Editing Atomic orbital (section)

== Electron placement and the periodic table ==
[[File:Electron orbitals.svg|right|thumb|upright=1.6|Electron atomic and [[molecular orbital|molecular]] orbitals. The chart of orbitals ('''left''') is arranged by increasing energy (see [[Madelung rule]]). ''Atomic orbits are functions of three variables (two angles, and the distance&nbsp;{{mvar|r}} from the nucleus). These images are faithful to the angular component of the orbital, but not entirely representative of the orbital as a whole.'']]

[[File:Atomic orbitals and periodic table construction.ogv|thumb|Atomic orbitals and periodic table construction]]

{{Main|Electron configuration|Electron shell}}

Several rules govern the placement of electrons in orbitals (''[[electron configuration]]''). The first dictates that no two electrons in an atom may have the same set of values of quantum numbers (this is the [[Pauli exclusion principle]]). These quantum numbers include the three that define orbitals, as well as the [[spin magnetic quantum number]]  {{mvar|m<sub>s</sub>}}. Thus, two electrons may occupy a single  orbital, so long as they have different values of {{mvar|m<sub>s</sub>}}. Because {{mvar|m<sub>s</sub>}} takes one of only two values ({{sfrac|1|2}} or −{{sfrac|1|2}}), at most two electrons can occupy each orbital.

Additionally, an electron always tends to fall to the lowest possible energy state. It is possible for it to occupy any orbital so long as it does not violate the Pauli exclusion principle, but if lower-energy orbitals are available, this condition is unstable. The electron will eventually lose energy (by releasing a [[photon]]) and drop into the lower orbital. Thus, electrons fill orbitals in the order specified by the energy sequence given above.

This behavior is responsible for the structure of the [[periodic table]]. The table may be divided into several rows (called 'periods'), numbered starting with 1 at the top. The presently known elements occupy seven periods. If a certain period has number ''i'', it consists of elements whose outermost electrons fall in the ''i''th shell. [[Niels Bohr]] was the first to propose (1923) that the [[Periodic table|periodicity]] in the properties of the elements might be explained by the periodic filling of the electron energy levels, resulting in the electronic structure of the atom.<ref name="Bohr">{{cite journal | last = Bohr | first = Niels | author-link = Niels Bohr | title = Über die Anwendung der Quantumtheorie auf den Atombau. I | journal = [[Zeitschrift für Physik]] | year = 1923 | volume = 13 | issue = 1 | page = 117|bibcode = 1923ZPhy...13..117B |doi = 10.1007/BF01328209 | s2cid = 123582460 }}</ref>

The periodic table may also be divided into several numbered rectangular '[[Periodic table block|blocks]]'. The elements belonging to a given block have this common feature: their highest-energy electrons all belong to the same {{mvar|ℓ}}-state (but the {{mvar|n}} associated with that {{mvar|ℓ}}-state depends upon the period). For instance, the leftmost two columns constitute the 's-block'. The outermost electrons of [[Lithium|Li]] and [[Beryllium|Be]] respectively belong to the 2s&nbsp;subshell, and those of [[sodium|Na]] and [[magnesium|Mg]] to the 3s&nbsp;subshell.

The following is the order for filling the "subshell" orbitals, which also gives the order of the "blocks" in the periodic table:

:'''1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p'''

The "periodic" nature of the filling of orbitals, as well as emergence of the '''s''', '''p''', '''d''', and '''f''' "blocks", is more obvious if this order of filling is given in matrix form, with increasing principal quantum numbers starting the new rows ("periods") in the matrix. Then, each subshell (composed of the first two quantum numbers) is repeated as many times as required for each pair of electrons it may contain. The result is a compressed periodic table, with each entry representing two successive elements:

{| class="wikitable"
|1s|| || || || || || || || || || || || || || ||
|-
|2s|| || || || || || || || || || || || ||2p||2p||2p
|-
|3s|| || || || || || || || || || || || ||3p||3p||3p
|-
|4s|| || || || || || || ||3d||3d||3d||3d||3d||4p||4p||4p
|-
|5s|| || || || || || || ||4d||4d||4d||4d||4d||5p||5p||5p
|-
|6s||4f||4f||4f||4f||4f||4f||4f||5d||5d||5d||5d||5d||6p||6p||6p
|-
|7s||5f||5f||5f||5f||5f||5f||5f||6d||6d||6d||6d||6d||7p||7p||7p
|}

Although this is the general order of orbital filling according to the Madelung rule, there are exceptions, and the actual electronic energies of each element are also dependent upon additional details of the atoms (see {{slink|Electron configuration#Atoms: Aufbau principle and Madelung rule}}).

The number of electrons in an electrically neutral atom increases with the [[atomic number]]. The electrons in the outermost shell, or ''[[valence electron]]s'', tend to be responsible for an element's chemical behavior. Elements that contain the same number of valence electrons can be grouped together and display similar chemical properties.

=== Relativistic effects ===
{{Main|Relativistic quantum chemistry}}
{{See also|Extended periodic table}}

For elements with high atomic number {{mvar|Z}}, the effects of relativity become more pronounced, and especially so for s&nbsp;electrons, which move at relativistic velocities as they penetrate the screening electrons near the core of high-{{mvar|Z}} atoms. This relativistic increase in momentum for high speed electrons causes a corresponding decrease in wavelength and contraction of 6s orbitals relative to 5d orbitals (by comparison to corresponding s and d electrons in lighter elements in the same column of the periodic table); this results in 6s valence electrons becoming lowered in energy.

Examples of significant physical outcomes of this effect include the lowered melting temperature of [[mercury (element)|mercury]] (which results from 6s electrons not being available for metal bonding) and the golden color of gold and [[caesium]].<ref>{{cite web|url=http://www.chem1.com/acad/webtut/atomic/qprimer/#Q26|title= Primer on Quantum Theory of the Atom|first=Stephen |last=Lower}}</ref>

In the [[Bohr model]], an {{math|1=''n'' = 1}}&nbsp;electron has a velocity given by <math>v = Z \alpha c</math>, where {{mvar|Z}} is the atomic number, <math>\alpha</math> is the [[fine-structure constant]], and {{math|''c''}} is the speed of light. In non-relativistic quantum mechanics, therefore, any atom with an atomic number greater than 137 would require its 1s electrons to be traveling faster than the speed of light. Even in the [[Dirac equation]], which accounts for relativistic effects, the wave function of the electron for atoms with <math>Z > 137</math> is oscillatory and [[unbounded function|unbounded]]. The significance of element 137, also known as [[untriseptium]], was first pointed out by the physicist [[Richard Feynman]]. Element 137 is sometimes informally called [[feynmanium]] (symbol Fy).<ref>{{cite journal|last1=Poliakoff|first1=Martyn|last2=Tang|first2=Samantha|title=The periodic table: icon and inspiration|journal=Philosophical Transactions of the Royal Society A|date=9 February 2015|volume=373|issue=2037|page=20140211|doi=10.1098/rsta.2014.0211|pmid=25666072|bibcode = 2015RSPTA.37340211P |doi-access=free}}</ref> However, Feynman's approximation fails to predict the exact critical value of&nbsp;{{mvar|Z}} due to the non-point-charge nature of the nucleus and very small orbital radius of inner electrons, resulting in a potential seen by inner electrons which is effectively less than {{mvar|Z}}. The critical {{mvar|Z}}&nbsp;value, which makes the atom unstable with regard to high-field breakdown of the vacuum and production of electron-positron pairs, does not occur until {{mvar|Z}} is about 173. These conditions are not seen except transiently in collisions of very heavy nuclei such as lead or uranium in accelerators, where such electron-positron production from these effects has been claimed to be observed.
	
There are no nodes in relativistic orbital densities, although individual components of the wave function will have nodes.<ref>{{cite journal|doi=10.1021/ed046p678|title=Contour diagrams for relativistic orbitals|year=1969|last1=Szabo|first1=Attila|journal=Journal of Chemical Education|volume=46|issue=10|pages=678|bibcode = 1969JChEd..46..678S }}</ref>

=== pp hybridization (conjectured) ===
In late [[Extended periodic table|period 8 elements]], a [[orbital hybridisation|hybrid]] of 8p<sub>3/2</sub> and 9p<sub>1/2</sub> is expected to exist,<ref name="BFricke">{{Cite book |last1=Fricke |first1=Burkhard |year=1975 |chapter=Superheavy elements: a prediction of their chemical and physical properties |series=Recent Impact of Physics on Inorganic Chemistry |volume=21 |pages=89–144 |doi=10.1007/BFb0116498 |chapter-url=https://archive.org/details/recentimpactofph0000unse/page/89 |access-date=4 October 2013 |title=Structure and Bonding |isbn=978-3-540-07109-9 }}</ref> where "3/2" and "1/2" refer to the [[total angular momentum quantum number]]. This "pp" hybrid may be responsible for the [[p-block]] of the period due to properties similar to p&nbsp;subshells in ordinary [[valence shell]]s. Energy levels of 8p<sub>3/2</sub> and 9p<sub>1/2</sub> come close due to relativistic [[spin–orbit interaction|spin–orbit effects]]; the 9s subshell should also participate, as these elements are expected to be analogous to the respective 5p elements [[indium]] through [[xenon]].