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==== Order of subshell filling ==== [[File:Aufbau Principle-en.svg|thumb|right|192px|Idealized order of subshell filling according to the [[Madelung rule]] ]] The sequence in which the subshells are filled is given in most cases by the [[Aufbau principle]], also known as the Madelung or Klechkovsky rule (after [[Erwin Madelung]] and [[Vsevolod Klechkovsky]] respectively). This rule was first observed empirically by Madelung, and Klechkovsky and later authors gave it theoretical justification.<ref name=Jolly>{{cite book |last1=Jolly |first1=William L. |title=Modern Inorganic Chemistry |edition=1st |publisher=McGraw-Hill |date=1984 |pages=[https://archive.org/details/trent_0116300649799/page/10 10–12] |isbn=0-07-032760-2 |url=https://archive.org/details/trent_0116300649799/page/10 }}</ref><ref name=Ostrovsky/><ref name=Ostrovsky1981/><ref name=Wong/>{{efn|name=lowdin}} The shells overlap in energies, and the Madelung rule specifies the sequence of filling according to:<ref name="Ostrovsky">{{cite journal |last1=Ostrovsky |first1=V. N. |date=May 2001 |title=What and How Physics Contributes to Understanding the Periodic Law |journal=Foundations of Chemistry |volume=3 |issue=2 |pages=145–181 |doi=10.1023/A:1011476405933 |s2cid=15679915 }}</ref> :1s ≪ 2s < 2p ≪ 3s < 3p ≪ 4s < 3d < 4p ≪ 5s < 4d < 5p ≪ 6s < 4f < 5d < 6p ≪ 7s < 5f < 6d < 7p ≪ ... <!--write in 8s and 5g when they get discovered--> Here the sign ≪ means "much less than" as opposed to < meaning just "less than".<ref name="Ostrovsky"/> Phrased differently, electrons enter orbitals in order of increasing ''n'' + ℓ, and if two orbitals are available with the same value of ''n'' + ℓ, the one with lower ''n'' is occupied first.<ref name="Goudsmit" /><ref name="Wong">{{cite journal |title=Theoretical justification of Madelung's rule |journal=[[Journal of Chemical Education|J. Chem. Educ.]] |last=Wong |first=D. Pan |date=1979 |issue=11 |pages=714–718 |volume=56 |doi=10.1021/ed056p714 |bibcode = 1979JChEd..56..714W }}</ref> In general, orbitals with the same value of ''n'' + ℓ are similar in energy, but in the case of the s orbitals (with ℓ = 0), quantum effects raise their energy to approach that of the next ''n'' + ℓ group. Hence the periodic table is usually drawn to begin each row (often called a period) with the filling of a new s orbital, which corresponds to the beginning of a new shell.<ref name=Ostrovsky/><ref name=Ostrovsky1981>{{cite journal |last1=Ostrovsky |first1=V. N. |date=1981 |title=Dynamic symmetry of atomic potential |url= |journal=Journal of Physics B: Atomic and Molecular Physics |volume=14 |issue=23 |pages=4425–4439 |doi=10.1088/0022-3700/14/23/008 |bibcode=1981JPhB...14.4425O }}</ref><ref name="Petrucci331" /> Thus, with the exception of the first row, each period length appears twice:<ref name=Ostrovsky/> :2, 8, 8, 18, 18, 32, 32, ... The overlaps get quite close at the point where the d orbitals enter the picture,<ref name="Petrucci328"/> and the order can shift slightly with atomic number<ref name=Cao/> and atomic charge.<ref name="Jorgensen"/>{{efn| Once two to four electrons are removed, the d and f orbitals usually become lower in energy than the s ones:<ref name="Jorgensen"/> :1s ≪ 2s < 2p ≪ 3s < 3p ≪ 3d < 4s < 4p ≪ 4d < 5s < 5p ≪ 4f < 5d < 6s < 6p ≪ 5f < 6d < 7s < 7p ≪ ... and in the limit for extremely highly charged ions, orbitals simply fill in the order of increasing ''n'' instead. There is a gradual transition between the limiting situations of highly charged ions (increasing ''n'') and neutral atoms (Madelung's rule).<ref name="Goudsmit"/> Thus for example, the energy order for the 55th electron outside the xenon core proceeds as follows in the isoelectronic series of caesium (55 electrons):<ref name=elyashevich/> :Cs<sup>0</sup>: 6s < 6p < 5d < 7s < 4f :Ba<sup>+</sup>: 6s < 5d < 6p < 7s < 4f :La<sup>2+</sup>: 5d < 4f < 6s < 6p < 7s :Ce<sup>3+</sup>: 4f < 5d < 6s < 6p < 7s and in the isoelectronic series of holmium (67 electrons), a Ho<sup>0</sup> atom is [Xe]4f<sup>11</sup>6s<sup>2</sup>, but Er<sup>+</sup> is [Xe]4f<sup>12</sup>6s<sup>1</sup>, Tm<sup>2+</sup> through W<sup>7+</sup> are [Xe]4f<sup>13</sup>, and from Re<sup>8+</sup> onward the configuration is [Cd]4f<sup>14</sup>5p<sup>5</sup> following the hydrogenic order.<ref name=rareearths/><ref>{{cite web |url=https://physics.nist.gov/cgi-bin/ASD/ie.pl?spectra=Ho-like&submit=Retrieve+Data&units=1&format=0&order=0&at_num_out=on&sp_name_out=on&ion_charge_out=on&el_name_out=on&seq_out=on&shells_out=on&level_out=on&ion_conf_out=on&e_out=0&unc_out=on&biblio=on |title=NIST Atomic Spectra Database: Ionization Energies Data: All Ho-like |author=NIST |date=2023 |website=nist.gov |publisher=NIST |access-date=5 January 2024 |quote=}}</ref> : Also, the ordering of the orbitals between each ≪ changes somewhat throughout each period. For example, the ordering in argon and potassium is 3p ≪ 4s < 4p ≪ 3d; by calcium it has become 3p ≪ 4s < 3d < 4p; from scandium to copper it is 3p ≪ 3d < 4s < 4p; and from zinc to krypton it is 3p < 3d ≪ 4s < 4p<ref name=Cao>{{cite journal |last1=Cao |first1=Changsu |last2=Vernon |first2=René E. |first3=W. H. Eugen |last3=Schwarz |first4=Jun |last4=Li |date=6 January 2021 |title=Understanding Periodic and Non-periodic Chemistry in Periodic Tables |journal=Frontiers in Chemistry |volume=8 |issue=813 |page=813 |doi=10.3389/fchem.2020.00813 |pmid=33490030 |pmc=7818537 |bibcode=2021FrCh....8..813S |doi-access=free }}</ref> as the d orbitals fall into the core at gallium.<ref>{{cite journal |last1=Tossell |first1=J.A. |date=1 November 1977 |title=Theoretical studies of valence orbital binding energies in solid zinc sulfide, zinc oxide, and zinc fluoride |journal=Inorganic Chemistry |volume=16 |issue=11 |pages=2944–2949 |doi=10.1021/ic50177a056}}</ref><ref name=KW/> Deeply buried core shells in heavy atoms thus come closer to the hydrogenic order: around osmium (''Z'' {{=}} 76) 4f falls below 5p, and around bismuth (''Z'' {{=}} 83) 4f falls below 5s as well.<ref name=rareearths/> }} Starting from the simplest atom, this lets us build up the periodic table one at a time in order of atomic number, by considering the cases of single atoms. In [[hydrogen]], there is only one electron, which must go in the lowest-energy orbital 1s. This [[electron configuration]] is written 1s<sup>1</sup>, where the superscript indicates the number of electrons in the subshell. [[Helium]] adds a second electron, which also goes into 1s, completely filling the first shell and giving the configuration 1s<sup>2</sup>.<ref name="FIII19">{{cite book |last1=Feynman |first1=Richard |last2=Leighton |first2=Robert B. |last3=Sands |first3=Matthew |date=1964 |title=The Feynman Lectures on Physics |url=https://feynmanlectures.caltech.edu/III_19.html |publisher=Addison–Wesley |volume=3 |chapter=19. The Hydrogen Atom and The Periodic Table |isbn=0-201-02115-3 |access-date=15 August 2021 |archive-date=19 October 2021 |archive-url=https://web.archive.org/web/20211019202245/https://www.feynmanlectures.caltech.edu/III_19.html |url-status=live }}</ref><ref name=jensenlaw>{{cite web|url=http://www.che.uc.edu/jensen/W.%20B.%20Jensen/Reprints/081.%20Periodic%20Table.pdf|archive-url=https://web.archive.org/web/20201110113324/http://www.che.uc.edu/jensen/W.%20B.%20Jensen/Reprints/081.%20Periodic%20Table.pdf|archive-date=10 November 2020|last1=Jensen|first1=William B.|author-link=William B. Jensen|title=The Periodic Law and Table|date=2000|access-date=10 December 2022}}</ref>{{efn|In fact, electron configurations represent a first-order approximation: an atom really exists in a superposition of multiple configurations, and electrons in an atom are indistinguishable.<ref name=Scerri2009/> The elements in the d- and f-blocks have multiple configurations separated by small energies and can change configuration depending on the chemical environment.<ref name=Jorgensen/> In some of the undiscovered g-block elements, mixing of configurations may become so important that the result can no longer be well-described by a single configuration.<ref name=nefedov/>}} Starting from the third element, [[lithium]], the first shell is full, so its third electron occupies a 2s orbital, giving a 1s<sup>2</sup> 2s<sup>1</sup> configuration. The 2s electron is lithium's only valence electron, as the 1s subshell is now too tightly bound to the nucleus to participate in chemical bonding to other atoms: such a shell is called a "[[Core electron|core shell]]". The 1s subshell is a core shell for all elements from lithium onward. The 2s subshell is completed by the next element [[beryllium]] (1s<sup>2</sup> 2s<sup>2</sup>). The following elements then proceed to fill the 2p subshell. [[Boron]] (1s<sup>2</sup> 2s<sup>2</sup> 2p<sup>1</sup>) puts its new electron in a 2p orbital; [[carbon]] (1s<sup>2</sup> 2s<sup>2</sup> 2p<sup>2</sup>) fills a second 2p orbital; and with [[nitrogen]] (1s<sup>2</sup> 2s<sup>2</sup> 2p<sup>3</sup>) all three 2p orbitals become singly occupied. This is consistent with [[Hund's rule]], which states that atoms usually prefer to singly occupy each orbital of the same type before filling them with the second electron. [[Oxygen]] (1s<sup>2</sup> 2s<sup>2</sup> 2p<sup>4</sup>), [[fluorine]] (1s<sup>2</sup> 2s<sup>2</sup> 2p<sup>5</sup>), and [[neon]] (1s<sup>2</sup> 2s<sup>2</sup> 2p<sup>6</sup>) then complete the already singly filled 2p orbitals; the last of these fills the second shell completely.<ref name="FIII19" /><ref name=jensenlaw/> Starting from element 11, [[sodium]], the second shell is full, making the second shell a core shell for this and all heavier elements. The eleventh electron begins the filling of the third shell by occupying a 3s orbital, giving a configuration of 1s<sup>2</sup> 2s<sup>2</sup> 2p<sup>6</sup> 3s<sup>1</sup> for sodium. This configuration is abbreviated [Ne] 3s<sup>1</sup>, where [Ne] represents neon's configuration. [[Magnesium]] ([Ne] 3s<sup>2</sup>) finishes this 3s orbital, and the following six elements [[aluminium]], [[silicon]], [[phosphorus]], [[sulfur]], [[chlorine]], and [[argon]] fill the three 3p orbitals ([Ne] 3s<sup>2</sup> 3p<sup>1</sup> through [Ne] 3s<sup>2</sup> 3p<sup>6</sup>).<ref name="FIII19"/><ref name=jensenlaw/> This creates an analogous series in which the outer shell structures of sodium through argon are analogous to those of lithium through neon, and is the basis for the periodicity of chemical properties that the periodic table illustrates:<ref name="FIII19" /> at regular but changing intervals of atomic numbers, the properties of the chemical elements approximately repeat.<ref name="Scerri17">Scerri, p. 17</ref> The first 18 elements can thus be arranged as the start of a periodic table. Elements in the same column have the same number of valence electrons and have analogous valence electron configurations: these columns are called groups. The single exception is helium, which has two valence electrons like beryllium and magnesium, but is typically placed in the column of neon and argon to emphasise that its outer shell is full. (Some contemporary authors question even this single exception, preferring to consistently follow the valence configurations and place helium over beryllium.) There are eight columns in this periodic table fragment, corresponding to at most eight outer-shell electrons.<ref name="cartoon">{{cite book |last1=Gonick |first1=First |last2=Criddle |first2=Craig |date=2005 |title=The Cartoon Guide to Chemistry |publisher=Collins |pages=17–65 |isbn=0-06-093677-0}}</ref> A period begins when a new shell starts filling.<ref name="Petrucci331" /> Finally, the colouring illustrates the [[block (periodic table)|blocks]]: the elements in the s-block (coloured red) are filling s orbitals, while those in the p-block (coloured yellow) are filling p orbitals.<ref name="Petrucci331" /> {| class="wikitable" style="margin:auto;" | bgcolor="{{element color|s-block}}" | 1<br />[[hydrogen|H]] | | | | | | | bgcolor="{{element color|s-block}} | 2<br />[[helium|He]] | 2×1 = '''2''' elements<br />{{inline block|bg={{element color|s-block}}|1s}} {{inline block|{{0|0p}}}} |- | bgcolor="{{element color|s-block}}" | 3<br />[[lithium|Li]] | bgcolor="{{element color|s-block}}" | 4<br />[[beryllium|Be]] | bgcolor="{{element color|p-block}}" | 5<br />[[boron|B]] | bgcolor="{{element color|p-block}}" | 6<br />[[carbon|C]] | bgcolor="{{element color|p-block}}" | 7<br />[[nitrogen|N]] | bgcolor="{{element color|p-block}}" | 8<br />[[oxygen|O]] | bgcolor="{{element color|p-block}}" | 9<br />[[fluorine|F]] | bgcolor="{{element color|p-block}}" | 10<br />[[neon|Ne]] | {{nowrap|2×(1+3) {{=}} '''8''' elements}}<br />{{inline block|bg={{element color|s-block}}|2s}} {{inline block|bg={{element color|p-block}}|2p}} |- | bgcolor="{{element color|s-block}}" | 11<br />[[sodium|Na]] | bgcolor="{{element color|s-block}}" | 12<br />[[magnesium|Mg]] | bgcolor="{{element color|p-block}}" | 13<br />[[aluminium|Al]] | bgcolor="{{element color|p-block}}" | 14<br />[[silicon|Si]] | bgcolor="{{element color|p-block}}" | 15<br />[[phosphorus|P]] | bgcolor="{{element color|p-block}}" | 16<br />[[sulfur|S]] | bgcolor="{{element color|p-block}}" | 17<br />[[chlorine|Cl]] | bgcolor="{{element color|p-block}}" | 18<br />[[argon|Ar]] | 2×(1+3) = '''8''' elements<br />{{inline block|bg={{element color|s-block}}|3s}} {{inline block|bg={{element color|p-block}}|3p}} |} Starting the next row, for [[potassium]] and [[calcium]] the 4s subshell is the lowest in energy, and therefore they fill it.<ref name="FIII19"/><ref name=jensenlaw/> Potassium adds one electron to the 4s shell ([Ar] 4s<sup>1</sup>), and calcium then completes it ([Ar] 4s<sup>2</sup>). However, starting from [[scandium]] ([Ar] 3d<sup>1</sup> 4s<sup>2</sup>) the 3d subshell becomes the next highest in energy. The 4s and 3d subshells have approximately the same energy and they compete for filling the electrons, and so the occupation is not quite consistently filling the 3d orbitals one at a time. The precise energy ordering of 3d and 4s changes along the row, and also changes depending on how many electrons are removed from the atom. For example, due to the repulsion between the 3d electrons and the 4s ones, at [[chromium]] the 4s energy level becomes slightly higher than 3d, and so it becomes more profitable for a chromium atom to have a [Ar] 3d<sup>5</sup> 4s<sup>1</sup> configuration than an [Ar] 3d<sup>4</sup> 4s<sup>2</sup> one. A similar anomaly occurs at [[copper]], whose atom has a [Ar] 3d<sup>10</sup> 4s<sup>1</sup> configuration rather than the expected [Ar] 3d<sup>9</sup> 4s<sup>2</sup>.<ref name="FIII19" /> These are violations of the Madelung rule. Such anomalies, however, do not have any chemical significance:<ref name="Jorgensen" /> most chemistry is not about isolated gaseous atoms,<ref>Wulfsberg, p. 27</ref> and the various configurations are so close in energy to each other<ref name="Petrucci328">Petrucci et al., p. 328</ref> that the presence of a nearby atom can shift the balance.<ref name="FIII19" /> Therefore, the periodic table ignores them and considers only idealized configurations.<ref name="Jensen2009">{{cite journal|author1-link=William B. Jensen |last1=Jensen |first1=William B. |date=2009 |title=Misapplying the Periodic Law |journal=Journal of Chemical Education |volume=86 |issue=10 |page=1186 |doi=10.1021/ed086p1186 |bibcode=2009JChEd..86.1186J |doi-access=free }}</ref> At [[zinc]] ([Ar] 3d<sup>10</sup> 4s<sup>2</sup>), the 3d orbitals are completely filled with a total of ten electrons.<ref name="FIII19"/><ref name=jensenlaw/> Next come the 4p orbitals, completing the row, which are filled progressively by [[gallium]] ([Ar] 3d<sup>10</sup> 4s<sup>2</sup> 4p<sup>1</sup>) through [[krypton]] ([Ar] 3d<sup>10</sup> 4s<sup>2</sup> 4p<sup>6</sup>), in a manner analogous to the previous p-block elements.<ref name="FIII19" /><ref name=jensenlaw/> From gallium onwards, the 3d orbitals form part of the electronic core, and no longer participate in chemistry.<ref name=KW/> The s- and p-block elements, which fill their outer shells, are called [[main-group element]]s; the d-block elements (coloured blue below), which fill an inner shell, are called [[transition element]]s (or transition metals, since they are all metals).<ref name="Petrucci326">Petrucci et al., pp. 326–7</ref> The next 18 elements fill the 5s orbitals ([[rubidium]] and [[strontium]]), then 4d ([[yttrium]] through [[cadmium]], again with a few anomalies along the way), and then 5p ([[indium]] through [[xenon]]).<ref name=Petrucci331/><ref name=jensenlaw/> Again, from indium onward the 4d orbitals are in the core.<ref name=jensenlaw/><ref>{{cite journal |last1=Farberovich |first1=O. V. |last2=Kurganskii |first2=S. I. |last3=Domashevskaya |first3=E. P. |date=1980 |title=Problems of the OPW Method. II. Calculation of the Band Structure of ZnS and CdS |url= |journal=Physica Status Solidi B |volume=97 |issue=2 |pages=631–640 |doi=10.1002/pssb.2220970230 |bibcode=1980PSSBR..97..631F }}</ref> Hence the fifth row has the same structure as the fourth.<ref name="Petrucci331" /> {| class="wikitable" style="margin:auto;" | bgcolor="{{element color|s-block}}" | 1<br />[[hydrogen|H]] | | | | | | | | | | | | | | | | | bgcolor="{{element color|s-block}} | 2<br />[[helium|He]] | 2×1 = '''2''' elements<br />{{inline block|bg={{element color|s-block}}|1s}} {{inline block|{{0|0d}}}} {{inline block|{{0|0p}}}} |- | bgcolor="{{element color|s-block}}" | 3<br />[[lithium|Li]] | bgcolor="{{element color|s-block}}" | 4<br />[[beryllium|Be]] | | | | | | | | | | | bgcolor="{{element color|p-block}}" | 5<br />[[boron|B]] | bgcolor="{{element color|p-block}}" | 6<br />[[carbon|C]] | bgcolor="{{element color|p-block}}" | 7<br />[[nitrogen|N]] | bgcolor="{{element color|p-block}}" | 8<br />[[oxygen|O]] | bgcolor="{{element color|p-block}}" | 9<br />[[fluorine|F]] | bgcolor="{{element color|p-block}}" | 10<br />[[neon|Ne]] | 2×(1+3) = '''8''' elements<br />{{inline block|bg={{element color|s-block}}|2s}} {{inline block|{{0|0d}}}} {{inline block|bg={{element color|p-block}}|2p}} |- | bgcolor="{{element color|s-block}}" | 11<br />[[sodium|Na]] | bgcolor="{{element color|s-block}}" | 12<br />[[magnesium|Mg]] | | | | | | | | | | | bgcolor="{{element color|p-block}}" | 13<br />[[aluminium|Al]] | bgcolor="{{element color|p-block}}" | 14<br />[[silicon|Si]] | bgcolor="{{element color|p-block}}" | 15<br />[[phosphorus|P]] | bgcolor="{{element color|p-block}}" | 16<br />[[sulfur|S]] | bgcolor="{{element color|p-block}}" | 17<br />[[chlorine|Cl]] | bgcolor="{{element color|p-block}}" | 18<br />[[argon|Ar]] | 2×(1+3) = '''8''' elements<br />{{inline block|bg={{element color|s-block}}|3s}} {{inline block|{{0|0d}}}} {{inline block|bg={{element color|p-block}}|3p}} |- | bgcolor="{{element color|s-block}}" | 19<br />[[potassium|K]] | bgcolor="{{element color|s-block}}" | 20<br />[[calcium|Ca]] | bgcolor="{{element color|d-block}}" | 21<br />[[scandium|Sc]] | bgcolor="{{element color|d-block}}" | 22<br />[[titanium|Ti]] | bgcolor="{{element color|d-block}}" | 23<br />[[vanadium|V]] | bgcolor="{{element color|d-block}}" | 24<br />[[chromium|Cr]] | bgcolor="{{element color|d-block}}" | 25<br />[[manganese|Mn]] | bgcolor="{{element color|d-block}}" | 26<br />[[iron|Fe]] | bgcolor="{{element color|d-block}}" | 27<br />[[cobalt|Co]] | bgcolor="{{element color|d-block}}" | 28<br />[[nickel|Ni]] | bgcolor="{{element color|d-block}}" | 29<br />[[copper|Cu]] | bgcolor="{{element color|d-block}}" | 30<br />[[zinc|Zn]] | bgcolor="{{element color|p-block}}" | 31<br />[[gallium|Ga]] | bgcolor="{{element color|p-block}}" | 32<br />[[germanium|Ge]] | bgcolor="{{element color|p-block}}" | 33<br />[[arsenic|As]] | bgcolor="{{element color|p-block}}" | 34<br />[[selenium|Se]] | bgcolor="{{element color|p-block}}" | 35<br />[[bromine|Br]] | bgcolor="{{element color|p-block}}" | 36<br />[[krypton|Kr]] | {{nowrap|2×(1+3+5) {{=}} '''18''' elements}}<br />{{inline block|bg={{element color|s-block}}|4s}} {{inline block|bg={{element color|d-block}}|3d}} {{inline block|bg={{element color|p-block}}|4p}} |- | bgcolor="{{element color|s-block}}" | 37<br />[[rubidium|Rb]] | bgcolor="{{element color|s-block}}" | 38<br />[[strontium|Sr]] | bgcolor="{{element color|d-block}}" | 39<br />[[yttrium|Y]] | bgcolor="{{element color|d-block}}" | 40<br />[[zirconium|Zr]] | bgcolor="{{element color|d-block}}" | 41<br />[[niobium|Nb]] | bgcolor="{{element color|d-block}}" | 42<br />[[molybdenum|Mo]] | bgcolor="{{element color|d-block}}" | 43<br />[[technetium|Tc]] | bgcolor="{{element color|d-block}}" | 44<br />[[ruthenium|Ru]] | bgcolor="{{element color|d-block}}" | 45<br />[[rhodium|Rh]] | bgcolor="{{element color|d-block}}" | 46<br />[[palladium|Pd]] | bgcolor="{{element color|d-block}}" | 47<br />[[silver|Ag]] | bgcolor="{{element color|d-block}}" | 48<br />[[cadmium|Cd]] | bgcolor="{{element color|p-block}}" | 49<br />[[indium|In]] | bgcolor="{{element color|p-block}}" | 50<br />[[tin|Sn]] | bgcolor="{{element color|p-block}}" | 51<br />[[antimony|Sb]] | bgcolor="{{element color|p-block}}" | 52<br />[[tellurium|Te]] | bgcolor="{{element color|p-block}}" | 53<br />[[iodine|I]] | bgcolor="{{element color|p-block}}" | 54<br />[[xenon|Xe]] | 2×(1+3+5) = '''18''' elements<br />{{inline block|bg={{element color|s-block}}|5s}} {{inline block|bg={{element color|d-block}}|4d}} {{inline block|bg={{element color|p-block}}|5p}} |} The sixth row of the table likewise starts with two s-block elements: [[caesium]] and [[barium]].<ref name=jensenlaw/> After this, the first f-block elements (coloured green below) begin to appear, starting with [[lanthanum]]. These are sometimes termed inner transition elements.<ref name="Petrucci326" /> As there are now not only 4f but also 5d and 6s subshells at similar energies, competition occurs once again with many irregular configurations;<ref name="Petrucci328" /> this resulted in some dispute about where exactly the f-block is supposed to begin, but most who study the matter agree that it starts at lanthanum in accordance with the Aufbau principle.<ref name="Jensen-2015" /> Even though lanthanum does not itself fill the 4f subshell as a single atom, because of repulsion between electrons,<ref name="Jorgensen">{{cite journal |last1=Jørgensen |first1=Christian |date=1973 |title=The Loose Connection between Electron Configuration and the Chemical Behavior of the Heavy Elements (Transuranics) |journal=Angewandte Chemie International Edition |volume=12 |issue=1 |pages=12–19 |doi=10.1002/anie.197300121}}</ref> its 4f orbitals are low enough in energy to participate in chemistry.<ref name="Hamilton">{{cite journal |last1=Hamilton |first1=David C. |date=1965 |title=Position of Lanthanum in the Periodic Table |journal=American Journal of Physics |volume=33 |issue=8 |pages=637–640 |doi=10.1119/1.1972042|bibcode=1965AmJPh..33..637H}}</ref><ref name=elyashevich>{{cite book |last=El'yashevich |first=M. A. |author-link= |date=1953 |title=Spectra of the Rare Earths |url= |location=Moscow |publisher=State Publishing House of Technical-Theoretical Literature |pages=382, 397 |isbn=}}</ref><ref name=Cp3Ln>{{cite journal | last1=Krinsky | first1=Jamin L. | last2=Minasian | first2=Stefan G. | last3=Arnold | first3=John | title=Covalent Lanthanide Chemistry Near the Limit of Weak Bonding: Observation of (CpSiMe<sub>3</sub>)<sub>3</sub>Ce−ECp* and a Comprehensive Density Functional Theory Analysis of Cp<sub>3</sub>Ln−ECp (E = Al, Ga) | journal=Inorganic Chemistry | publisher=American Chemical Society (ACS) | volume=50 | issue=1 | date=8 December 2010 | issn=0020-1669 | doi=10.1021/ic102028d | pages=345–357| pmid=21141834 }}</ref> At [[ytterbium]], the seven 4f orbitals are completely filled with fourteen electrons; thereafter, a series of ten transition elements ([[lutetium]] through [[mercury (element)|mercury]]) follows,<ref name=jensenlaw/><ref name="JensenLr">{{cite web|url=https://www.che.uc.edu/jensen/W.%20B.%20Jensen/Reprints/251.%20Lawrencium.pdf |title=Some Comments on the Position of Lawrencium in the Periodic Table |last1=Jensen |first1=W. B. |date=2015 |access-date=20 September 2015 |archive-url=https://web.archive.org/web/20151223091325/https://www.che.uc.edu/jensen/W.%20B.%20Jensen/Reprints/251.%20Lawrencium.pdf |archive-date=23 December 2015 }}</ref><ref>{{cite journal |last1=Wang |first1=Fan |last2=Le-Min |first2=Li |date=2002 |title=镧系元素 4f 轨道在成键中的作用的理论研究 |trans-title=Theoretical Study on the Role of Lanthanide 4f Orbitals in Bonding |language=zh |journal=Acta Chimica Sinica |volume=62 |issue=8 |pages=1379–84}}</ref><ref name="LaF3">{{cite journal |last1=Xu |first1=Wei |last2=Ji |first2=Wen-Xin |first3=Yi-Xiang |last3=Qiu |first4=W. H. Eugen |last4=Schwarz |first5=Shu-Guang |last5=Wang |date=2013 |title=On structure and bonding of lanthanoid trifluorides LnF<sub>3</sub> (Ln = La to Lu) |journal=Physical Chemistry Chemical Physics |volume=2013 |issue=15 |pages=7839–47 |doi=10.1039/C3CP50717C|pmid=23598823 |bibcode=2013PCCP...15.7839X }}</ref> and finally six main-group elements ([[thallium]] through [[radon]]) complete the period.<ref name=jensenlaw/><ref name="Pyykko">{{cite journal | title = Octacarbonyl Ion Complexes of Actinides [An(CO)8]+/− (An=Th, U) and the Role of f Orbitals in Metal–Ligand Bonding | first1= Chaoxian |last1=Chi |first2=Sudip |last2=Pan | first3= Jiaye |last3=Jin |first4=Luyan |last4=Meng | first5= Mingbiao |last5=Luo |first6=Lili |last6=Zhao |first7=Mingfei |last7=Zhou |first8=Gernot |last8=Frenking | journal = [[Chemistry: A European Journal|Chem. Eur. J.]] | year = 2019 | volume = 25 | issue = 50 | pages = 11772–11784 | doi = 10.1002/chem.201902625 | pmid= 31276242 | pmc= 6772027 |doi-access=free }}</ref> From lutetium onwards the 4f orbitals are in the core,<ref name=jensenlaw/><ref name=Cp3Ln/> and from thallium onwards so are the 5d orbitals.<ref name=jensenlaw/><ref name=KW/><ref>{{cite journal |last1=Singh |first1=Prabhakar P. |date=1994 |title=Relativistic effects in mercury: Atom, clusters, and bulk |url= |journal=Physical Review B |volume=49 |issue=7 |pages=4954–4958 |doi=10.1103/PhysRevB.49.4954 |pmid=10011429 |bibcode=1994PhRvB..49.4954S }}</ref> The seventh row is analogous to the sixth row: 7s fills ([[francium]] and [[radium]]), then 5f ([[actinium]] to [[nobelium]]), then 6d ([[lawrencium]] to [[copernicium]]), and finally 7p ([[nihonium]] to [[oganesson]]).<ref name=jensenlaw/> Starting from lawrencium the 5f orbitals are in the core,<ref name=jensenlaw/> and probably the 6d orbitals join the core starting from nihonium.<ref name=jensenlaw/><ref name=VI>{{cite journal |last1=Hu |first1=Shu-Xian |last2=Zou |first2=Wenli |date=23 September 2021 |title=Stable copernicium hexafluoride (CnF<sub>6</sub>) with an oxidation state of VI+ |journal=Physical Chemistry Chemical Physics |volume=2022 |issue=24 |pages=321–325 |doi=10.1039/D1CP04360A|pmid=34889909 |bibcode=2021PCCP...24..321H }}</ref>{{efn|Compounds that would use the 6d orbitals of nihonium as valence orbitals have been theoretically investigated, but they are all expected to be too unstable to observe.<ref name="Seth">{{cite journal |last1=Seth |first1=Michael |last2=Schwerdtfeger |first2=Peter |first3=Knut |last3=Fægri |date=1999 |title=The chemistry of superheavy elements. III. Theoretical studies on element 113 compounds |journal=Journal of Chemical Physics |volume=111 |issue=14 |pages=6422–6433 |doi=10.1063/1.480168 |bibcode=1999JChPh.111.6422S|s2cid=41854842 |doi-access=free |hdl=2292/5178 |hdl-access=free }}</ref>}} Again there are a few anomalies along the way:<ref name="Petrucci331">Petrucci et al., p. 331</ref> for example, as single atoms neither actinium nor [[thorium]] actually fills the 5f subshell, and lawrencium does not fill the 6d shell, but all these subshells can still become filled in chemical environments.<ref>{{cite journal |last1=Kelley |first1=Morgan P. |last2=Deblonde |first2=Gauthier J.-P. |first3=Jing |last3=Su |first4=Corwin H. |last4=Booth |first5=Rebecca J. |last5=Abergel |first6=Enrique R. |last6=Batista |first7=Ping |last7=Yang |date=2018 |title=Bond Covalency and Oxidation State of Actinide Ions Complexed with Therapeutic Chelating Agent 3,4,3-LI(1,2-HOPO) |url= https://escholarship.org/uc/item/4tc1b0xz|journal=Inorganic Chemistry |volume=57 |issue=9 |pages=5352–5363 |doi=10.1021/acs.inorgchem.8b00345 |pmid=29624372 |osti=1458511 }}</ref><ref name="Johansson">{{cite journal|last1=Johansson |first1=B. |last2=Abuja |first2=R. |last3=Eriksson |first3=O. |last4=Wills |first4=J. M. |display-authors=3 |year=1995 |title=Anomalous fcc crystal structure of thorium metal. |journal=Physical Review Letters |volume=75 |issue=2 |pages=280–283 |doi=10.1103/PhysRevLett.75.280|pmid=10059654 |bibcode=1995PhRvL..75..280J|url=https://zenodo.org/record/1233903 }}</ref><ref name=XuPyykko> {{cite journal |last1=Xu |first1=Wen-Hua |last2=Pyykkö |first2=Pekka |date=8 June 2016 |url=http://pubs.rsc.org/-/content/articlehtml/2016/cp/c6cp02706g |title=Is the chemistry of lawrencium peculiar |journal=Phys. Chem. Chem. Phys. |volume=2016 |issue=18 |pages=17351–5 |doi=10.1039/c6cp02706g |pmid=27314425 |access-date=24 April 2017|bibcode=2016PCCP...1817351X |hdl=10138/224395 |s2cid=31224634 |hdl-access=free }}</ref> For a very long time, the seventh row was incomplete as most of its elements do not occur in nature. The missing [[transuranic element|elements beyond uranium]] started to be synthesized in the laboratory in 1940, when neptunium was made.<ref name="Scerri354" /> (However, the first element to be discovered by synthesis rather than in nature was technetium in 1937.) The row was completed with the synthesis of [[tennessine]] in 2010<ref name="117s">{{cite journal |last1=Oganessian |first1=Yu.Ts. |author-link1=Yuri Oganessian |last2=Abdullin |first2=F.Sh. |last3=Bailey |first3=P.D. |last4=Benker |first4=D.E. |last5=Bennett |first5=M.E. |last6=Dmitriev |first6=S.N. |last7=Ezold |first7=J.G. |last8=Hamilton |first8=J.H. |last9=Henderson |first9=R.A. |first10=M.G. |last10=Itkis |first11=Yuri V. |last11=Lobanov |first12=A.N. |last12=Mezentsev |first13=K. J. |last13=Moody |first14=S.L. |last14=Nelson |first15=A.N. |last15=Polyakov |first16=C.E. |last16=Porter |first17=A.V. |last17=Ramayya |first18=F.D. |last18=Riley |first19=J.B. |last19=Roberto |first20=M. A. |last20=Ryabinin |first21=K.P. |last21=Rykaczewski |first22=R.N. |last22=Sagaidak |first23=D.A. |last23=Shaughnessy |first24=I.V. |last24=Shirokovsky |first25=M.A. |last25=Stoyer |first26=V.G. |last26=Subbotin |first27=R. |last27=Sudowe |first28=A.M. |last28=Sukhov |first29=Yu.S. |last29=Tsyganov |first30=Vladimir K. |last30=Utyonkov |first31=A.A. |last31=Voinov |first32=G.K. |last32=Vostokin |first33=P.A. |last33=Wilk |display-authors=6 |title=Synthesis of a new element with atomic number {{nowrap|''Z'' {{=}} 117}} |year=2010 |journal=Physical Review Letters |volume=104 |issue=14 |page=142502 |doi=10.1103/PhysRevLett.104.142502 |pmid=20481935 |bibcode=2010PhRvL.104n2502O |s2cid=3263480 |doi-access=free }}</ref> (the last element [[oganesson]] had already been made in 2002),<ref name="pp2002">{{cite journal|author=Oganessian, Yu. T.|display-authors=etal|title=Results from the first <sup>249</sup>Cf+<sup>48</sup>Ca experiment|url=https://www.jinr.ru/publish/Preprints/2002/287(D7-2002-287)e.pdf|journal=JINR Communication|date=2002|access-date=13 June 2009|archive-date=13 December 2004|archive-url=https://web.archive.org/web/20041213100709/https://www.jinr.ru/publish/Preprints/2002/287%28D7-2002-287%29e.pdf}}</ref> and the last elements in this seventh row were given names in 2016.<ref name="IUPAC-20161130">{{cite news |author=<!--Not stated--> |title=IUPAC Announces the Names of the Elements 113, 115, 117, and 118 |url=https://iupac.org/iupac-announces-the-names-of-the-elements-113-115-117-and-118/ |date=30 November 2016 |work=[[IUPAC]] |access-date=1 December 2016 |archive-date=30 November 2016 |archive-url=https://web.archive.org/web/20161130111959/https://iupac.org/iupac-announces-the-names-of-the-elements-113-115-117-and-118/ |url-status=live }}</ref> <div style="overflow-x:auto"> {| class="wikitable" style="margin:auto;" | bgcolor="{{element color|s-block}}" | 1<br />[[hydrogen|H]] | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | bgcolor="{{element color|s-block}} | 2<br />[[helium|He]] | 2×1 = '''2''' elements<br />{{inline block|bg={{element color|s-block}}|1s}} {{inline block|{{0|0f}}}} {{inline block|{{0|0d}}}} {{inline block|{{0|0p}}}} |- | bgcolor="{{element color|s-block}}" | 3<br />[[lithium|Li]] | bgcolor="{{element color|s-block}}" | 4<br />[[beryllium|Be]] | | | | | | | | | | | | | | | | | | | | | | | | | bgcolor="{{element color|p-block}}" | 5<br />[[boron|B]] | bgcolor="{{element color|p-block}}" | 6<br />[[carbon|C]] | bgcolor="{{element color|p-block}}" | 7<br />[[nitrogen|N]] | bgcolor="{{element color|p-block}}" | 8<br />[[oxygen|O]] | bgcolor="{{element color|p-block}}" | 9<br />[[fluorine|F]] | bgcolor="{{element color|p-block}}" | 10<br />[[neon|Ne]] | 2×(1+3) = '''8''' elements<br />{{inline block|bg={{element color|s-block}}|2s}} {{inline block|{{0|0f}}}} {{inline block|{{0|0d}}}} {{inline block|bg={{element color|p-block}}|2p}} |- | bgcolor="{{element color|s-block}}" | 11<br />[[sodium|Na]] | bgcolor="{{element color|s-block}}" | 12<br />[[magnesium|Mg]] | | | | | | | | | | | | | | | | | | | | | | | | | bgcolor="{{element color|p-block}}" | 13<br />[[aluminium|Al]] | bgcolor="{{element color|p-block}}" | 14<br />[[silicon|Si]] | bgcolor="{{element color|p-block}}" | 15<br />[[phosphorus|P]] | bgcolor="{{element color|p-block}}" | 16<br />[[sulfur|S]] | bgcolor="{{element color|p-block}}" | 17<br />[[chlorine|Cl]] | bgcolor="{{element color|p-block}}" | 18<br />[[argon|Ar]] | 2×(1+3) = '''8''' elements<br />{{inline block|bg={{element color|s-block}}|3s}} {{inline block|{{0|0f}}}} {{inline block|{{0|0d}}}} {{inline block|bg={{element color|p-block}}|3p}} |- | bgcolor="{{element color|s-block}}" | 19<br />[[potassium|K]] | bgcolor="{{element color|s-block}}" | 20<br />[[calcium|Ca]] | | | | | | | | | | | | | | | bgcolor="{{element color|d-block}}" | 21<br />[[scandium|Sc]] | bgcolor="{{element color|d-block}}" | 22<br />[[titanium|Ti]] | bgcolor="{{element color|d-block}}" | 23<br />[[vanadium|V]] | bgcolor="{{element color|d-block}}" | 24<br />[[chromium|Cr]] | bgcolor="{{element color|d-block}}" | 25<br />[[manganese|Mn]] | bgcolor="{{element color|d-block}}" | 26<br />[[iron|Fe]] | bgcolor="{{element color|d-block}}" | 27<br />[[cobalt|Co]] | bgcolor="{{element color|d-block}}" | 28<br />[[nickel|Ni]] | bgcolor="{{element color|d-block}}" | 29<br />[[copper|Cu]] | bgcolor="{{element color|d-block}}" | 30<br />[[zinc|Zn]] | bgcolor="{{element color|p-block}}" | 31<br />[[gallium|Ga]] | bgcolor="{{element color|p-block}}" | 32<br />[[germanium|Ge]] | bgcolor="{{element color|p-block}}" | 33<br />[[arsenic|As]] | bgcolor="{{element color|p-block}}" | 34<br />[[selenium|Se]] | bgcolor="{{element color|p-block}}" | 35<br />[[bromine|Br]] | bgcolor="{{element color|p-block}}" | 36<br />[[krypton|Kr]] | 2×(1+3+5) = '''18''' elements<br />{{inline block|bg={{element color|s-block}}|4s}} {{inline block|{{0|0f}}}} {{inline block|bg={{element color|d-block}}|3d}} {{inline block|bg={{element color|p-block}}|4p}} |- | bgcolor="{{element color|s-block}}" | 37<br />[[rubidium|Rb]] | bgcolor="{{element color|s-block}}" | 38<br />[[strontium|Sr]] | | | | | | | | | | | | | | | bgcolor="{{element color|d-block}}" | 39<br />[[yttrium|Y]] | bgcolor="{{element color|d-block}}" | 40<br />[[zirconium|Zr]] | bgcolor="{{element color|d-block}}" | 41<br />[[niobium|Nb]] | bgcolor="{{element color|d-block}}" | 42<br />[[molybdenum|Mo]] | bgcolor="{{element color|d-block}}" | 43<br />[[technetium|Tc]] | bgcolor="{{element color|d-block}}" | 44<br />[[ruthenium|Ru]] | bgcolor="{{element color|d-block}}" | 45<br />[[rhodium|Rh]] | bgcolor="{{element color|d-block}}" | 46<br />[[palladium|Pd]] | bgcolor="{{element color|d-block}}" | 47<br />[[silver|Ag]] | bgcolor="{{element color|d-block}}" | 48<br />[[cadmium|Cd]] | bgcolor="{{element color|p-block}}" | 49<br />[[indium|In]] | bgcolor="{{element color|p-block}}" | 50<br />[[tin|Sn]] | bgcolor="{{element color|p-block}}" | 51<br />[[antimony|Sb]] | bgcolor="{{element color|p-block}}" | 52<br />[[tellurium|Te]] | bgcolor="{{element color|p-block}}" | 53<br />[[iodine|I]] | bgcolor="{{element color|p-block}}" | 54<br />[[xenon|Xe]] | 2×(1+3+5) = '''18''' elements<br />{{inline block|bg={{element color|s-block}}|5s}} {{inline block|{{0|0f}}}} {{inline block|bg={{element color|d-block}}|4d}} {{inline block|bg={{element color|p-block}}|5p}} |- | bgcolor="{{element color|s-block}}" | 55<br />[[caesium|Cs]] | bgcolor="{{element color|s-block}}" | 56<br />[[barium|Ba]] | bgcolor="{{element color|f-block}}" | 57<br />[[lanthanum|La]] | bgcolor="{{element color|f-block}}" | 58<br />[[cerium|Ce]] | bgcolor="{{element color|f-block}}" | 59<br />[[praseodymium|Pr]] | bgcolor="{{element color|f-block}}" | 60<br />[[neodymium|Nd]] | bgcolor="{{element color|f-block}}" | 61<br />[[promethium|Pm]] | bgcolor="{{element color|f-block}}" | 62<br />[[samarium|Sm]] | bgcolor="{{element color|f-block}}" | 63<br />[[europium|Eu]] | bgcolor="{{element color|f-block}}" | 64<br />[[gadolinium|Gd]] | bgcolor="{{element color|f-block}}" | 65<br />[[terbium|Tb]] | bgcolor="{{element color|f-block}}" | 66<br />[[dysprosium|Dy]] | bgcolor="{{element color|f-block}}" | 67<br />[[holmium|Ho]] | bgcolor="{{element color|f-block}}" | 68<br />[[erbium|Er]] | bgcolor="{{element color|f-block}}" | 69<br />[[thulium|Tm]] | bgcolor="{{element color|f-block}}" | 70<br />[[ytterbium|Yb]] | bgcolor="{{element color|d-block}}" | 71<br />[[lutetium|Lu]] | bgcolor="{{element color|d-block}}" | 72<br />[[hafnium|Hf]] | bgcolor="{{element color|d-block}}" | 73<br />[[tantalum|Ta]] | bgcolor="{{element color|d-block}}" | 74<br />[[tungsten|W]] | bgcolor="{{element color|d-block}}" | 75<br />[[rhenium|Re]] | bgcolor="{{element color|d-block}}" | 76<br />[[osmium|Os]] | bgcolor="{{element color|d-block}}" | 77<br />[[iridium|Ir]] | bgcolor="{{element color|d-block}}" | 78<br />[[platinum|Pt]] | bgcolor="{{element color|d-block}}" | 79<br />[[gold|Au]] | bgcolor="{{element color|d-block}}" | 80<br />[[mercury (element)|Hg]] | bgcolor="{{element color|p-block}}" | 81<br />[[thallium|Tl]] | bgcolor="{{element color|p-block}}" | 82<br />[[lead|Pb]] | bgcolor="{{element color|p-block}}" | 83<br />[[bismuth|Bi]] | bgcolor="{{element color|p-block}}" | 84<br />[[polonium|Po]] | bgcolor="{{element color|p-block}}" | 85<br />[[astatine|At]] | bgcolor="{{element color|p-block}}" | 86<br />[[radon|Rn]] | {{nowrap|2×(1+3+5+7) {{=}} '''32''' elements}}<br />{{nowrap|{{inline block|bg={{element color|s-block}}|6s}} {{inline block|bg={{element color|f-block}}|4f}} {{inline block|bg={{element color|d-block}}|5d}} {{inline block|bg={{element color|p-block}}|6p}}}} |- | bgcolor="{{element color|s-block}}" | 87<br />[[francium|Fr]] | bgcolor="{{element color|s-block}}" | 88<br />[[radium|Ra]] | bgcolor="{{element color|f-block}}" | 89<br />[[actinium|Ac]] | bgcolor="{{element color|f-block}}" | 90<br />[[thorium|Th]] | bgcolor="{{element color|f-block}}" | 91<br />[[protactinium|Pa]] | bgcolor="{{element color|f-block}}" | 92<br />[[uranium|U]] | bgcolor="{{element color|f-block}}" | 93<br />[[neptunium|Np]] | bgcolor="{{element color|f-block}}" | 94<br />[[plutonium|Pu]] | bgcolor="{{element color|f-block}}" | 95<br />[[americium|Am]] | bgcolor="{{element color|f-block}}" | 96<br />[[curium|Cm]] | bgcolor="{{element color|f-block}}" | 97<br />[[berkelium|Bk]] | bgcolor="{{element color|f-block}}" | 98<br />[[californium|Cf]] | bgcolor="{{element color|f-block}}" | 99<br />[[einsteinium|Es]] | bgcolor="{{element color|f-block}}" | 100<br />[[fermium|Fm]] | bgcolor="{{element color|f-block}}" | 101<br />[[mendelevium|Md]] | bgcolor="{{element color|f-block}}" | 102<br />[[nobelium|No]] | bgcolor="{{element color|d-block}}" | 103<br />[[lawrencium|Lr]] | bgcolor="{{element color|d-block}}" | 104<br />[[rutherfordium|Rf]] | bgcolor="{{element color|d-block}}" | 105<br />[[dubnium|Db]] | bgcolor="{{element color|d-block}}" | 106<br />[[seaborgium|Sg]] | bgcolor="{{element color|d-block}}" | 107<br />[[bohrium|Bh]] | bgcolor="{{element color|d-block}}" | 108<br />[[hassium|Hs]] | bgcolor="{{element color|d-block}}" | 109<br />[[meitnerium|Mt]] | bgcolor="{{element color|d-block}}" | 110<br />[[darmstadtium|Ds]] | bgcolor="{{element color|d-block}}" | 111<br />[[roentgenium|Rg]] | bgcolor="{{element color|d-block}}" | 112<br />[[copernicium|Cn]] | bgcolor="{{element color|p-block}}" | 113<br />[[nihonium|Nh]] | bgcolor="{{element color|p-block}}" | 114<br />[[flerovium|Fl]] | bgcolor="{{element color|p-block}}" | 115<br />[[moscovium|Mc]] | bgcolor="{{element color|p-block}}" | 116<br />[[livermorium|Lv]] | bgcolor="{{element color|p-block}}" | 117<br />[[tennessine|Ts]] | bgcolor="{{element color|p-block}}" | 118<br />[[oganesson|Og]] | 2×(1+3+5+7) = '''32''' elements<br />{{inline block|bg={{element color|s-block}}|7s}} {{inline block|bg={{element color|f-block}}|5f}} {{inline block|bg={{element color|d-block}}|6d}} {{inline block|bg={{element color|p-block}}|7p}} |} </div> This completes the modern periodic table, with all seven rows completely filled to capacity.<ref name="IUPAC-20161130" /><!--when 8th row elements are discovered, replace them here and write "The eighth row finishes prematurely as we run out of elements discovered."-->
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