Aufbau principle
Overview
 
The Aufbau principle is used to determine the electron configuration
Electron configuration
In atomic physics and quantum chemistry, electron configuration is the arrangement of electrons of an atom, a molecule, or other physical structure...

 of an atom
Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...

, molecule
Molecule
A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...

 or ion
Ion
An ion is an atom or molecule in which the total number of electrons is not equal to the total number of protons, giving it a net positive or negative electrical charge. The name was given by physicist Michael Faraday for the substances that allow a current to pass between electrodes in a...

. 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 orbital
Electron orbital
An electron orbital may refer to:* An atomic orbital, describing the behaviour of an electron in an atom* A molecular orbital, describing the behaviour of an electron in a molecule- See also :...

s) with respect to the nucleus and those electrons already there.

According to the principle, electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

s fill orbitals starting at the lowest available (possible) energy states before filling higher states (e.g.
Encyclopedia
The Aufbau principle is used to determine the electron configuration
Electron configuration
In atomic physics and quantum chemistry, electron configuration is the arrangement of electrons of an atom, a molecule, or other physical structure...

 of an atom
Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...

, molecule
Molecule
A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...

 or ion
Ion
An ion is an atom or molecule in which the total number of electrons is not equal to the total number of protons, giving it a net positive or negative electrical charge. The name was given by physicist Michael Faraday for the substances that allow a current to pass between electrodes in a...

. 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 orbital
Electron orbital
An electron orbital may refer to:* An atomic orbital, describing the behaviour of an electron in an atom* A molecular orbital, describing the behaviour of an electron in a molecule- See also :...

s) with respect to the nucleus and those electrons already there.

According to the principle, electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

s fill orbitals starting at the lowest available (possible) energy states before filling higher states (e.g. 1s before 2s).
The number of electrons that can occupy each orbital is limited by the Pauli exclusion principle
Pauli exclusion principle
The Pauli exclusion principle is the quantum mechanical principle that no two identical fermions may occupy the same quantum state simultaneously. A more rigorous statement is that the total wave function for two identical fermions is anti-symmetric with respect to exchange of the particles...

. If multiple orbitals of the same energy are available, Hund's rule states that unoccupied orbitals will be filled before occupied orbitals are reused (by electrons having different spin
Spin (physics)
In quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...

s).

A version of the Aufbau principle can also be used to predict the configuration of proton
Proton
The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....

s and neutron
Neutron
The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...

s in an atomic nucleus
Atomic nucleus
The nucleus is the very dense region consisting of protons and neutrons at the center of an atom. It was discovered in 1911, as a result of Ernest Rutherford's interpretation of the famous 1909 Rutherford experiment performed by Hans Geiger and Ernest Marsden, under the direction of Rutherford. The...

.

The Madelung energy ordering rule

The order in which these orbitals are filled is given by the n + l rule (also known as the Madelung rule (after Erwin Madelung
Erwin Madelung
Erwin Madelung was a German physicist.He was born in 1881 in Bonn. His father was the surgeon Otto Wilhelm Madelung. He earned a doctorate in 1905 from the University of Göttingen, specializing in crystal structure, and eventually became a professor...

), or the Klechkowski rule (after Vsevolod Klechkovsky
Vsevolod Klechkovsky
Vsevolod Mavrikievich Klechkovsky, also transliterated as Klechkovskii and Klechkowski was a Soviet-era agricultural chemist known for his work with radioisotopes...

 in some, mostly French
French language
French is a Romance language spoken as a first language in France, the Romandy region in Switzerland, Wallonia and Brussels in Belgium, Monaco, the regions of Quebec and Acadia in Canada, and by various communities elsewhere. Second-language speakers of French are distributed throughout many parts...

- and Russian
Russian language
Russian is a Slavic language used primarily in Russia, Belarus, Uzbekistan, Kazakhstan, Tajikistan and Kyrgyzstan. It is an unofficial but widely spoken language in Ukraine, Moldova, Latvia, Turkmenistan and Estonia and, to a lesser extent, the other countries that were once constituent republics...

-speaking, countries), where orbitals with a lower n + l value are filled before those with higher n + l values. In this context, n represents the principal quantum number
Principal quantum number
In atomic physics, the principal quantum symbolized as n is the firstof a set of quantum numbers of an atomic orbital. The principal quantum number can only have positive integer values...

 and l the azimuthal quantum number
Azimuthal quantum number
The azimuthal quantum number is a quantum number for an atomic orbital that determines its orbital angular momentum and describes the shape of the orbital...

; the values l = 0, 1, 2, 3 correspond to the s, p, d, and f labels, respectively.

The rule is based on the total number of nodes in the atomic orbital, n + l, which is related to the energy. In the case of equal n + l values, the orbital with a lower n value is filled first. The fact that most of the ground state configurations of neutral atoms fill orbitals following this n + l, n pattern was obtained experimentally, by reference to the spectroscopic characteristics of the elements.

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. Copper
Copper
Copper is a chemical element with the symbol Cu and atomic number 29. It is a ductile metal with very high thermal and electrical conductivity. Pure copper is soft and malleable; an exposed surface has a reddish-orange tarnish...

 and chromium
Chromium
Chromium is a chemical element which has the symbol Cr and atomic number 24. It is the first element in Group 6. It is a steely-gray, lustrous, hard metal that takes a high polish and has a high melting point. It is also odorless, tasteless, and malleable...

 are common examples of this property. According to the Madelung rule, the 4s orbital (n + l = 4 + 0 = 4) is occupied before the 3d orbital (n + l = 3 + 2 = 5). The rule then predicts the configuration of 29Cu to be 1s22s22p63s2 3p64s23d9, abbreviated [Ar]4s23d9 where [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]4s13d5 instead of [Ar]4s23d4. In this case, chromium has a half-full 3d shell.

The Aufbau principle in the old quantum theory

The principle takes its name from the German
German language
German is a West Germanic language, related to and classified alongside English and Dutch. With an estimated 90 – 98 million native speakers, German is one of the world's major languages and is the most widely-spoken first language in the European Union....

, Aufbauprinzip, "building-up principle", rather than being named for a scientist. In fact, it was formulated by Niels Bohr
Niels Bohr
Niels Henrik David Bohr was a Danish physicist who made foundational contributions to understanding atomic structure and quantum mechanics, for which he received the Nobel Prize in Physics in 1922. Bohr mentored and collaborated with many of the top physicists of the century at his institute in...

 and Wolfgang Pauli
Wolfgang Pauli
Wolfgang Ernst Pauli was an Austrian theoretical physicist and one of the pioneers of quantum physics. In 1945, after being nominated by Albert Einstein, he received the Nobel Prize in Physics for his "decisive contribution through his discovery of a new law of Nature, the exclusion principle or...

 in the early 1920s, and states that:
This was an early application of quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

 to the properties of electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

s, and explained chemical properties in physical
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

 terms. Each added electron is subject to the electric field created by the positive charge of atomic nucleus
Atomic nucleus
The nucleus is the very dense region consisting of protons and neutrons at the center of an atom. It was discovered in 1911, as a result of Ernest Rutherford's interpretation of the famous 1909 Rutherford experiment performed by Hans Geiger and Ernest Marsden, under the direction of Rutherford. The...

 and the 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 theory
Old quantum theory
The old quantum theory was a collection of results from the years 1900–1925 which predate modern quantum mechanics. The theory was never complete or self-consistent, but was a collection of heuristic prescriptions which are now understood to be the first quantum corrections to classical mechanics...

 prior to quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

, electrons were supposed to occupy classical elliptical orbita. The orbits with the highest angular momentum are 'circular orbits' outside the inner electrons, but orbits with low angular momentum (s- and p-orbitals) have high orbital eccentricity
Orbital eccentricity
The orbital eccentricity of an astronomical body is the amount by which its orbit deviates from a perfect circle, where 0 is perfectly circular, and 1.0 is a parabola, and no longer a closed orbit...

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

The n + l energy ordering rule

A periodic table in which each row corresponds to one value of n + l was suggested by Charles Janet
Charles Janet
Charles Janet was a French engineer, company director, inventor and biologist.-Life and work:Janet graduated from the Ecole des Mines and worked for some years in munitions. He then married the daughter of the owner of a manufacturing company and worked for it for the rest of his life, finding...

 in 1927. In 1936, the German physicist Erwin Madelung
Erwin Madelung
Erwin Madelung was a German physicist.He was born in 1881 in Bonn. His father was the surgeon Otto Wilhelm Madelung. He earned a doctorate in 1905 from the University of Göttingen, specializing in crystal structure, and eventually became a professor...

 proposed 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 Madelung rule. In 1962 the Russian agricultural chemist V.M. Klechkowski proposed the first theoretical explanation for the importance of the sum n + l, based on the statistical Thomas-Fermi model
Thomas-Fermi model
The Thomas–Fermi model, named after Llewellyn Thomas and Enrico Fermi, is a quantum mechanical theory for the electronic structure of many-body systems developed semiclassically shortly after the introduction of the Schrödinger equation...

 of the atom. Many French-language sources therefore refer to the Klechkowski rule.

Further reading

  • Image: Understanding order of shell filling
  • Boeyens, J. C. A.
    Jan C. A. Boeyens
    Jan C. A. Boeyens is a South African chemist.Boeyens was educated at the University of Pretoria. 1965 he worked in the National Physics Research Laboratory of South Africa, 1965 in Stanford...

    : Chemistry from First Principles. Berlin: Springer Science 2008, ISBN 978-1-4020-8546-8 Abstract.

External links

The source of this article is wikipedia, the free encyclopedia.  The text of this article is licensed under the GFDL.
 
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