Editing Atomic orbital (section)

== History ==
{{Main|Atomic theory}}

The term ''orbital'' was introduced by [[Robert S. Mulliken]] in 1932 as short for ''one-electron orbital wave function''.<ref>{{cite journal|last=Mulliken | first=Robert S. | title=Electronic Structures of Polyatomic Molecules and Valence. II. General Considerations
|date=July 1932|journal=[[Physical Review]] | volume=41 | issue=1 | pages=49–71|bibcode=1932PhRv...41...49M| doi=10.1103/PhysRev.41.49}}</ref><ref>{{Cite journal |last=Murrell |first=John N |date=2012-09-05 |title=The origins and later developments of molecular orbital theory |url=https://onlinelibrary.wiley.com/doi/10.1002/qua.23293 |journal=International Journal of Quantum Chemistry |language=en |volume=112 |issue=17 |pages=2875–2879 |doi=10.1002/qua.23293 |issn=0020-7608}}</ref> [[Niels Bohr]] explained around 1913 that electrons might revolve around a compact nucleus with definite angular momentum.<ref name="Bohr 1913 476">{{cite journal|last=Bohr|first=Niels
| title=On the Constitution of Atoms and Molecules|journal=Philosophical Magazine|year=1913| volume=26 | issue=1 | page=476|url=http://www.chemteam.info/Chem-History/Bohr/Bohr-1913a.html| bibcode=1914Natur..93..268N| doi=10.1038/093268a0|s2cid=3977652
}}</ref> Bohr's model was an improvement on the 1911 explanations of [[Ernest Rutherford]], that of the electron moving around a nucleus. Japanese physicist [[Hantaro Nagaoka]] published an orbit-based hypothesis for electron behavior as early as 1904.<ref name="Nagaoka 1904 445–455">{{cite journal|first=Hantaro|last=Nagaoka|title=Kinetics of a System of Particles illustrating the Line and the Band Spectrum and the Phenomena of Radioactivity|journal=Philosophical Magazine|date=May 1904|volume=7|pages=445–455|url=http://www.chemteam.info/Chem-History/Nagaoka-1904.html|doi=10.1080/14786440409463141|issue=41|access-date=30 May 2009|archive-url=https://web.archive.org/web/20171127144221/http://www.chemteam.info/Chem-History/Nagaoka-1904.html|archive-date=27 November 2017|url-status=dead}}</ref> These theories were each built upon new observations starting with simple understanding and becoming more correct and complex.  Explaining the behavior of these electron "orbits" was one of the driving forces behind the development of [[quantum mechanics]].<ref>{{cite book | first=Bill | last=Bryson | year=2003 | title=A Short History of Nearly Everything | pages=[https://archive.org/details/shorthistoryofne00brys/page/141 141]–143 | publisher=Broadway Books | isbn=978-0-7679-0818-4 | url=https://archive.org/details/shorthistoryofne00brys | url-access=registration }}</ref>

=== Early models ===
With [[J. J. Thomson]]'s discovery of the electron in 1897,<ref name="referenceC">{{cite journal|first= J. J. |last=Thomson |year=1897|title=Cathode rays|journal=Philosophical Magazine|volume= 44|page=293|doi= 10.1080/14786449708621070|issue= 269|url=https://zenodo.org/record/1431235 }}</ref> it became clear that atoms were not the [[Elementary particle|smallest building blocks of nature]], but were rather composite particles. The newly discovered structure within atoms tempted many to imagine how the atom's constituent parts might interact with each other. Thomson theorized that multiple electrons revolve in orbit-like rings within a positively charged jelly-like substance,<ref>{{cite journal|first=J. J.|last= Thomson |title=On the Structure of the Atom: an Investigation of the Stability and Periods of Oscillation of a number of Corpuscles arranged at equal intervals around the Circumference of a Circle; with Application of the Results to the Theory of Atomic Structure |url=http://www.chemteam.info/Chem-History/Thomson-Structure-Atom.html | doi = 10.1080/14786440409463107 |journal=[[Philosophical Magazine]] |series=Series 6 |volume=7 |issue=39 |pages=237–265 |format=extract of paper|year=1904}}</ref> and between the electron's discovery and 1909, this "[[plum pudding model]]" was the most widely accepted explanation of atomic structure.

Shortly after Thomson's discovery, [[Hantaro Nagaoka]] predicted a different model for electronic structure.<ref name="Nagaoka 1904 445–455" /> Unlike the plum pudding model, the positive charge in Nagaoka's "Saturnian Model" was concentrated into a central core, pulling the electrons into circular orbits reminiscent of Saturn's rings. Few people took notice of Nagaoka's work at the time,<ref>{{cite book|last=Rhodes| first = Richard| title = The Making of the Atomic Bomb| publisher = Simon & Schuster| year = 1995| pages = 50–51| url = https://books.google.com/books?id=aSgFMMNQ6G4C&q=making+of+the+atomic+bomb| isbn = 978-0-684-81378-3}}</ref> and Nagaoka himself recognized a fundamental defect in the theory even at its conception, namely that a classical charged object cannot sustain orbital motion because it is accelerating and therefore loses energy due to electromagnetic radiation.<ref>{{cite journal|first=Hantaro|last=Nagaoka|title=Kinetics of a System of Particles illustrating the Line and the Band Spectrum and the Phenomena of Radioactivity|journal=Philosophical Magazine|date=May 1904|volume=7|issue=41|page=446|url=http://www.chemteam.info/Chem-History/Nagaoka-1904.html|doi=10.1080/14786440409463141|access-date=30 May 2009|archive-url=https://web.archive.org/web/20171127144221/http://www.chemteam.info/Chem-History/Nagaoka-1904.html|archive-date=27 November 2017|url-status=dead}}</ref> Nevertheless, the [[Saturnian model]] turned out to have more in common with modern theory than any of its contemporaries.

=== Bohr atom ===
In 1909, [[Ernest Rutherford]] discovered that the bulk of the atomic mass was tightly condensed into a nucleus, which was also found to be positively charged. It became clear from his analysis in 1911 that the plum pudding model could not explain atomic structure. In 1913, Rutherford's post-doctoral student, [[Niels Bohr]], proposed a new model of the atom, wherein electrons orbited the nucleus with classical periods, but were permitted to have only discrete values of angular momentum, quantized in units [[Planck constant|ħ]].<ref name="Bohr 1913 476" /> This constraint automatically allowed only certain electron energies. The [[Bohr model]] of the atom fixed the problem of energy loss from radiation from a ground state (by declaring that there was no state below this), and more importantly explained the origin of spectral lines.

[[File:Bohr atom model.svg|thumb|The [[Bohr model|Rutherford–Bohr model]] of the hydrogen atom]]
After Bohr's use of [[Albert Einstein|Einstein]]'s explanation of the [[photoelectric effect]] to relate energy levels in atoms with the wavelength of emitted light, the connection between the structure of electrons in atoms and the [[Emission spectra|emission]] and [[absorption spectra]] of atoms became an increasingly useful tool in the understanding of electrons in atoms. The most prominent feature of emission and absorption spectra (known experimentally since the middle of the 19th century), was that these atomic spectra contained discrete lines. The significance of the Bohr model was that it related the lines in emission and absorption spectra to the energy differences between the orbits that electrons could take around an atom. This was, however, ''not'' achieved by Bohr through giving the electrons some kind of wave-like properties, since the idea that electrons could behave as [[matter waves]] was not suggested until eleven years later. Still, the Bohr model's use of quantized angular momenta and therefore quantized energy levels was a significant step toward the understanding of electrons in atoms, and also a significant step towards the development of [[quantum mechanics]] in suggesting that quantized restraints must account for all discontinuous energy levels and spectra in atoms.

With [[Louis de Broglie|de Broglie]]'s suggestion of the existence of electron matter waves in 1924, and for a short time before the full 1926 [[Schrödinger equation]] treatment of [[hydrogen-like atom]]s, a Bohr electron "wavelength" could be seen to be a function of its momentum; so a Bohr orbiting electron was seen to orbit in a circle at a multiple of its half-wavelength. The Bohr model for a short time could be seen as a classical model with an additional constraint provided by the 'wavelength' argument. However, this period was immediately superseded by the full three-dimensional wave mechanics of 1926. In our current understanding of physics, the Bohr model is called a semi-classical model because of its quantization of angular momentum, not primarily because of its relationship with electron wavelength, which appeared in hindsight a dozen years after the Bohr model was proposed.

The Bohr model was able to explain the emission and absorption spectra of [[hydrogen]]. The energies of electrons in the ''n''&nbsp;=&nbsp;1, 2, 3, etc. states in the Bohr model match those of current physics. However, this did not explain similarities between different atoms, as expressed by the periodic table, such as the fact that [[helium]] (two electrons), neon (10 electrons), and [[argon]] (18 electrons) exhibit similar chemical inertness. Modern [[quantum mechanics]] explains this in terms of [[electron shell]]s and subshells which can each hold a number of electrons determined by the [[Pauli exclusion principle]]. Thus the ''n''&nbsp;=&nbsp;1 state can hold one or two electrons, while the ''n'' = 2 state can hold up to eight electrons in 2s and 2p subshells. In helium, all ''n''&nbsp;=&nbsp;1 states are fully occupied; the same is true for ''n''&nbsp;=&nbsp;1 and ''n''&nbsp;=&nbsp;2 in neon. In argon, the 3s and 3p subshells are similarly fully occupied by eight electrons; quantum mechanics also allows a 3d subshell but this is at higher energy than the 3s and 3p in argon (contrary to the situation for hydrogen) and remains empty.

=== Modern conceptions and connections to the Heisenberg uncertainty principle ===
Immediately after [[Werner Heisenberg|Heisenberg]] discovered his [[uncertainty principle]],<ref>{{cite journal|last=Heisenberg| first=W.|title=Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik|journal=[[Zeitschrift für Physik A]] |date=March 1927| volume=43 | pages=172–198|doi=10.1007/BF01397280|bibcode = 1927ZPhy...43..172H| issue=3–4| s2cid=122763326}}</ref> [[Niels Bohr|Bohr]] noted that the existence of any sort of [[wave packet]] implies uncertainty in the wave frequency and wavelength, since a spread of frequencies is needed to create the packet itself.<ref>{{cite journal|last=Bohr | first=Niels| title=The Quantum Postulate and the Recent Development of Atomic Theory|journal=Nature |date=April 1928| volume=121 | pages=580–590|doi=10.1038/121580a0 |bibcode = 1928Natur.121..580B| issue=3050 |doi-access=free}}</ref> In quantum mechanics, where all particle momenta are associated with waves, it is the formation of such a wave packet which localizes the wave, and thus the particle, in space. In states where a quantum mechanical particle is bound, it must be localized as a wave packet, and the existence of the packet and its minimum size implies a spread and minimal value in particle wavelength, and thus also momentum and energy. In quantum mechanics, as a particle is localized to a smaller region in space, the associated compressed wave packet requires a larger and larger range of momenta, and thus larger kinetic energy. Thus the binding energy to contain or trap a particle in a smaller region of space increases without bound as the region of space grows smaller. Particles cannot be restricted to a geometric point in space, since this would require infinite particle momentum.

In chemistry, [[Erwin Schrödinger]], [[Linus Pauling]], Mulliken and others noted that the consequence of Heisenberg's relation was that the electron, as a wave packet, could not be considered to have an exact location in its orbital. [[Max Born]] suggested that the electron's position needed to be described by a [[probability distribution]] which was connected with finding the electron at some point in the wave-function which described its associated wave packet. The new quantum mechanics did not give exact results, but only the probabilities for the occurrence of a variety of possible such results. Heisenberg held that the path of a moving particle has no meaning if we cannot observe it, as we cannot with electrons in an atom.

In the quantum picture of Heisenberg, Schrödinger and others, the Bohr atom number&nbsp;''n'' for each orbital became known as an ''n-sphere''{{citation needed|date=January 2013}} in a three-dimensional atom and was pictured as the most probable energy of the probability cloud of the electron's wave packet which surrounded the atom.