Electron configuration

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Electron atomic and molecular orbitals

In atomic physics and quantum chemistry, the electron configuration is the arrangement of electrons in an atom, molecule, or other physical structure (eg, a crystal).

Like other elementary particles, the electron is subject to the laws of quantum mechanics, and exhibits both particle-like and wave-like properties. Formally, the quantum state of a particular electron is defined by its wavefunction, a complex-valued function of space and time. According to the Copenhagen interpretation of quantum mechanics, a particular electron is both "nowhere at all" and "everywhere all at once" until an act of measurement causes it to be detected. The probability that the act of measurement will detect the electron at a particular point in space is proportional to the square of the absolute value of the wavefunction at that point.

Electrons are able to jump from one energy level to another by emission or absorption of a quantum of energy, in the form of a photon. Because of the Pauli exclusion principle, no more than two electrons may exist in a given atomic orbital; therefore an electron may only leap to another orbital if there is a vacancy there.

Knowledge of the electron configuration of different atoms helps us understand the structure of the periodic table of elements. The concept is also useful for describing the chemical bonds that hold molecules together. And in a macro sense this same idea helps explain the peculiar properties of lasers and semiconductors.

Contents

[edit] Electron configuration in atoms

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

[edit] 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 numberninteger, 1 or morePartly the overall energy of the orbital, and by extension its general distance from the nucleus
azimuthal quantum numberlinteger, 0 to n-1The orbital's angular momentum, also seen as the number of nodes in the density plot
magnetic quantum numberminteger, -l to +l, including zero.Determines energy shift of an atomic orbital due to external magnetic field (Zeeman effect). Indicates spatial orientation.
spin quantum numberms+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).

[edit] Shells and subshells

Shells and subshells (also called energy levels and sublevels) are defined by the quantum numbers, and 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.

[edit] 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).

[edit] Notation

Physicists and chemists use a standard notation to describe atomic electron configurations. In this notation, a subshell is written in the form nxy, where n is the shell number, x is the subshell label and y 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: [Ne]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.

[edit] 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:

<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 order of increasing energy of the subshells can be constructed by going through downward-leftward diagonals of the table above (also see the diagram at the top of the page), going from the topmost diagonals to the bottom. The first (topmost) diagonal goes through 1s; the second diagonal goes through 2s; the third goes through 2p and 3s; the fourth goes through 3p and 4s; the fifth goes through 3d, 4p, and 5s; and so on. In general, a subshell that is not "s" is always followed by a "lower" subshell of the next shell; e.g. 2p is followed by 3s; 3d is followed by 4p, which is followed by 5s, 4f is followed by 5d, which is followed by 6p, and then 7s. This explains the ordering of the blocks in the periodic table.

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 <math>l>0</math> (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).

[edit] 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 [Ar]4s1 3d10, not [Ar]4s2 3d9 as one would expect by the Aufbau principle. Likewise, chromium (atomic number 24) has a configuration of [Ar]4s1 3d5, not [Ar]4s2 3d4.

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

This can be most easily understood by stepping through the electron configuration shown at [1]

Period 5 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 [2]

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 [3]

[edit] 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).

[edit] Electron configuration in molecules

In molecules, the situation becomes more complex, as each molecule has a different orbital structure. See the molecular orbital article and the linear combination of atomic orbitals method for an introduction and the computational chemistry article for more advanced discussions.

[edit] Electron configuration in solids

In a solid, the electron states become very numerous. They cease to be discrete, and effectively blend together into continuous ranges of possible states (an electron band). The notion of electron configuration ceases to be relevant, and yields to band theory.

[edit] See also

ar:توزيع إلكتروني ca:Configuració electrònica cs:Elektronová konfigurace de:Elektronenkonfiguration es:Configuración electrónica fr:Configuration électronique is:Rafeindahýsing it:Configurazione elettronica lt:Elektronų konfigūracija hu:Elektronszerkezet mk:Електронска конфигурација nl:Elektronenconfiguratie ja:電子配置 pl:Konfiguracja elektronowa pt:Configuração electrónica ro:Configuraţie electronică ru:Электронная конфигурация sl:Elektronska konfiguracija sr:Електронска конфигурација sh:Elektronska konfiguracija sv:Elektronkonfiguration tr:Elektron dizilimi uk:Електронна конфігурація uz:Elektron konfiguratsiyasi zh:电子排布

Electron configuration

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