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In
atomic physics and
quantum chemistry, the
electron configuration is the arrangement of electrons in an atom, molecule, or other physical structure (
e.g., a
crystal).Like other
elementary particles, the electron is subject to the laws of quantum mechanics, and exhibits both particle-like and wave-like nature. Formally, the
quantum state of a particular electron is defined by its
wavefunction, a
Complex number function of space and time. According to the Copenhagen interpretation of quantum mechanics, the position of a particular electron is not well defined 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 move 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 is useful in understanding the structure of the periodic table of elements. The concept is also useful for describing the chemical bonds that hold atoms together. In bulk materials this same idea helps explain the peculiar properties of lasers and
semiconductors.
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).{]||
n||integer, 1 or more||Partly the overall energy of the orbital, and by extension its general distance from the nucleus. In short, the energy level it is in. (1+)|-|
azimuthal quantum number||m||integer, -l to +l, including zero.||Determines energy shift of an [atomic orbital due to external magnetic field (
Zeeman effect). Indicates spatial orientation.]||
ms||+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.]).
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, or even their overall energy. In large atoms, shells above the second shell overlap (see Electron configuration#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, and those electrons having the same
n and
l are called
equivalent electrons.
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 4
l+2 electrons; a shell can contain up to 2
n² electrons; where
n equals the shell number.
Worked example
Here is the electron configuration for a filled fifth shell:{| cellspacing="0" border="1" class="wikitable" bgcolor="white"|
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).
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 orbital of the first shell, so its configuration is written 1s1.
Lithium has two electrons in the 1s subshell and one in the (higher-energy) 2
s subshell, so its ground-state configuration is written 1
s2 2
s1. Phosphorus (atomic number 15), is as follows: 1
s2 2
s2 2
p6 3
s2 3
p3.
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 (1
s2 2
s2 2
p6) only by the presence of a third shell. Thus, the electron configuration of neon is pulled out, and phosphorus is written as follows: 3
s2 3
p3.
An even simpler version is simply to quote the number of electrons in each shell, e.g. (again for phosphorus): 2-8-5.
The orbital labels
s,
p,
d, and
f originate from a now-discredited system of categorizing
spectral lines as
sharp,
principal,
diffuse, and
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. For mnemonic reasons, some call the s and p orbitals
spherical and
peripheral.
===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:
{].
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).
Orbitals table
This table shows all orbital configurations up to 7
s, therefore it covers the simple electronic configuration for all elements from the
periodic table up to
Ununbium (element 112) with the exception of
Lawrencium (element 103), which would require a 7
p orbital.
{| class="wikitable"|-!!
s (l=0)!
p (l=1)!
d (l=2)!
f (l=3)|-!n=1| ||||-!n=2| | |||-!n=3| | | ||-!n=4| | | | |-!n=5| | | ||-!n=6| | |||-!n=7| ||||}
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 4s1 3d10, not 4s2 3d9 as one would expect by the Aufbau principle. Likewise,
chromium (atomic number 24) has a configuration of 4s1 3d5, not 4s2 3d4 where represents the configuration for argon.
Exceptions in Period 4:
{] || 21 || 1s2 2s2 2p6 3s2 3p6 4s2 3d1|| [argon] 4s2 3d1|-| Titanium ]] 4s2 3d2|-| Vanadium ]] 4s2 3d3|-| Chromium ]] 4s1 3d5 |-|
Manganese ]] 4s2 3d5|-|
Iron ]] 4s2 3d6|-|
Cobalt ]] 4s2 3d7|-|
Nickel ]] 4s2 3d8|-| Copper ]] 4s1 3d10|-|
Zinc ]] 4s2 3d10|-| Gallium ]] 3d10 4s2 4p1|-|}
Exceptions in Period 5:
{| cellspacing="0" border="1" class="wikitable" bgcolor="white"|
Element ||
Z ||
Electron configuration ||
Short electron conf.|-|
Yttrium ]] 5s2 4d1|-| Zirconium ]] 5s2 4d2|-| Niobium ]] 5s1 4d4|-| Molybdenum ]] 5s1 4d5|-|
Technetium ]] 5s1 4d6|-|
Ruthenium ]] 5s1 4d7 |-|
Rhodium ]] 5s1 4d8|-| Palladium ]] 4d10|-| Silver ]] 5s1 4d10|-|
Cadmium ]] 5s2 4d10|-|
Indium ]] 5s2 4d10 5p1|-|}
Exceptions in Period 6:
{| cellspacing="0" border="1" class="wikitable" bgcolor="white"|
Element ||
Z ||
Short electron conf.|-| Iridium ]] 6s2 4f14 5d7|-| Platinum ]] 6s1 4f14 5d9|-|
Gold ]] 6s1 4f14 5d10|-| Mercury (element) || 80|| [xenon] 6s2 4f14 5d10|-|
Thallium ]] 6s2 4f14 5d10 6p1|-|}
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) therefore elements in the same
Periodic_table_group are chemically similar because they contain the same number of "valence" electrons.
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.
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.
See also
Notes
In atomic physics and quantum chemistry, the
electron configuration is the arrangement of
electrons in an atom, molecule, or other physical structure (
e.g., a crystal).Like other elementary particles, the electron is subject to the laws of
quantum mechanics, and exhibits both particle-like and wave-like nature. Formally, the
quantum state of a particular electron is defined by its wavefunction, a Complex number function of space and time. According to the
Copenhagen interpretation of quantum mechanics, the position of a particular electron is not well defined 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 move 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 is useful in understanding the structure of the
periodic table of elements. The concept is also useful for describing the chemical bonds that hold atoms together. In bulk materials this same idea helps explain the peculiar properties of lasers and
semiconductors.
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).{]||
n||integer, 1 or more||Partly the overall energy of the orbital, and by extension its general distance from the nucleus. In short, the energy level it is in. (1+)|-|azimuthal quantum number||
m||integer, -
l to +
l, including zero.||Determines energy shift of an [atomic orbital due to external magnetic field (
Zeeman effect). Indicates spatial orientation.]||
ms||+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.]).
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, or even their overall energy. In large atoms, shells above the second shell overlap (see Electron configuration#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, and those electrons having the same
n and
l are called
equivalent electrons.
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 4
l+2 electrons; a shell can contain up to 2
n² electrons; where
n equals the shell number.
Worked example
Here is the electron configuration for a filled fifth shell:{| cellspacing="0" border="1" class="wikitable" bgcolor="white"|
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).
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 orbital of the first shell, so its configuration is written 1s1.
Lithium has two electrons in the 1s subshell and one in the (higher-energy) 2
s subshell, so its ground-state configuration is written 1
s2 2
s1. Phosphorus (atomic number 15), is as follows: 1
s2 2
s2 2
p6 3
s2 3
p3.
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 (1
s2 2
s2 2
p6) only by the presence of a third shell. Thus, the electron configuration of neon is pulled out, and phosphorus is written as follows: 3
s2 3
p3.
An even simpler version is simply to quote the number of electrons in each shell, e.g. (again for phosphorus): 2-8-5.
The orbital labels
s,
p,
d, and
f originate from a now-discredited system of categorizing spectral lines as
sharp,
principal,
diffuse, and
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. For
mnemonic reasons, some call the s and p orbitals
spherical and
peripheral.
===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:
{].
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).
Orbitals table
This table shows all orbital configurations up to 7
s, therefore it covers the simple electronic configuration for all elements from the periodic table up to Ununbium (element 112) with the exception of
Lawrencium (element 103), which would require a 7
p orbital.
{| class="wikitable"|-!!
s (l=0)!
p (l=1)!
d (l=2)!
f (l=3)|-!n=1| ||||-!n=2| | |||-!n=3| | | ||-!n=4| | | | |-!n=5| | | ||-!n=6| | |||-!n=7| ||||}
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 4s1 3d10, not 4s2 3d9 as one would expect by the
Aufbau principle. Likewise, chromium (atomic number 24) has a configuration of 4s1 3d5, not 4s2 3d4 where represents the configuration for argon.
Exceptions in Period 4:
{] || 21 || 1s2 2s2 2p6 3s2 3p6 4s2 3d1|| [argon] 4s2 3d1|-| Titanium ]] 4s2 3d2|-| Vanadium ]] 4s2 3d3|-|
Chromium ]] 4s1 3d5 |-| Manganese ]] 4s2 3d5|-| Iron ]] 4s2 3d6|-|
Cobalt ]] 4s2 3d7|-|
Nickel ]] 4s2 3d8|-| Copper ]] 4s1 3d10|-| Zinc ]] 4s2 3d10|-| Gallium ]] 3d10 4s2 4p1|-|}
Exceptions in Period 5:
{| cellspacing="0" border="1" class="wikitable" bgcolor="white"|
Element ||
Z ||
Electron configuration ||
Short electron conf.|-| Yttrium ]] 5s2 4d1|-|
Zirconium ]] 5s2 4d2|-|
Niobium ]] 5s1 4d4|-|
Molybdenum ]] 5s1 4d5|-| Technetium ]] 5s1 4d6|-| Ruthenium ]] 5s1 4d7 |-| Rhodium ]] 5s1 4d8|-|
Palladium ]] 4d10|-|
Silver ]] 5s1 4d10|-|
Cadmium ]] 5s2 4d10|-|
Indium ]] 5s2 4d10 5p1|-|}
Exceptions in Period 6:
{| cellspacing="0" border="1" class="wikitable" bgcolor="white"|
Element ||
Z ||
Short electron conf.|-| Iridium ]] 6s2 4f14 5d7|-|
Platinum ]] 6s1 4f14 5d9|-| Gold ]] 6s1 4f14 5d10|-|
Mercury (element) || 80|| [xenon] 6s2 4f14 5d10|-| Thallium ]] 6s2 4f14 5d10 6p1|-|}
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) therefore elements in the same Periodic_table_group are chemically similar because they contain the same number of "valence" electrons.
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.
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.
See also
Notes
Electron Configuration
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