Editing Periodic table (section)

=== Electron shells ===

The Danish physicist [[Niels Bohr]] applied [[Max Planck]]'s idea of quantization to the atom. He concluded that the energy levels of electrons were quantised: only a discrete set of stable energy states were allowed. Bohr then attempted to understand periodicity through electron configurations, surmising in 1913 that the inner electrons should be responsible for the chemical properties of the element.<ref>See Bohr table from 1913 paper below.</ref><ref>Helge Kragh, Aarhus, Lars Vegard, Atomic Structure, and the Periodic System, Bull. Hist. Chem., VOLUME 37, Number 1 (2012), p.43.</ref> In 1913, he produced the first electronic periodic table based on a quantum atom.<ref name="Scerri208">Scerri, pp. 208–218</ref>

Bohr called his electron shells "rings" in 1913: atomic orbitals within shells did not exist at the time of his planetary model. Bohr explains in Part 3 of his famous 1913 paper that the maximum electrons in a shell is eight, writing, "We see, further, that a ring of {{Var|n}} electrons cannot rotate in a single ring round a nucleus of charge ne unless {{Var|n}} < 8." For smaller atoms, the electron shells would be filled as follows: "rings of electrons will only join if they contain equal numbers of electrons; and that accordingly the numbers of electrons on inner rings will only be 2, 4, 8." However, in larger atoms the innermost shell would contain eight electrons: "on the other hand, the periodic system of the elements strongly suggests that already in neon {{Var|N}} = 10 an inner ring of eight electrons will occur." His proposed electron configurations for the atoms (shown to the right) mostly do not accord with those now known.<ref>Niels Bohr, "On the Constitution of Atoms and Molecules, Part III, Systems containing several nuclei" Philosophical Magazine 26:857--875 (1913)</ref><ref>{{Cite journal|last=Kragh|first=Helge|date=1 January 1979|title=Niels Bohr's Second Atomic Theory|url=https://online.ucpress.edu/hsns/article/doi/10.2307/27757389/47571/Niels-Bohr-s-Second-Atomic-Theory|journal=Historical Studies in the Physical Sciences|language=en|volume=10|pages=123–186|doi=10.2307/27757389|jstor=27757389 |issn=0073-2672|url-access=subscription}}</ref> They were improved further after the work of [[Arnold Sommerfeld]] and [[Edmund Stoner]] discovered more quantum numbers.<ref name=7elements/>

{| class="wikitable" style="float:right; font-size:95%; margin:0.5em;"
|+ Bohr's electron configurations for light elements
|-
! Element !! Electrons per shell
|-
| 4 || 2,2
|-
| 6 || 2,4
|-
| 7 || 4,3
|-
| 8 || 4,2,2
|-
| 9 || 4,4,1
|-
| 10 || 8,2
|-
| 11 || 8,2,1
|-
| 16 || 8,4,2,2
|-
| 18 || 8,8,2
|}

The first one to systematically expand and correct the chemical potentials of Bohr's atomic theory was [[Walther Kossel]] in 1914 and in 1916. Kossel explained that in the periodic table new elements would be created as electrons were added to the outer shell. In Kossel's paper, he writes: <blockquote>This leads to the conclusion that the electrons, which are added further, should be put into concentric rings or shells, on each of which ... only a certain number of electrons—namely, eight in our case—should be arranged. As soon as one ring or shell is completed, a new one has to be started for the next element; the number of electrons, which are most easily accessible, and lie at the outermost periphery, increases again from element to element and, therefore, in the formation of each new shell the chemical periodicity is repeated.<ref>W. Kossel, "Über Molekülbildung als Folge des Atom- baues", Ann. Phys., 1916, 49, 229–362 (237).</ref><ref>Translated in Helge Kragh, Aarhus, Lars Vegard, Atomic Structure, and the Periodic System, Bull. Hist. Chem., VOLUME 37, Number 1 (2012), p.43.</ref></blockquote>

In a 1919 paper, [[Irving Langmuir]] postulated the existence of "cells" which we now call orbitals, which could each only contain eight electrons each, and these were arranged in "equidistant layers" which we now call shells. He made an exception for the first shell to only contain two electrons.<ref>{{Cite journal |last=Langmuir |first=Irving |author-link=Irving Langmuir |date=June 1919 |title=The Arrangement of Electrons in Atoms and Molecules |url=https://pubs.acs.org/doi/abs/10.1021/ja02227a002 |url-status=live |journal=[[Journal of the American Chemical Society]] |language=en |volume=41 |issue=6 |pages=868–934 |doi=10.1021/ja02227a002 |bibcode=1919JAChS..41..868L |issn=0002-7863 |archive-url=https://web.archive.org/web/20210126003324/https://zenodo.org/record/1429026 |archive-date=26 January 2021 |access-date=22 October 2021|url-access=subscription }}</ref> The chemist [[Charles Rugeley Bury]] suggested in 1921 that eight and eighteen electrons in a shell form stable configurations. Bury proposed that the electron configurations in transitional elements depended upon the valence electrons in their outer shell.<ref name="Bury">{{Cite journal |last=Bury |first=Charles R. |author-link=Charles Rugeley Bury |date=July 1921 |title=Langmuir's Theory of the Arrangement of Electrons in Atoms and Molecules |url=https://pubs.acs.org/doi/abs/10.1021/ja01440a023 |url-status=live |journal=[[Journal of the American Chemical Society]] |language=en |volume=43 |issue=7 |pages=1602–1609 |doi=10.1021/ja01440a023 |bibcode=1921JAChS..43.1602B |issn=0002-7863 |archive-url=https://web.archive.org/web/20211030145903/https://zenodo.org/record/1428812 |archive-date=30 October 2021 |access-date=22 October 2021|url-access=subscription }}</ref> He introduced the word ''transition'' to describe the elements now known as [[transition metal]]s or transition elements.<ref name="Jensen2003">{{cite journal|last=Jensen|first=William B.|year=2003|title=The Place of Zinc, Cadmium, and Mercury in the Periodic Table|url=https://www.uv.es/~borrasj/ingenieria_web/temas/tema_1/lecturas_comp/p952.pdf|journal=Journal of Chemical Education|volume=80|issue=8|pages=952–961|bibcode=2003JChEd..80..952J|doi=10.1021/ed080p952|quote=The first use of the term "transition" in its modern electronic sense appears to be due to the British chemist C. R.Bury, who first used the term in his 1921 paper on the electronic structure of atoms and the periodic table|access-date=18 September 2021|archive-date=19 April 2012|archive-url=https://web.archive.org/web/20120419082806/https://www.uv.es/~borrasj/ingenieria_web/temas/tema_1/lecturas_comp/p952.pdf|url-status=live}}</ref> Bohr's theory was vindicated by the discovery of element 72: [[Georges Urbain]] claimed to have discovered it as the [[rare earth element]] ''celtium'', but Bury and Bohr had predicted that element 72 could not be a rare earth element and had to be a homologue of [[zirconium]]. [[Dirk Coster]] and [[Georg von Hevesy]] searched for the element in zirconium ores and found element 72, which they named [[hafnium]] after Bohr's hometown of [[Copenhagen]] (''Hafnia'' in Latin).<ref name="CosterHevesy1923">{{cite journal|journal = Nature|volume = 111|page=79|date=1923|doi = 10.1038/111079a0|title = On the Missing Element of Atomic Number 72|first = D.|last = Coster|author2=Hevesy, G.|issue=2777|bibcode=1923Natur.111...79C|doi-access = free}}</ref><ref>{{cite journal|title = Hafnium|url = http://www.jce.divched.org/Journal/Issues/1982/Mar/jceSubscriber/JCE1982p0242.pdf|journal = Journal of Chemical Education|last = Fernelius|first = W. C.|date = 1982|page = 242|doi = 10.1021/ed059p242|volume = 59|issue = 3|bibcode = 1982JChEd..59..242F|access-date = 3 September 2009|archive-date = 15 March 2020|archive-url = https://web.archive.org/web/20200315031648/http://www.jce.divched.org/Journal/Issues/1982/Mar/jceSubscriber/JCE1982p0242.pdf|url-status = dead}}</ref> Urbain's celtium proved to be simply purified [[lutetium]] (element 71).<ref>{{cite journal |last1=Burdette |first1=Shawn C. |last2=Thornton |first2=Brett F. |date=2018 |title=Hafnium the lutécium I used to be |url=https://www.nature.com/articles/s41557-018-0140-6 |journal=Nature Chemistry |volume=10 |issue= 10|pages=1074 |doi=10.1038/s41557-018-0140-6 |pmid=30237529 |bibcode=2018NatCh..10.1074B |access-date=8 February 2024}}</ref> Hafnium and rhenium thus became the last stable elements to be discovered.<ref name=7elements/>

Prompted by Bohr, [[Wolfgang Pauli]] took up the problem of electron configurations in 1923. Pauli extended Bohr's scheme to use four [[quantum number]]s, and formulated his [[Pauli exclusion principle|exclusion principle]] which stated that no two electrons could have the same four quantum numbers. This explained the lengths of the periods in the periodic table (2, 8, 18, and 32), which corresponded to the number of electrons that each shell could occupy.<ref name="Scerri218">Scerri, pp. 218–23</ref> In 1925, [[Friedrich Hund]] arrived at configurations close to the modern ones.<ref>{{cite journal |last1=Jensen |first1=William B. |date=2007 |title=The Origin of the s, p, d, f Orbital Labels |url=https://www.che.uc.edu/jensen/w.%20b.%20jensen/reprints/137.%20s,%20p,%20d,%20f.pdf |journal=Journal of Chemical Education |volume=84 |issue=5 |pages=757–8 |doi=10.1021/ed084p757 |bibcode=2007JChEd..84..757J |archive-url=https://web.archive.org/web/20181123140649/https://www.che.uc.edu/jensen/w.%20b.%20jensen/reprints/137.%20s,%20p,%20d,%20f.pdf |access-date=15 August 2021|archive-date=23 November 2018 }}</ref> As a result of these advances, periodicity became based on the number of chemically active or valence electrons rather than by the valences of the elements.<ref name=jensenlaw/> The [[Aufbau principle]] that describes the electron configurations of the elements was first empirically observed by [[Erwin Madelung]] in 1926,<ref name="Goudsmit">{{cite journal |title=The Order of Electron Shells in Ionized Atoms |last1=Goudsmit |first1=S. A. |last2=Richards |first2=Paul I. |journal=[[Proceedings of the National Academy of Sciences of the United States of America|Proc. Natl. Acad. Sci.]] |pages=664–671 (with correction on p&nbsp;906) |volume=51 |issue=4 |date=1964 |url=https://www.pnas.org/content/51/4/664.full.pdf |bibcode=1964PNAS...51..664G |doi=10.1073/pnas.51.4.664 |pmid=16591167 |doi-access=free |pmc=300183 |access-date=15 August 2021 |archive-date=10 October 2017 |archive-url=https://web.archive.org/web/20171010113455/https://www.pnas.org/content/51/4/664.full.pdf |url-status=live }}</ref> though the first to publish it was [[Vladimir Karapetoff]] in 1930.<ref>{{cite journal |last1=Karapetoff |first1=Vladimir |date=1930 |title=A chart of consecutive sets of electronic orbits within atoms of chemical elements |url= |journal=Journal of the Franklin Institute |volume=210 |issue=5 |pages=609–624 |doi=10.1016/S0016-0032(30)91131-3 }}</ref><ref name=Ostro>{{cite journal |last1=Ostrovsky |first1=Valentin N. |date=2003 |title=Physical Explanation of the Periodic Table |url= |journal=Annals of the New York Academy of Sciences |volume=988 |issue=1 |pages=182–192 |doi=10.1111/j.1749-6632.2003.tb06097.x |pmid=12796101 |bibcode=2003NYASA.988..182O |s2cid=21629328 }}</ref> In 1961, [[Vsevolod Klechkovsky]] derived the first part of the Madelung rule (that orbitals fill in order of increasing ''n'' + ℓ) from the [[Thomas–Fermi model]];<ref>{{cite journal |last1=Klechkovskii |first1=V.M. |title=Justification of the Rule for Successive Filling of (n+l) Groups |journal=Journal of Experimental and Theoretical Physics |date=1962 |volume=14 |issue=2 |page=334 |url=http://jetp.ras.ru/cgi-bin/e/index?t=&au=+Klechkovskii&yf=2022&yt=2022&se=1&a=s |access-date=23 June 2022}}</ref> the complete rule was derived from a similar potential in 1971 by Yury N. Demkov and Valentin N. Ostrovsky.<ref name=DO>{{cite journal |last1=Demkov |first1=Yury N. |last2=Ostrovsky |first2=Valentin N. |date=1972 |title=n+l Filling Rule in the Periodic System and Focusing Potentials |url=http://jetp.ras.ru/cgi-bin/e/index/e/35/1/p66?a=list |journal=Journal of Experimental and Theoretical Physics |volume=35 |issue=1 |pages=66–69 |doi= |bibcode=1972JETP...35...66D |access-date=25 November 2022}}</ref>{{efn|Demkov and Ostrovsky consider the potential <math>U_{1/2}(r) =  -\frac{2v}{rR(r+R)^2}</math> where <math>R</math> and <math>v</math> are constant parameters; this approaches a [[Coulomb potential]] for small <math>r</math>. When <math>v</math> satisfies the condition <math>v=v_N=\frac{1}{4}R^2 N(N+1)</math>, where <math>N=n+l</math>, the zero-energy solutions to the [[Schrödinger equation]] for this potential can be described analytically with [[Gegenbauer polynomials]]. As <math>v</math> passes through each of these values, a manifold containing all states with that value of <math>N</math> arises at zero energy and then becomes bound, recovering the Madelung order. Perturbation-theory considerations show that states with smaller <math>n</math> have lower energy, and that the s&nbsp;orbitals (with <math>l=0</math>) have their energies approaching the next <math>n+l</math> group.<ref name=DO/><ref name=shattered/>}}

[[File:Taula periòdica de Werner (1905).gif|thumb|right|512px|Periodic table of Alfred Werner (1905), the first appearance of the long form<ref name=Thyssen/>]]
The quantum theory clarified the transition metals and lanthanides as forming their own separate groups, transitional between the main groups, although some chemists had already proposed tables showing them this way before then: the English chemist Henry Bassett did so in 1892, the Danish chemist [[Julius Thomsen]] in 1895, and the Swiss chemist [[Alfred Werner]] in 1905. Bohr used Thomsen's form in his 1922 Nobel Lecture; Werner's form is very similar to the modern 32-column form. In particular, this supplanted Brauner's asteroidal hypothesis.<ref name="Thyssen">{{cite book|last1=Thyssen|first1=P.|last2=Binnemans|first2=K.|editor1-last=Gschneidner|editor1-first= K. A. Jr.|editor2-last=Bünzli|editor2-first=J-C.G|editor3-last=Vecharsky|editor3-first=Bünzli|date=2011|chapter=Accommodation of the Rare Earths in the Periodic Table: A Historical Analysis|title=Handbook on the Physics and Chemistry of Rare Earths|publisher=Elsevier|location=Amsterdam|volume=41|pages=1–93|isbn=978-0-444-53590-0|doi=10.1016/B978-0-444-53590-0.00001-7}}</ref>

The exact position of the lanthanides, and thus the composition of [[group 3 element|group 3]], remained under dispute for decades longer because their electron configurations were initially measured incorrectly.<ref name=Jensen1982/><ref name="PTSS">Scerri, pp. 392−401</ref> On chemical grounds Bassett, Werner, and Bury grouped scandium and yttrium with lutetium rather than lanthanum (the former two left an empty space below yttrium as lutetium had not yet been discovered).<ref name=Thyssen/><ref name=Bury/> Hund assumed in 1927 that all the lanthanide atoms had configuration [Xe]4f<sup>0−14</sup>5d<sup>1</sup>6s<sup>2</sup>, on account of their prevailing trivalency. It is now known that the relationship between chemistry and electron configuration is more complicated than that.{{efn|For example, the early actinides continue to behave more like the d-block transition metals in their propensity towards high oxidation states all the way from actinium to uranium, even though it is actually only actinium and thorium that have d-block-like configurations in the gas phase; f-electrons appear already at protactinium.<ref name=johnson/> Uranium's actual configuration of [Rn]5f<sup>3</sup>6d<sup>1</sup>7s<sup>2</sup> is in fact analogous to that Hund assumed for the lanthanides, but uranium does not favour the trivalent state, preferring to be tetravalent or hexavalent.<ref name=rareearths/> On the other hand, lanthanide-like configurations for the actinides begin at plutonium, but the shift towards lanthanide-like behaviour is only clear at curium: the elements between uranium and curium form a transition from transition-metal-like behaviour to lanthanide-like behaviour.<ref name=johnson/> Thus chemical behaviour and electron configuration do not exactly match each other.<ref name=johnson/>}}<ref name=rareearths>{{cite book |last1=Jørgensen |first1=Christian Klixbüll |editor1-last=Gschneidner Jr. |editor1-first=Karl A. |editor2-last=Eyring |editor2-first=Leroy |date=1988 |title=Handbook on the Physics and Chemistry of Rare Earths |publisher=Elsevier |volume=11 |pages=197–292 |chapter=Influence of Rare Earths on Chemical Understanding and Classification |isbn=978-0-444-87080-3}}</ref> Early spectroscopic evidence seemed to confirm these configurations, and thus the periodic table was structured to have group 3 as scandium, yttrium, lanthanum, and actinium, with fourteen f-elements breaking up the d-block between lanthanum and hafnium.<ref name=Jensen1982/> But it was later discovered that this is only true for four of the fifteen lanthanides (lanthanum, cerium, gadolinium, and lutetium), and that the other lanthanide atoms do not have a d-electron. In particular, ytterbium completes the 4f shell and thus Soviet physicists Lev Landau and Evgeny Lifshitz noted in 1948 that lutetium is correctly regarded as a d-block rather than an f-block element;<ref name=Landau/> that bulk lanthanum is an f-metal was first suggested by [[Jun Kondō]] in 1963, on the grounds of its low-temperature [[superconductivity]].<ref name=Kondo>{{cite journal |last1=Kondō |first1=Jun |date=January 1963 |title=Superconductivity in Transition Metals |url= |journal=Progress of Theoretical Physics |volume=29 |issue=1 |pages=1–9 |doi=10.1143/PTP.29.1 |bibcode=1963PThPh..29....1K |doi-access=free }}</ref> This clarified the importance of looking at low-lying excited states of atoms that can play a role in chemical environments when classifying elements by block and positioning them on the table.<ref name=Hamilton/><ref name=JensenLr/><ref name=Jensen1982/> Many authors subsequently rediscovered this correction based on physical, chemical, and electronic concerns and applied it to all the relevant elements, thus making group 3 contain scandium, yttrium, lutetium, and lawrencium<ref name=Hamilton/><ref name=Fluck/><ref name=PTSS/> and having lanthanum through ytterbium and actinium through nobelium as the f-block rows:<ref name=Hamilton/><ref name=Fluck/> this corrected version achieves consistency with the Madelung rule and vindicates Bassett, Werner, and Bury's initial chemical placement.<ref name=Thyssen/>

In 1988, IUPAC released a report supporting this composition of group 3,<ref name=Fluck/> a decision that was reaffirmed in 2021.<ref name="2021IUPAC">{{cite journal |last1=Scerri |first1=Eric |date=18 January 2021 |title=Provisional Report on Discussions on Group 3 of the Periodic Table |url=https://iupac.org/wp-content/uploads/2021/04/ChemInt_Jan2021_PP.pdf |journal=Chemistry International |volume=43 |issue=1 |pages=31–34 |doi=10.1515/ci-2021-0115 |s2cid=231694898 |access-date=9 April 2021 |archive-date=13 April 2021 |archive-url=https://web.archive.org/web/20210413150110/https://iupac.org/wp-content/uploads/2021/04/ChemInt_Jan2021_PP.pdf |url-status=live }}</ref> Variation can still be found in textbooks on the composition of group 3,<ref name=2015IUPAC/> and some argumentation against this format is still published today,<ref name="Jensen-2015" /> but chemists and physicists who have considered the matter largely agree on group 3 containing scandium, yttrium, lutetium, and lawrencium and challenge the counterarguments as being inconsistent.<ref name="Jensen-2015" />