electron configuration

5/26/2018 Electron Configuration

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Electron configuration

Electron atomic and molecular orbitals

In atomic physicsand quantum chemistry,electron configurationis the arrangement of

electronsof an atom, a molecule, or other physical structure.[1]It concerns the wayelectrons can be distributed in theorbitalsof the given system (atomicor molecularfor

instance.

!i"e other elementary particles, the electron is sub#ect to the laws of quantum mechanics,

and e$hibits both particle%li"e and wave%li"e nature. &ormally, the quantum stateof aparticular electron is defined by its wave function,acomple$%valuedfunction of space

and time. 'ccording to the openhagen interpretationof quantum mechanics, the

position of a particular electron is not well defined until an act of measurementcauses itto be detected. )he probability that the act of measurement will detect the electron at a

particular point in space is proportional to the square of the absolute valueof the

wavefunction at that point.

'n energy is associated with each electron configuration and, upon certain conditions,electrons are able to move from one orbital to another by emission or absorption of a

quantumof energy, in the form of aphoton.

*nowledge of the electron configuration of different atoms is useful in understanding the

structure of theperiodic tableof elements. )he concept is also useful for describing the

chemical bonds that hold atoms together. In bul" materials this same idea helps e$plainthe peculiar properties of lasersand semiconductors.
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Shells and subshells

+ee also Electron shell

Electron configuration table

Electron configuration was first conceived of under the -ohr modelof the atom, and it isstill common to spea" of shells and subshells despite the advances in understanding of the

quantum%mechanicalnature of electrons.

'n electron shell is the set of allowed stateselectrons may occupy which share the same

principal quantum number,n(the number before the letter in the orbital label. 'n atomsnth electron shell can accommodate /n/electrons, e.g.the first shell can accommodate

/ electrons, the second shell 0 electrons, and the third shell 10 electrons. )he factor of

two arises because the allowed states are doubled due toelectron spineach atomicorbitaladmits up to two otherwise identical electrons with opposite spin, one with a spin

213/ (usually noted by an up%arrow and one with a spin %13/ (with a down%arrow.

' subshell is the set of states defined by a common a4imuthal quantum number, l, within

a shell. )he values l5 6, 1, /, 7 correspond to thes,p, d, andflabels, respectively. )hema$imum number of electrons which can be placed in a subshell is given by /(/l2 1.

)his gives two electrons in an s subshell, si$ electrons in a p subshell, ten electrons in a

d subshell and fourteen electrons in an f subshell.

)he numbers of electrons that can occupy each shell and each subshell arise from theequations of quantum mechanics,[/]in particular the 8auli e$clusion principle, which

states that no two electrons in the same atom can have the same values of the four

quantum numbers.[7]

[edit] Notation

+ee also 'tomic orbital

8hysicists and chemists use a standard notation to indicate the electron configurations of

atoms and molecules. &or atoms, the notation consists of a sequence of atomic orbital

labels (e.g. for phosphorus the sequence 1s, /s, /p, 7s, 7p with the number of electronsassigned to each orbital (or set of orbitals sharing the same label placed as a superscript.

&or e$ample, hydrogenhas one electron in the s%orbital of the first shell, so its
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configuration is written 1s1. !ithiumhas two electrons in the 1s%subshell and one in the

(higher%energy /s%subshell, so its configuration is written 1s//s1(pronounced 9one%s%

two, two%s%one9. 8hosphorus(atomic number1:, is as follows 1s//s//p;7s/7p7.

&or atoms with many electrons, this notation can become lengthy and so an abbreviated

notation is used, since all but the last few subshells are identical to those of one oranother of the noble gases.8hosphorus, for instance, differs from neon(1s//s//p; only

by the presence of a third shell. )hus, the electron configuration of neon is pulled out,and phosphorus is written as follows [ence the electron configuration of ironcan be written as ['r] 7d;?s/

("eeping the 7d%electrons with the 7s% and 7p%electrons which are implied by the

configuration of argon or as ['r] ?s/7d;(following the 'ufbau principle, see below.

)he superscript 1 for a singly%occupied orbital is not compulsory.[?]It is quite common to

see the letters of the orbital labels (s, p, d, f written in an italic or slanting typeface,

although the International @nion of 8ure and 'pplied hemistry(I@8' recommends a

normal typeface (as used here. )he choice of letters originates from a now%obsoletesystem of categori4ing spectral linesas 9sharp9, 9principal9, 9diffuse9 and 9fine9, based

on their observed fine structure their modern usage indicates orbitals with ana4imuthal

quantum number, l, of 6, 1, / or 7 respectively. 'fter 9f9, the sequence continuesalphabetically 9g9, 9h9, 9i9... (l5 ?, :, ;..., s"ipping 9#9, although orbitals of these types

are rarely required.

)he electron configurations of molecules are written in a similar way, e$cept thatmolecular orbitallabels are used instead of atomic orbital labels (see below.

[edit] Energy ground state and excited states

)he energy associated to an electron is that of its orbital. )he energy of a configuration is

often appro$imated as the sum of the energy of each electron, neglecting the electron%

electron interactions. )he configuration that corresponds to the lowest electronic energyis called the ground state.'ny other configuration is ane$cited state.

's an e$ample, the ground state configuration of the sodiumatom is 1s//s//p;7s, as

deduced from the 'ufbau principle (see below. )he first e$cited state is obtained bypromoting a 7s electron to the 7p orbital, to obtain the 1s//s//p;7p configuration,

abbreviated as the 7p level. 'toms can move from one configuration to another by

absorbing or emitting energy. In a sodium%vapor lampfor e$ample, sodium atoms are

e$cited to the 7p level by an electrical discharge, and return to the ground state byemitting yellow light of wavelength :0A nm.
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@sually the e$citation of valence electrons(such as 7s for sodium involves energies

corresponding tophotonsof visible or ultravioletlight. )he e$citation of core electronsis

possible, but requires much higher energies generally corresponding to $%rayphotons.)his would be the case for e$ample to e$cite a /p electron to the 7s level and form the

e$cited 1s//s//p:7s/configuration.

)he remainder of this article deals only with the ground%state configuration, often

referred to as 9the9 configuration of an atom or molecule.

[edit] History

is proposals werebased on the then current-ohr modelof the atom, in which the electron shells were

orbits at a fi$ed distance from the nucleus. -ohrs original configurations would seem

strange to a present%day chemist sulfurwas given as /.?.?.; instead of 1s//s//p;7s/7p?

(/.0.;.

)he following year, E. . +toner incorporated +ommerfeldsthird quantum number into

the description of electron shells, and correctly predicted the shell structure of sulfur to be

/.0.;.[;]>owever neither -ohrs system nor +toners could correctly describe the changes

in atomic spectrain a magnetic field(the Beeman effect.

-ohr was well aware of this shortcoming (and others, and had written to his friend

Colfgang 8aulito as" for his help in saving quantum theory (the system now "nown as

9old quantum theory9. 8auli reali4ed that the Beeman effect must be due only to theoutermost electrons of the atom, and was able to reproduce +toners shell structure, but

with the correct structure of subshells, by his inclusion of a fourth quantum number andhis e$clusion principle(1A/:[D]

It should be forbidden for more than one electron with the same value of the mainquantum numbern to have the same value for the other three quantum numbers" [l],#

[ml] andm [ms].

)he +chrdinger equation, published in 1A/;, gave three of the four quantum numbers as

a direct consequence of its solution for the hydrogen atom[/]this solution yields theatomic orbitals which are shown today in te$tboo"s of chemistry (and above. )he

e$amination of atomic spectra allowed the electron configurations of atoms to be

determined e$perimentally, and led to an empirical rule ("nown as =adelungs rule(1A7;,[0]see below for the order in which atomic orbitals are filled with electrons.

[edit] Aufbau principle and Madelung rule

)he 'ufbau principle(from the FermanAufbau, 9building up, construction9 was an

important part of -ohrs original concept of electron configuration. It may be stated as[A]
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a maximum of two electrons are put into orbitals in the order of increasing

orbital energy: the lowestenergy orbitals are filled before electrons are placed in

higherenergy orbitals.

)he appro$imate order of filling of atomic orbitals, following the arrows.

)he principle wor"s very well (for the ground states of the atoms for the first10 elements, then decreasingly well for the following 166 elements. )he modern form of

the 'ufbau principle describes an order of orbital energies given by =adelungs rule (or

*lech"ows"is rule. )his rule was first stated by harles Ganetin 1A/A, rediscovered by

Erwin =adelungin 1A7;,[0]and later given a theoretical #ustification by H.=.*lech"ows"i[16]

1. rbitals are filled in the order of increasing n2lJ

/. Chere two orbitals have the same value of n2l, they are filled in order ofincreasing n.

)his gives the following order for filling the orbitals

1s, /s, /p, 7s, 7p, ?s, 7d, ?p, :s, ?d, :p, ;s, ?f, :d, ;p, Ds, :f, ;d, and Dp

)he 'ufbau principle can be applied, in a modified form, to theprotonsand neutronsinthe atomic nucleus, as in the shell modelofnuclear physicsand nuclear chemistry.

[edit] The periodic table

)he form of theperiodic tableis closely related to the electron configuration of the atomsof the elements. &or e$ample, all the elements of group /have an electron configuration

of [E] ns/(where [E] is an inert gas configuration, and have notable similarities in their

chemical properties. )he outermost electron shell is often referred to as the 9valence

shell9 and (to a first appro$imation determines the chemical properties. It should beremembered that the similarities in the chemical properties were remar"ed more than a

century before the idea of electron configuration,[11]It is not clear how far =adelungsrule explains(rather than simply describes the periodic table,[1/]although someproperties (such as the common 2/ o$idation statein the first row of the transition

metals would obviously be different with a different order of orbital filling.

[edit] Shortcomings of the Aufbau principle
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)he 'ufbau principle rests on a fundamental postulate that the order of orbital energies is

fi$ed, both for a given element and between different elements neither of these is true

(although they are appro$imately true enough for the principle to be useful. It considersatomic orbitals as 9bo$es9 of fi$ed energy into which can be placed two electrons and no

more. >owever the energy of an electron 9in9 an atomic orbital depends on the energies

of all the other electrons of the atom (or ion, or molecule, etc.. )here are no 9one%electron solutions9 for systems of more than one electron, only a set of many%electron

solutions which cannot be calculated e$actly[17](although there are mathematical

appro$imations available, such the>artreeK&oc" method.

)he fact that the 'ufbau principle is based on an appro$imation can be seen from the factthat there is an almost%fi$ed filling order at all, that, within a given shell, the s%orbital is

always filled before the p%orbitals. In a hydrogen%li"e atom, which only has one electron,

the s%orbital and the p%orbitals of the same shell have e$actly the same energy, to a verygood appro$imation in the absence of e$ternal electromagnetic fields. (>owever, in a real

hydrogen atom, the energy levels are slightly split by the magnetic field of the nucleus,

and by the quantum electrodynamiceffects of the!amb shift.

[edit] oni!ation of the transition metals

)he naive application of the 'ufbau principle leads to a well%"nownparado$(or apparentparado$ in the basic chemistry of the transition metals. 8otassiumandcalciumappear in

the periodic table before the transition metals, and have electron configurations ['r] ?s 1

and ['r] ?s/respectively, i.e. the ?s%orbital is filled before the 7d%orbital. )his is in line

with =adelungs rule, as the ?s%orbital has n2l 5 ? (n5 ?, l5 6 while the 7d%orbital hasn2l 5 : (n5 7, l5 /. >owever, chromiumandcopperhave electron configurations

['r] 7d:?s1and ['r] 7d16?s1respectively, i.e. one electron has passed from the ?s%orbital

to a 7d%orbital to generate a half%filled or filled subshell. In this case, the usuale$planation is that 9half%filled or completely%filled subshells are particularly stable

arrangements of electrons9.

)he apparent parado$ arises when electrons are removedfrom the transition metal atoms

to form ions. )he first electrons to be ioni4ed come not from the 7d%orbital, as one woulde$pect if it were 9higher in energy9, but from the ?s%orbital. )he same is true when

chemical compounds are formed. hromium he$acarbonylcan be described as a

chromium atom (not ion, it is in the o$idation state6 surrounded by si$ carbonmono$ideligands it is diamagnetic,and the electron configuration of the central

chromium atom is described as 7d;, i.e. the electron which was in the ?s%orbital in the

free atom has passed into a 7d%orbital on forming the compound. )his interchange ofelectrons between ?s and 7d is universal among the first series of the transition metals.[1?]

)he phenomenon is only parado$ical if it is assumed that the energies of atomic orbitals

are fi$ed and unaffected by the presence of electrons in other orbitals. If that were the

case, the 7d%orbital would have the same energy as the 7p%orbital, as it does in hydrogen,yet it clearly doesnt. )here is no special reason why the &e/2ion should have the same

electron configuration as the chromium atom, given that ironhas two more protons in its
http://en.wikipedia.org/wiki/Electron_configuration#cite_note-12%23cite_note-12http://en.wikipedia.org/wiki/Hartree-Fockhttp://en.wikipedia.org/wiki/Hartree-Fockhttp://en.wikipedia.org/wiki/Hydrogen-like_atomhttp://en.wikipedia.org/wiki/Quantum_electrodynamichttp://en.wikipedia.org/wiki/Lamb_shifthttp://en.wikipedia.org/wiki/Lamb_shifthttp://en.wikipedia.org/w/index.php?title=Electron_configuration&action=edit&section=8http://en.wikipedia.org/wiki/Paradoxhttp://en.wikipedia.org/wiki/Transition_metalhttp://en.wikipedia.org/wiki/Potassiumhttp://en.wikipedia.org/wiki/Potassiumhttp://en.wikipedia.org/wiki/Calciumhttp://en.wikipedia.org/wiki/Calciumhttp://en.wikipedia.org/wiki/Chromiumhttp://en.wikipedia.org/wiki/Copperhttp://en.wikipedia.org/wiki/Copperhttp://en.wikipedia.org/wiki/Ionhttp://en.wikipedia.org/wiki/Chromium_hexacarbonylhttp://en.wikipedia.org/wiki/Oxidation_statehttp://en.wikipedia.org/wiki/Carbon_monoxidehttp://en.wikipedia.org/wiki/Carbon_monoxidehttp://en.wikipedia.org/wiki/Ligandhttp://en.wikipedia.org/wiki/Diamagnetichttp://en.wikipedia.org/wiki/Diamagnetichttp://en.wikipedia.org/wiki/Electron_configuration#cite_note-13%23cite_note-13http://en.wikipedia.org/wiki/Ironhttp://en.wikipedia.org/wiki/Ironhttp://en.wikipedia.org/wiki/Electron_configuration#cite_note-12%23cite_note-12http://en.wikipedia.org/wiki/Hartree-Fockhttp://en.wikipedia.org/wiki/Hydrogen-like_atomhttp://en.wikipedia.org/wiki/Quantum_electrodynamichttp://en.wikipedia.org/wiki/Lamb_shifthttp://en.wikipedia.org/w/index.php?title=Electron_configuration&action=edit&section=8http://en.wikipedia.org/wiki/Paradoxhttp://en.wikipedia.org/wiki/Transition_metalhttp://en.wikipedia.org/wiki/Potassiumhttp://en.wikipedia.org/wiki/Calciumhttp://en.wikipedia.org/wiki/Chromiumhttp://en.wikipedia.org/wiki/Copperhttp://en.wikipedia.org/wiki/Ionhttp://en.wikipedia.org/wiki/Chromium_hexacarbonylhttp://en.wikipedia.org/wiki/Oxidation_statehttp://en.wikipedia.org/wiki/Carbon_monoxidehttp://en.wikipedia.org/wiki/Carbon_monoxidehttp://en.wikipedia.org/wiki/Ligandhttp://en.wikipedia.org/wiki/Diamagnetichttp://en.wikipedia.org/wiki/Electron_configuration#cite_note-13%23cite_note-13http://en.wikipedia.org/wiki/Iron


7/9

nucleus than chromium and that the chemistry of the two species is very different. Chen

care is ta"en to compare 9li"e with li"e9, the parado$ disappears.[1:]

[edit] "ther exceptions to Madelung#s rule

)here are several more e$ceptions to =adelungs rule among the heavier elements, and itis more and more difficult to resort to simple e$planations such as the stability of half%filled subshells. It is possible to predict most of the e$ceptions by >artreeK&oc"

calculations,[1;]which are an appro$imate method for ta"ing account of the effect of the

other electrons on orbital energies. &or the heavier elements, it is also necessary to ta"eaccount of the effects of +pecial Lelativityon the energies of the atomic orbitals, as the

inner%shell electrons are moving at speeds approaching thespeed of light. In general,

these relativistic effects[1D]tend to decrease the energy of the s%orbitals in relation to theother atomic orbitals.[10]

Electron shells filled in violation of =adelungs rule (red

$eriod % $eriod & $eriod '

Element (

Electron

)onfigurati

on

Element (

Electron

)onfigurati

on

Element (

Electron

)onfigurati

on

!anthanum:

D[Me] ;s/:d1 'ctinium 0A [Ln] Ds/;d1

erium:

0

[Me] ;s/?f1

:d1 )horium A6 [Ln] Ds/;d/

8raseodymi

um

:

A

[Me] ;s/?f7 8rotactiniu

m

A1[Ln] Ds/:f/

;d

1


8/9

Birconium?6

[*r] :s/?d/ >afniumD/

[Me] ;s/?f1?:d/

Lutherfordium

16?

!un"nown#


9/9

)he most widespread application of electron configurations is in the rationali4ation of

chemical properties, in both inorganic and organic chemistry. In effect, electron

configurations, along with some simplified form of molecular orbital theory, havebecome the modern equivalent of the valenceconcept, describing the number and type of

chemical bonds that an atom can be e$pected to form.

)his approach is ta"en further in computational chemistry,which typically attempts to

ma"e quantitative estimates of chemical properties. &or many years, most suchcalculations relied upon the 9linear combination of atomic orbitals9 (!'

appro$imation, using an ever larger and more comple$basis setof atomic orbitals as the

starting point. )he last step in such a calculation is the assignment of electrons among themolecular orbitals according to the 'ufbau principle.

electron configuration

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