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"Atomic build-up" redirects here. For the spread of nuclear weapons, see Nuclear proliferation.

The Aufbau principle (from the GermanAufbaumeaning "building up, construction": also

Aufbau ruleor building-upprinciple) is used to determine the electron configurationof an

atom, moleculeor ion. The principle postulates a hypothetical process in which an atom is "built

up" by progressively adding electrons. As they are added, they assume their most stable

conditions (electron orbitals) with respect to the nucleus and those electrons already there.

According to the principle, electronsfill orbitals starting at the lowestavailable (possible) energy

levelsbefore filling higher levels (e.g. 1s before 2s). The number of electrons that can occupy

each orbital is limited by the Pauli exclusion principle. If multiple orbitals of the same energyare

available, Hund's rulestates that unoccupied orbitals will be filled before occupied orbitals are

reused (by electrons having different spins).

A version of the Aufbau principle can also be used to predict the configuration of protonsand

neutronsin an atomic nucleus.

Contents [hide]

1 The Madelung energy ordering rule

2 History

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Order in which orbitals are arranged by increasing

energy according to the Madelung rule. Each diagonal red

arrow corresponds to a different value of n + .

2.1 The Aufbau principle in the old quantum theory

2.2 The n + energy ordering rule

3 See also

4 References

5 Further reading

6 External links

The Madelung energy ordering rule [edit]

The order in which these orbitals are

filled is given by the n + rule(also

known as the Madelung rule(after

Erwin Madelung), or the Klechkowski

rule(after Vsevolod Klechkovskyin

some, mostly Frenchand Russian-

speaking, countries), or the diagonal

rule.[1]Orbitals with a lower n + value

are filled before those with higher n +

values. In this context, nrepresents the

principal quantum numberandtheazimuthal quantum number; the values

= 0, 1, 2, 3 correspond to the s,p, d, and

flabels, respectively.

The rule is based on the total number of

nodes in the atomic orbital, n + , which is

related to the energy.[2]In the case of

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equal n + values, the orbital with a lower nvalue is filled first. The fact that most of the ground

state configurations of neutral atoms fill orbitals following this n + , npattern was obtained

experimentally, by reference to the spectroscopic characteristics of the elements. [3]

The Madelung energy ordering rule applies only to neutral atoms in their ground state, and even

in that case, there are several elements for which it predicts configurations that differ from those

determined experimentally.[4]

Copper, chromium, and palladiumare common examples of thisproperty. According to the Madelung rule, the 4s orbital (n + = 4 + 0 = 4) is occupied before the

3d orbital (n + = 3 + 2 = 5). The rule then predicts the configuration of 29Cu to be 1s22s22p63s2

3p64s23d9, abbreviated [Ar]4s23d9where [Ar] denotes the configuration of Ar (the preceding

noble gas). However the experimental electronic configuration of the copper atom is [Ar]4s13d10.

By filling the 3d orbital, copper can be in a lower energy state. Similarly, chromium takes the

electronic configuration of [Ar]4s13d5instead of [Ar]4s23d4. In this case, chromium has a half-full

3d shell. For palladium, the Madelung rule predicts [Kr]5s24d8, but the experimental configuration

[Kr]4d10differs in the placement of two electrons.

History [edit]

The Aufbau principle in the old quantum theory [edit]

The principle takes its name from the German,Aufbauprinzip, "building-up principle", rather than being

named for a scientist. In fact, it was formulated by Niels

Bohrand Wolfgang Pauliin the early 1920s, and states

that:

The orbitals of lower energy are filled in
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In the old quantum theory, orbits

with low angular momentum (s- andp-

orbitals) get closer to the nucleus.

first with the electrons and only then the

orbitals of high energy are filled.

This was an early application of quantum mechanicsto the

properties of electrons, and explained chemical properties

in physicalterms. Each added electron is subject to the electric field created by the positive charge

of the atomic nucleusandthe negative charge of other electrons that are bound to the nucleus.Although in hydrogen there is no energy difference between orbitals with the same principal

quantum number n, this is not true for the outer electrons of other atoms.

In the old quantum theoryprior to quantum mechanics, electrons were supposed to occupy

classical elliptical orbits. The orbits with the highest angular momentum are 'circular orbits' outside

the inner electrons, but orbits with low angular momentum (s- andp-orbitals) have high orbital

eccentricity, so that they get closer to the nucleus and feel on average a less strongly screened

nuclear charge.

The n + energy ordering rule [edit]

A periodic table in which each row corresponds to one value of n + was suggested by Charles

Janetin 1927. In 1936, the German physicist Erwin Madelungproposed his empirical rules for the

order of filling atomic subshells, based on knowledge of atomic ground states determined by the

analysis of atomic spectra, and most English-language sources therefore refer to the Madelungrule. Madelung may have been aware of this pattern as early as 1926. [5]In 1962 the Russian

agricultural chemist V.M. Klechkowskiproposed the first theoretical explanation for the importance

of the sum n + , based on the statistical ThomasFermi modelof the atom.[6]Many French- and

Russian-language sources therefore refer to the Klechkowski rule.
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See also [edit]

Electron configuration

Valence electrons

Wiswesser's rule

References [edit]1. ^http://www.wyzant.com/resources/lessons/science/chemistry/electron_configuration

2. ^Weinhold, Frank; Landis, Clark R. (2005). Valency and bonding: A Natural Bond Orbital Donor-

Acceptor Perspective. Cambridge: Cambridge University Press. pp. 71516. ISBN0-521-83128-8.

3. ^Scerri, Eric R. (1998). "How Good is the Quantum Mechanical Explanation of the Periodic

System?" .J. Chem. Ed.75(11): 138485. Bibcode:1998JChEd..75.1384S .

doi:10.1021/ed075p1384 .

4. ^Meek, Terry L.; Allen, Leland C. (2002). "Configuration irregularities: deviations from the Madelung

rule and inversion of orbital energy levels" . Chem. Phys. Lett.362(56): 36264.

Bibcode:2002CPL...362..362M . doi:10.1016/S0009-2614(02)00919-3 .

5. ^Goudsmit, S. A.; Richards, Paul I. (1964). "The Order of Electron Shells in Ionized Atoms" .

Proc. Natl. Acad. Sci.51(4): 664671 (with correction on p 906). Bibcode:1964PNAS...51..664G .

doi:10.1073/pnas.51.4.664 .

6. ^Wong, D. Pan (1979). "Theoretical justification of Madelung's rule" .J. Chem. Ed.56(11): 714

18. Bibcode:1979JChEd..56..714W . doi:10.1021/ed056p714 .

Further reading [edit]

Image: Understanding order of shell filling

Boeyens, J. C. A.: Chemistry from First Principles. Berlin: Springer Science 2008, ISBN 978-1-

4020-8546-8
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Ostrovsky, V.N. (2005). "On Recent Discussion Concerning Quantum Justification of the

Periodic Table of the Elements" . Foundations of Chemistry7(3): 23539.

doi:10.1007/s10698-005-2141-y . Abstract .

Kitagawara, Y.; Barut, A.O. (1984). "On the dynamical symmetry of the periodic table. II.

Modified Demkov-Ostrovsky atomic model" .J. Phys. B: At. Mol. Phys.17(21): 425159.

Bibcode:1984JPhB...17.4251K . doi:10.1088/0022-3700/17/21/013 .

Scerri, E.R. (2013). "The Trouble with the Aufbau Principle" . Education in Chemistry

(November): 2426.

Vanquickenborne, L. G. (1994). "Transition Metals and the Aufbau Principle" .Journal of

Chemical Education71(6): 469471. Bibcode:1994JChEd..71..469V .

doi:10.1021/ed071p469 .

External links [edit]Electron Configurations, the Aufbau Principle, Degenerate Orbitals, and Hund's Rule

Categories: Atomic physics
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