Editing Bohr model (section)

== Shell model (heavier atoms) ==
{{Main|Electron shell}}

Bohr's original three papers in 1913 described mainly the electron configuration in lighter elements. 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 ''n'' electrons cannot rotate in a single ring round a nucleus of charge ''n<sub>e</sub>'' unless ''n'' < 8." For smaller atoms, the electron shells would be filled as follows: "rings of electrons will only join together 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 ''N'' = 10 an inner ring of eight electrons will occur". Bohr wrote "From the above we are led to the following possible scheme for the arrangement of the electrons in light atoms:"<ref name="Bohr 1913">{{Cite journal |last=Bohr |first=N. |date=1913 |title=On the Constitution of Atoms and Molecules, Part II. Systems containing only a Single Nucleus |journal=Philosophical Magazine |volume=26 |pages=476–502}}</ref><ref name=Kragh1979/><ref name="Heilbron & Kuhn 1969" />
{| class="wikitable" style="margin-left: auto; margin-right: auto;" <!-- this style idiom centers the table --> 
|+ Bohr's 1913 proposed configurations
|-
! Element !! Electrons per shell !! Element !! Electrons per shell !! Element !! Electrons per shell
|-
| 1 || 1    ||  9 || 4, 4, 1 || 17 || 8, 4, 4, 1
|-
| 2 || 2    || 10 || 8, 2    || 18 || 8, 8, 2
|-
| 3 || 2, 1 || 11 || 8, 2, 1 || 19 || 8, 8, 2, 1
|-
| 4 || 2, 2 || 12 || 8, 2, 2 || 20 || 8, 8, 2, 2
|-
| 5 || 2, 3 || 13 || 8, 2, 3 || 21 || 8, 8, 2, 3
|-
| 6 || 2, 4 || 14 || 8, 2, 4 || 22 || 8, 8, 2, 4
|-
| 7 || 4, 3 || 15 || 8, 4, 3 || 23 || 8, 8, 4, 3
|-
| 8 || 4, 2, 2 || 16 || 8, 4, 2, 2 || 24 || 8, 8, 4, 2, 2
|}
In Bohr's third 1913 paper Part III called "Systems Containing Several Nuclei", he says that two atoms form molecules on a symmetrical plane and he reverts to describing hydrogen.<ref>{{Cite journal |last=Bohr |first=N. |date=1 November 1913 |title=LXXIII. On the constitution of atoms and molecules |url=https://zenodo.org/record/1430922 |journal=The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science |volume=26 |issue=155 |pages=857–875 |doi=10.1080/14786441308635031|bibcode=1913PMag...26..857B }}</ref> The 1913 Bohr model did not discuss higher elements in detail and John William Nicholson was one of the first to prove in 1914 that it couldn't work for lithium, but was an attractive theory for hydrogen and ionized helium.<ref name="Heilbron & Kuhn 1969" /><ref>{{Cite journal |last=Nicholson |first=J. W. |date=May 1914 |title=The Constitution of Atoms and Molecules |url=https://zenodo.org/record/1429591 |journal=Nature |volume=93 |issue=2324 |pages=268–269 |bibcode=1914Natur..93..268N |doi=10.1038/093268a0 |s2cid=3977652}}</ref>

In 1921, following the work of chemists and others involved in work on the [[periodic table]], Bohr extended the model of hydrogen to give an approximate model for heavier atoms. This gave a physical picture that reproduced many known atomic properties for the first time although these properties were proposed contemporarily with the identical work of chemist [[Charles Rugeley Bury]]<ref name=Kragh1979/><ref>{{Cite journal |last=Bury |first=Charles R. |date=July 1921 |title=Langmuir's Theory of the Arrangement of Electrons in Atoms and Molecules |url=https://zenodo.org/record/1428812 |journal=Journal of the American Chemical Society |volume=43 |issue=7 |pages=1602–1609 |doi=10.1021/ja01440a023|bibcode=1921JAChS..43.1602B }}</ref>

Bohr's partner in research during 1914 to 1916 was [[Walther Kossel]] who corrected Bohr's work to show that electrons interacted through the outer rings, and Kossel called the rings: "shells".<ref name="Kossel1916">{{Cite journal |last=Kossel |first=W. |date=1916 |title=Über Molekülbildung als Frage des Atombaus |trans-title=On molecular formation as a question of atomic structure |url=https://zenodo.org/record/1447311 |journal=Annalen der Physik |language=de |volume=354 |issue=3 |pages=229–362 |bibcode=1916AnP...354..229K |doi=10.1002/andp.19163540302}}</ref><ref name="Kragh2012">{{Cite journal |last=Kragh |first=Helge |date=2012 |title=Lars Vegard, atomic structure, and the periodic system |url=http://acshist.scs.illinois.edu/bulletin_open_access/v37-1/v37-1%20p42-49.pdf |url-status=live |journal=Bulletin for the History of Chemistry |volume=37 |issue=1 |pages=42–49 |oclc=797965772 |archive-url=https://ghostarchive.org/archive/20221009/http://acshist.scs.illinois.edu/bulletin_open_access/v37-1/v37-1%20p42-49.pdf |archive-date=2022-10-09 |s2cid=53520045}}</ref> [[Irving Langmuir]] is credited with the first viable arrangement of electrons in shells with only two in the first shell and going up to eight in the next according to the [[octet rule]] of 1904, although Kossel had already predicted a maximum of eight per shell in 1916.<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://zenodo.org/record/1429026 |journal=Journal of the American Chemical Society |volume=41 |issue=6 |pages=868–934 |doi=10.1021/ja02227a002|bibcode=1919JAChS..41..868L }}</ref> Heavier atoms have more protons in the nucleus, and more electrons to cancel the charge. Bohr took from these chemists the idea that each discrete orbit could only hold a certain number of electrons. Per [[Kossel]], after that the orbit is full, the next level would have to be used.<ref name=Kragh1979/> This gives the atom a [[electron configuration|shell structure]] designed by Kossel, Langmuir, and Bury, in which each shell corresponds to a Bohr orbit.

This model is even more approximate than the model of hydrogen, because it treats the electrons in each shell as non-interacting. But the repulsions of electrons are taken into account somewhat by the phenomenon of [[Shielding effect|screening]]. The electrons in outer orbits do not only orbit the nucleus, but they also move around the inner electrons, so the effective charge Z that they feel is reduced by the number of the electrons in the inner orbit.

For example, the lithium atom has two electrons in the lowest 1s orbit, and these orbit at ''Z''&nbsp;=&nbsp;2. Each one sees the nuclear charge of ''Z''&nbsp;=&nbsp;3 minus the screening effect of the other, which crudely reduces the nuclear charge by 1 unit. This means that the innermost electrons orbit at approximately 1/2 the Bohr radius. The outermost electron in lithium orbits at roughly the Bohr radius, since the two inner electrons reduce the nuclear charge by 2. This outer electron should be at nearly one Bohr radius from the nucleus. Because the electrons strongly repel each other, the effective charge description is very approximate; the effective charge ''Z'' doesn't usually come out to be an integer.

The shell model was able to qualitatively explain many of the mysterious properties of atoms which became codified in the late 19th century in the [[periodic table of the elements]]. One property was the size of atoms, which could be determined approximately by measuring the [[viscosity]] of gases and density of pure crystalline solids. Atoms tend to get smaller toward the right in the periodic table, and become much larger at the next line of the table. Atoms to the right of the table tend to gain electrons, while atoms to the left tend to lose them. Every element on the last column of the table is chemically inert ([[noble gas]]).

In the shell model, this phenomenon is explained by shell-filling. Successive atoms become smaller because they are filling orbits of the same size, until the orbit is full, at which point the next atom in the table has a loosely bound outer electron, causing it to expand. The first Bohr orbit is filled when it has two electrons, which explains why helium is inert. The second orbit allows eight electrons, and when it is full the atom is neon, again inert. The third orbital contains eight again, except that in the more correct Sommerfeld treatment (reproduced in modern quantum mechanics) there are extra "d" electrons. The third orbit may hold an extra 10 d electrons, but these positions are not filled until a few more orbitals from the next level are filled (filling the n=3 d orbitals produces the 10 [[transition elements]]). The irregular filling pattern is an effect of interactions between electrons, which are not taken into account in either the Bohr or Sommerfeld models and which are difficult to calculate even in the modern treatment.