). In francium, the heaviest element of the group, the outer-shell electron is in the seventh-shell orbital, significantly further out on average from the nucleus than those electrons filling all the shells below it in energy. As another example, both carbon and lead have four electrons in their outer shell orbitals.

Because of the importance of the outermost shell, the different regions of the periodic table are sometimes referred to as periodic table blocks, named according to the sub-shell in which the "last" electron resides, e.g. the s-block, the p-block, the d-block, etc.

An example of the notation commonly used to give the electron configuration of an atom, in this case silicon (atomic number 14), is as follows: 1s2 2s2 2p6 3s2 3p2 The numbers are the shell number, n; the letters refer to the angular momentum state, as given above, and the superscripted numbers are the number of electrons in that state for the atom in question. An even simpler version is simply to quote the number of electrons in each shell, eg (again for Si): 2-8-4.

In molecules, the situation becomes much more complex: see molecular orbitals for details. Similar, but not identical, arguments can be applied to the protons and neutrons in the atomic nucleus: see the shell model of nuclear physics.

There are two major ways to write an electron configuration. One is writing out the whole configuration, as in the example 1s2 2s2 2p6 3s2 3p2. The other is a shorthand using noble gases. An example of this would be argon, which is [Ne]3s23p6.

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