Electron configuration

In atomic physics and quantum chemistry, 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. The electrons occupy specific probability regions, whose shapes and electron capacity are denoted by the letters s,p,d,f and the as of yet unseen g,h, and i. The energy of an orbital is shown by a whole number (1-7) next to the letter, electrons are able to jump from one energy level (orbital filling laws allowing) to another by emission of a quantum of energy, in the form of a photon

Electron configuration in atoms

The discussion below presumes knowledge of material contained at Atomic orbital.

Summary of the quantum numbers

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

number	denoted	allowed range	represents
principal quantum number	n	integer, 1 or more	partly the overall energy of the orbital, and by extension its general distance from the nucleus
azimuthal quantum number	l	integer, 0 to n-1	the orbital's angular momentum, also seen as the number of nodes in the density plot
magnetic quantum number	m	integer, -l to +l	determines energy shift of an atomic orbital due to external magnetic field (Zeeman effect).
spin quantum number	s	+½ or -½ (sometimes called "up" and "down")	Spin is an intrinsic property of the electron and independent of the other numbers. s and l in part determine the electron's magnetic dipole moment.

No two electrons in one atom can have the same set of these four quantum numbers (Pauli exclusion principle).

Shells and subshells

Shells and subshells (also called energy levels and sublevels) are defined by the quantum numbers, NOT by the distance of its electrons from the nucleus. In large atoms, shells above the second shell overlap (see Aufbau principle).

States with the same value of n are related, and said to lie within the same electron shell.
States with the same value of n and also l are said to lie within the same electron subshell.
If the states also share the same value of m, they are said to lie in the same atomic orbital.
Because electrons have only two possible spin states, an atomic orbital cannot contain more than two electrons (Pauli exclusion principle).

A subshell can contain up to 4l+2 electrons; a shell can contain up to 2n² electrons.

Worked example

Here is the electron configuration for a filled fifth shell:

Shell	Subshell	Orbitals		Electrons
n = 5	l = 0	m = 0	→ 1 type s orbital	→ max 2 electrons
	l = 1	m = -1, 0, +1	→ 3 type p orbitals	→ max 6 electrons
	l = 2	m = -2, -1, 0, +1, +2	→ 5 type d orbitals	→ max 10 electrons
	l = 3	m = -3, -2, -1, 0, +1, +2, +3	→ 7 type f orbitals	→ max 14 electrons
	l = 4	m = -4, -3 -2, -1, 0, +1, +2, +3, +4	→ 9 type g orbitals	→ max 18 electrons
				Total: max 50 electrons

This information can be written as 5s² 5p⁶ 5d¹⁰ 5f¹⁴ 5g¹⁸ (see below for more details on notation).

The subshell labels s, p, d, and f originate from a now-discredited system of categorizing spectral lines as "sharp", "principal", "diffuse", or "fundamental", based on their observed fine structure. When the first four types of orbitals were described, they were associated with these spectral line types, but there were no other names. The designation g was derived by following alphabetical order. Shells with more than five subshells are theoretically permissible, but this covers all discovered elements.

Notation

Physicists and chemists use a standard notation to describe atomic electron configurations. In this notation, a subshell is written in the form nx^e, where n is the shell number, x is the subshell label and e is the number of electrons in the subshell. An atom's subshells are written in order of increasing energy - in other words, the sequence in which they are filled (see Aufbau principle below).

For instance, ground-state hydrogen has one electron in the s subshell of the first shell, so its configuration is written 1s¹. Lithium has two electrons in the 1s subshell and one in the (higher-energy) 2s subshell, so its ground-state configuration is written 1s² 2s¹. Phosphorus (atomic number 15), is as follows: 1s² 2s² 2p⁶ 3s² 3p³.

For atoms with many electrons, this notation can become lengthy. It is often abbreviated by noting that the first few subshells are identical to those of one or another noble gas. Phosphorus, for instance, differs from neon (1s² 2s² 2p⁶) only by the presence of a third shell. Thus, the electron configuration of neon is pulled out, and phosphorus is written as follows: ^*3s² 3p³.

An even simpler version is simply to quote the number of electrons in each shell, e.g. (again for phosphorus): 2-8-5.

Aufbau principle

In the ground state of an atom (the condition in which it is ordinarily found), the electron configuration generally follows the Aufbau principle. According to this principle, electrons enter into states in order of the states' increasing energy; i.e., the first electron goes into the lowest-energy state, the second into the next lowest, and so on. The order in which the states are filled is as follows:

	$s$	$p$	$d$	$f$	$g$
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

A pair of electrons with identical spins has slightly less energy than a pair of electrons with opposite spins. Since two electrons in the same orbital must have opposite spins, this causes electrons to prefer to occupy different orbitals. This preference manifests itself if a subshell with $l>0$ (one that contains more than one orbital) is less than full. For instance, if a p subshell contains four electrons, two electrons will be forced to occupy one orbital, but the other two electrons will occupy both of the other orbitals, and their spins will be equal. This phenomenon is called Hund's rule.

The Aufbau principle can be applied, in a modified form, to the protons and neutrons in the atomic nucleus (see the shell model of nuclear physics).

Exceptions in 3d, 4d, 5d

A d subshell that is half-filled or full (ie 5 or 10 electrons) is more stable than the s subshell of the next shell. This is the case because it takes less energy to maintain an electron in a half-filled d subshell than a filled s subshell. For instance, copper (atomic number 29) has a configuration of 3d¹⁰, not chromium (atomic number 24) has a configuration of ^*4s¹" target="_blank" >3d⁵, not [Ar4s² 3d⁴.

Element	Z	Electron configuration	Short electron conf.
Scandium	21	1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹	^* 4s² 3d¹
Titanium	22	1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d²	^* 4s² 3d²
Vanadium	23	1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d³	^* 4s² 3d³
Chromium	24	1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹ 3d⁵	^* 4s¹ 3d⁵
Manganese	25	1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁵	^* 4s² 3d⁵
Iron	26	1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁶	^* 4s² 3d⁶
Cobalt	27	1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁷	^* 4s² 3d⁷
Nickel	28	1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁸	^* 4s² 3d⁸
Copper	29	1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹ 3d¹⁰	^* 4s¹ 3d¹⁰
Zinc	30	1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰	^* 4s² 3d¹⁰
Gallium	31	1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p¹	^* 4s² 3d¹⁰ 4p¹

This can be most easily understood by stepping through the electron configuration shown at ^*

Period 5^th has more exceptions:

Element	Z	Electron configuration	Short electron conf.
Yttrium	39	1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d¹	[Kr] 5s² 4d¹
Zirconium	40	1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d²	[Kr] 5s² 4d²
Niobium	41	1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s¹ 4d⁴	[Kr] 5s¹ 4d⁴
Molybdenum	42	1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s¹ 4d⁵	[Kr] 5s¹ 4d⁵
Technetium	43	1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d⁵	[Kr] 5s² 4d⁵
Ruthenium	44	1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s¹ 4d⁷	[Kr] 5s¹ 4d⁷
Rhodium	45	1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s¹ 4d⁸	[Kr] 5s¹ 4d⁸
Palladium	46	1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 4d¹⁰	[Kr] 4d¹⁰
Silver	47	1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s¹ 4d¹⁰	[Kr] 5s¹ 4d¹⁰
Cadmium	48	1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d¹⁰	[Kr] 5s² 4d¹⁰
Indium	49	1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d¹⁰ 5p¹	[Kr] 5s² 4d¹⁰ 5p¹

This can be seen by stepping through the electron configuration shown at ^*

Element	Z	Short electron conf.
Iridium	77	[Xe] 6s² 4f¹⁴ 5d⁷
Platinum	78	[Xe] 6s¹ 4f¹⁴ 5d⁹
Gold	79	[Xe] 6s¹ 4f¹⁴ 5d¹⁰
Mercury	80	[Xe] 6s² 4f¹⁴ 5d¹⁰
Thallium	81	[Xe] 6s² 4f¹⁴ 5d¹⁰ 6p¹

This can be seen by stepping through the electron configuration shown at ^*

Relation to the structure of the periodic table

Electron configuration is intimately related 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).