Editing Niels Bohr (section)

== Physics ==

=== Bohr model ===
{{Main|Bohr model}}
In September 1911, Bohr, supported by a fellowship from the [[Carlsberg Foundation]], travelled to England, where most of the theoretical work on the structure of atoms and molecules was being done.{{sfn|Kragh|2012|p=122}} He met [[J. J. Thomson]] of the [[Cavendish Laboratory]] and [[Trinity College, Cambridge]]. He attended lectures on [[electromagnetism]] given by [[James Jeans]] and [[Joseph Larmor]], and did some research on [[cathode ray]]s, but failed to impress Thomson.{{sfn|Kennedy|1985|p=6}}{{sfn|Pais|1991|pp=117–121}} He had more success with younger physicists like the Australian [[William Lawrence Bragg]],{{sfn|Kragh|2012|p=46}} and New Zealand's [[Ernest Rutherford]], whose 1911 small central nucleus [[Rutherford model]] of the [[atom]] had challenged Thomson's 1904 [[plum pudding model]].{{sfn|Pais|1991|pp=121–125}} Bohr received an invitation from Rutherford to conduct post-doctoral work at [[Victoria University of Manchester]],{{sfn|Kennedy|1985|p=7}} where Bohr met [[George de Hevesy]] and [[Charles Galton Darwin]] (whom Bohr referred to as "the grandson of the [[Charles Darwin|real Darwin]]").{{sfn|Pais|1991|pp=125–129}}

Bohr returned to Denmark in July 1912 for his wedding, and travelled around England and Scotland on his honeymoon. On his return, he became a ''[[privatdocent]]'' at the University of Copenhagen, giving lectures on [[thermodynamics]]. [[Martin Knudsen]] put Bohr's name forward for a ''[[docent]]'', which was approved in July 1913, and Bohr then began teaching medical students.{{sfn|Pais|1991|pp=134–135}} His three papers, which later became famous as "the trilogy",{{sfn|Kennedy|1985|p=7}} were published in ''[[Philosophical Magazine]]'' in July, September and November of that year.<ref>{{cite journal | first=Niels | last=Bohr | title=On the Constitution of Atoms and Molecules, Part I | journal=[[Philosophical Magazine]] | year=1913 | volume=26 | pages=1–24 | doi=10.1080/14786441308634955 | url=http://web.ihep.su/dbserv/compas/src/bohr13/eng.pdf | issue=151 | bibcode=1913PMag...26....1B | access-date=4 June 2009 | archive-date=2 September 2011 | archive-url=https://web.archive.org/web/20110902020206/http://web.ihep.su/dbserv/compas/src/bohr13/eng.pdf | url-status=live }}</ref><ref name="Bohr 1913 476">{{cite journal | first=Niels | last=Bohr | title=On the Constitution of Atoms and Molecules, Part II Systems Containing Only a Single Nucleus | journal=[[Philosophical Magazine]] | year=1913 | volume=26 | pages=476–502 | url=http://web.ihep.su/dbserv/compas/src/bohr13b/eng.pdf | doi=10.1080/14786441308634993 | issue=153 | bibcode=1913PMag...26..476B | access-date=21 October 2013 | archive-date=9 December 2008 | archive-url=https://web.archive.org/web/20081209111729/http://web.ihep.su/dbserv/compas/src/bohr13b/eng.pdf | url-status=live }}</ref><ref>{{cite journal | first=Niels | last=Bohr | title=On the Constitution of Atoms and Molecules, Part III Systems containing several nuclei | journal=[[Philosophical Magazine]] | year=1913 | volume=26 | pages=857–875 | issue=155 | doi=10.1080/14786441308635031 | url=https://zenodo.org/record/1430922 | bibcode=1913PMag...26..857B | access-date=1 July 2019 | archive-date=22 June 2021 | archive-url=https://web.archive.org/web/20210622091927/https://zenodo.org/record/1430922 | url-status=live }}</ref>{{sfn|Pais|1991|p=149}} He adapted Rutherford's nuclear structure to [[Max Planck]]'s quantum theory and so created his [[Bohr model]] of the atom.<ref name="Bohr 1913 476" />

Planetary models of atoms were not new, but Bohr's treatment was.{{sfn|Kragh|2012|p=22}} Taking the 1912 paper by Darwin on the role of electrons in the interaction of alpha particles with a nucleus as his starting point,<ref name="Darwin1912">{{cite journal|last1=Darwin|first1=Charles Galton|title=A theory of the absorption and scattering of the alpha rays|journal=[[Philosophical Magazine]]|volume=23|issue=138|year=1912|pages=901–920|issn=1941-5982|doi=10.1080/14786440608637291|url=https://zenodo.org/record/1430804|access-date=1 July 2019|archive-date=7 April 2020|archive-url=https://web.archive.org/web/20200407004543/https://zenodo.org/record/1430804|url-status=live}}</ref><ref name="Arabatzis2006">{{cite book|last=Arabatzis|first=Theodore |title=Representing Electrons: A Biographical Approach to Theoretical Entities|url=https://books.google.com/books?id=CdKZYot85OcC&pg=PA118|year=2006|publisher=University of Chicago Press|isbn=978-0-226-02420-2|page=118}}</ref> he advanced the theory of electrons travelling in [[orbit]]s of quantised "stationary states" around the atom's nucleus in order to stabilise the atom, but it wasn't until his 1921 paper that he showed that the chemical properties of each element were largely determined by the number of electrons in the outer orbits of its atoms.<ref>Kragh, Helge. "Niels Bohr's Second Atomic Theory". Historical Studies in the Physical Sciences, vol. 10, University of California Press, 1979, pp. 123–86, https://doi.org/10.2307/27757389 {{Webarchive|url=https://web.archive.org/web/20221017193849/https://online.ucpress.edu/hsns/article-abstract/doi/10.2307/27757389/47571/Niels-Bohr-s-Second-Atomic-Theory?redirectedFrom=fulltext |date=17 October 2022 }}.</ref><ref>N. Bohr, "Atomic Structure", Nature, 107. Letter dated 14 February 1921.</ref><ref>See [[Bohr model]] and [[Periodic Table]] for full development of electron structure of atoms.</ref>{{sfn|Kragh|1985|pp=50–67}} He introduced the idea that an electron could drop from a higher-energy orbit to a lower one, in the process emitting a [[quantum]] of discrete energy. This became a basis for what is now known as the [[old quantum theory]].{{sfn|Heilbron|1985|pp=39–47}}

[[File:Bohr-atom-PAR.svg|thumb|right|The '''Bohr model''' of the [[hydrogen atom]]. A negatively charged electron, confined to an [[atomic orbital]], orbits a small, positively charged nucleus; a quantum jump between orbits is accompanied by an emitted or absorbed amount of [[electromagnetic radiation]].|alt=Diagram showing electrons with circular orbits around the nucleus labelled n=1, 2 and 3. An electron drops from 3 to 2, producing radiation delta E = hv]]
[[File:Evolution of atomic models infographic.svg|thumb|right|The evolution of [[atomic model]]s in the 20th century: [[Plum pudding model|Thomson]], [[Rutherford model|Rutherford]], [[Bohr model|Bohr]], [[Atomic orbital|Heisenberg/Schrödinger]]]]
In 1885, [[Johann Balmer]] had come up with his [[Balmer series]] to describe the visible [[spectral line]]s of a [[hydrogen]] atom:
:<math>\frac{1}{\lambda} = R_\mathrm{H}\left(\frac{1}{2^2} - \frac{1}{n^2}\right) \quad \text{for} \ n=3,4,5,...</math>
where λ is the wavelength of the absorbed or emitted light and ''R''<sub>H</sub> is the [[Rydberg constant]].{{sfn|Heilbron|1985|p=43}} Balmer's formula was corroborated by the discovery of additional spectral lines, but for thirty years, no one could explain why it worked. In the first paper of his trilogy, Bohr was able to derive it from his model:
:<math> R_Z = { 2\pi^2 m_e Z^2 e^4 \over h^3 } </math>
where ''m''<sub>e</sub> is the electron's mass, ''e'' is its charge, ''h'' is the [[Planck constant]] and ''Z'' is the atom's [[atomic number]] (1 for hydrogen).{{sfn|Pais|1991|pp=146–149}}

The model's first hurdle was the [[Pickering series]], lines that did not fit Balmer's formula. When challenged on this by [[Alfred Fowler]], Bohr replied that they were caused by [[ionised]] [[helium]], helium atoms with only one electron. The Bohr model was found to work for such ions.{{sfn|Pais|1991|pp=146–149}} Many older physicists, like Thomson, Rayleigh and [[Hendrik Lorentz]], did not like the trilogy, but the younger generation, including Rutherford, [[David Hilbert]], [[Albert Einstein]], [[Enrico Fermi]], [[Max Born]] and [[Arnold Sommerfeld]] saw it as a breakthrough.{{sfn|Pais|1991|pp=152–155}}{{sfn|Kragh|2012|pp=109–111}} Einstein called Bohr's model "the highest form of musicality in the sphere of thought."<ref>{{cite book| last=Pais| first=Abraham| title=Subtle is the Lord: The Science and the Life of Albert Einstein| year=1982| page=416}}</ref> The trilogy's acceptance was entirely due to its ability to explain phenomena that stymied other models, and to predict results that were subsequently verified by experiments.{{sfn|Kragh|2012|pp=90–91}}<ref>{{cite web|url=https://blogs.cranfield.ac.uk/leadership-management/cbp/forecasting-prediction-is-very-difficult-especially-if-its-about-the-future|title=Forecasting – Prediction is very difficult, especially if it's about the future!|website=cranfield.ac.cuk|date=10 July 2017|quote=Prediction is very difficult, especially if it's about the future|access-date=14 July 2021|archive-date=14 July 2021|archive-url=https://web.archive.org/web/20210714133210/https://blogs.cranfield.ac.uk/leadership-management/cbp/forecasting-prediction-is-very-difficult-especially-if-its-about-the-future|url-status=live}}</ref> Today, the Bohr model of the atom has been superseded, but is still the best known model of the atom, as it often appears in high school physics and chemistry texts.{{sfn|Kragh|2012|p=39}}

Bohr did not enjoy teaching medical students. He later admitted that he was not a good lecturer, because he needed a balance between clarity and truth, between "Klarheit und Wahrheit".<ref>{{cite book |last=Weisskopf |first=Victor |title="Niels Bohr, the Quantum, and the World" Social Research 51, no. 3 |date=1984 |pages=593}}</ref> He decided to return to Manchester, where Rutherford had offered him a job as a [[reader (academic rank)|reader]] in place of Darwin, whose tenure had expired. Bohr accepted. He took a leave of absence from the University of Copenhagen, which he started by taking a holiday in [[South Tyrol|Tyrol]] with his brother Harald and aunt [[Hanna Adler]]. There, he visited the [[University of Göttingen]] and the [[Ludwig Maximilian University of Munich]], where he met Sommerfeld and conducted seminars on the trilogy. The First World War broke out while they were in Tyrol, greatly complicating the trip back to Denmark and Bohr's subsequent voyage with Margrethe to England, where he arrived in October 1914. They stayed until July 1916, by which time he had been appointed to the Chair of Theoretical Physics at the University of Copenhagen, a position created especially for him. His docentship was abolished at the same time, so he still had to teach physics to medical students. New professors were formally introduced to King [[Christian X]], who expressed his delight at meeting such a famous football player.{{sfn|Pais|1991|pp=164–167}}

=== Institute of Physics ===
In April 1917, Bohr began a campaign to establish an Institute of Theoretical Physics. He gained the support of the Danish government and the Carlsberg Foundation, and sizeable contributions were also made by industry and private donors, many of them Jewish. Legislation establishing the institute was passed in November 1918. Now known as the [[Niels Bohr Institute]], it opened on 3 March 1921, with Bohr as its director. His family moved into an apartment on the first floor.<ref>{{cite web | url=http://www.nbi.ku.dk/english/www/institute/History/history/ | title=History of the institute: The establishment of an institute | publisher=Niels Bohr Institute |last=Aaserud |first=Finn |archive-url=https://web.archive.org/web/20080405160424/http://www.nbi.ku.dk/english/about/history/ |archive-date=5 April 2008 |access-date=11 May 2008| date=January 1921 }}</ref>{{sfn|Pais|1991|pp=169–171}} Bohr's institute served as a focal point for researchers into [[quantum mechanics]] and related subjects in the 1920s and 1930s, when most of the world's best-known theoretical physicists spent some time in his company. Early arrivals included [[Hans Kramers]] from the Netherlands, [[Oskar Klein]] from Sweden, George de Hevesy from Hungary, [[Wojciech Rubinowicz]] from Poland, and [[Svein Rosseland]] from Norway. Bohr became widely appreciated as their congenial host and eminent colleague.{{sfn|Kennedy|1985|pp=9, 12, 13, 15}}{{sfn|Hund|1985|pp=71–73}} Klein and Rosseland produced the institute's first publication even before it opened.{{sfn|Pais|1991|pp=169–171}}

[[File:Niels Bohr Institute 1.jpg|thumb|The [[Niels Bohr Institute]], part of the [[University of Copenhagen]]|alt=A block-shaped beige building with a sloped, red tiled roof]]
The Bohr model worked well for hydrogen and ionized single-electron helium, which impressed Einstein<ref>From Bohr's Atom to Electron Waves https://galileo.phys.virginia.edu/classes/252/Bohr_to_Waves/Bohr_to_Waves.html {{Webarchive|url=https://web.archive.org/web/20210810030204/http://galileo.phys.virginia.edu/classes/252/Bohr_to_Waves/Bohr_to_Waves.html |date=10 August 2021 }}</ref><ref>The Age of Entanglement, Louisa Gilder, p.799, 2008.</ref> but could not explain more complex elements. By 1919, Bohr was moving away from the idea that electrons orbited the nucleus and developed [[heuristic]]s to describe them. The [[rare-earth element]]s posed a particular classification problem for chemists because they were so chemically similar. An important development came in 1924 with [[Wolfgang Pauli]]'s discovery of the [[Pauli exclusion principle]], which put Bohr's models on a firm theoretical footing. Bohr was then able to declare that the as-yet-undiscovered element 72 was not a rare-earth element but an element with chemical properties similar to those of [[zirconium]]. (Elements had been predicted and discovered since 1871 by chemical properties<ref>See [[Periodic Table]] and [[History of the periodic table]] showing elements predicted by chemical properties since [[Mendeleev]].</ref>), and Bohr was immediately challenged by the French chemist [[Georges Urbain]], who claimed to have discovered a rare-earth element 72, which he called "celtium". At the Institute in Copenhagen, [[Dirk Coster]] and George de Hevesy took up the challenge of proving Bohr right and Urbain wrong. Starting with a clear idea of the chemical properties of the unknown element greatly simplified the search process. They went through samples from Copenhagen's Museum of Mineralogy looking for a zirconium-like element and soon found it. The element, which they named [[hafnium]] (''hafnia'' being the Latin name for Copenhagen), turned out to be more common than gold.{{sfn|Kragh|1985|pp=61–64}}{{sfn|Pais|1991|pp=202–210}}

In 1922, Bohr was awarded the [[Nobel Prize in Physics]] "for his services in the investigation of the structure of atoms and of the radiation emanating from them".{{sfn|Pais|1991|p=215}} The award thus recognised both the trilogy and his early leading work in the emerging field of quantum mechanics. For his Nobel lecture, Bohr gave his audience a comprehensive survey of what was then known about the structure of the atom, including the [[correspondence principle]], which he had formulated. This states that the behaviour of systems described by quantum theory reproduces [[classical physics]] in the limit of large [[quantum number]]s.{{sfn|Bohr|1985|pp=91–97}}

The discovery of [[Compton scattering]] by [[Arthur Holly Compton]] in 1923 convinced most physicists that light was composed of [[photon]]s and that energy and momentum were conserved in collisions between electrons and photons. In 1924, Bohr, Kramers, and [[John C. Slater]], an American physicist working at the Institute in Copenhagen, proposed the [[Bohr–Kramers–Slater theory]] (BKS). It was more of a program than a full physical theory, as the ideas it developed were not worked out quantitatively. The BKS theory became the final attempt at understanding the interaction of matter and electromagnetic radiation on the basis of the old quantum theory, in which quantum phenomena were treated by imposing quantum restrictions on a classical wave description of the electromagnetic field.<ref>{{cite journal|last1=Bohr |first1=N. |first2=H. A. |last2=Kramers |author-link2=Hans Kramers |last3=Slater |first3=J. C. |author-link3=John C. Slater |journal=Philosophical Magazine |doi=10.1080/14786442408565262 |url=http://www.cond-mat.physik.uni-mainz.de/~oettel/ws10/bks_PhilMag_47_785_1924.pdf |title=The Quantum Theory of Radiation |series=6 |volume=76 |issue=287 |year=1924 |access-date=18 February 2013 |pages=785–802 |archive-url=https://web.archive.org/web/20130522110143/http://www.cond-mat.physik.uni-mainz.de/~oettel/ws10/bks_PhilMag_47_785_1924.pdf |archive-date=22 May 2013 }}</ref>{{sfn|Pais|1991|pp=232–239}}

Modelling atomic behaviour under incident electromagnetic radiation using "virtual oscillators" at the absorption and emission frequencies, rather than the (different) apparent frequencies of the Bohr orbits, led Max Born, [[Werner Heisenberg]] and Kramers to explore different mathematical models. They led to the development of [[matrix mechanics]], the first form of modern [[quantum mechanics]]. The BKS theory also generated discussion of, and renewed attention to, difficulties in the foundations of the old quantum theory.{{sfn|Jammer|1989|p=188}} The most provocative element of BKS – that momentum and energy would not necessarily be conserved in each interaction, but only statistically – was soon shown to be in conflict with experiments conducted by [[Walther Bothe]] and [[Hans Geiger]].{{sfn|Pais|1991|p=237}} In light of these results, Bohr informed Darwin that "there is nothing else to do than to give our revolutionary efforts as honourable a funeral as possible".{{sfn|Pais|1991|p=238}}

=== Quantum mechanics ===
The introduction of [[Spin (physics)|spin]] by [[George Uhlenbeck]] and [[Samuel Goudsmit]] in November 1925 was a milestone. The next month, Bohr travelled to [[Leiden]] to attend celebrations of the 50th anniversary of Hendrick Lorentz receiving his doctorate. When his train stopped in [[Hamburg]], he was met by Wolfgang Pauli and [[Otto Stern]], who asked for his opinion of the spin theory. Bohr pointed out that he had concerns about the interaction between electrons and magnetic fields. When he arrived in Leiden, [[Paul Ehrenfest]] and Albert Einstein informed Bohr that Einstein had resolved this problem using [[Theory of relativity|relativity]]. Bohr then had Uhlenbeck and Goudsmit incorporate this into their paper. Thus, when he met Werner Heisenberg and [[Pascual Jordan]] in [[Göttingen]] on the way back, he had become, in his own words, "a prophet of the electron magnet gospel".{{sfn|Pais|1991|p=243}}

{{multiple image
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Heisenberg first came to Copenhagen in 1924, then returned to Göttingen in June 1925, shortly thereafter developing the mathematical foundations of quantum mechanics. When he showed his results to Max Born in Göttingen, Born realised that they could best be expressed using [[Matrix (mathematics)|matrices]]. This work attracted the attention of the British physicist [[Paul Dirac]],{{sfn|Pais|1991|pp=275–279}} who came to Copenhagen for six months in September 1926. Austrian physicist [[Erwin Schrödinger]] also visited in 1926. His attempt at explaining quantum physics in classical terms using wave mechanics impressed Bohr, who believed it contributed "so much to mathematical clarity and simplicity that it represents a gigantic advance over all previous forms of quantum mechanics".{{sfn|Pais|1991|pp=295–299}}

When Kramers left the institute in 1926 to take up a chair as professor of theoretical physics at the [[Utrecht University]], Bohr arranged for Heisenberg to return and take Kramers's place as a ''[[lektor]]'' at the University of Copenhagen.{{sfn|Pais|1991|p=263}} Heisenberg worked in Copenhagen as a university lecturer and assistant to Bohr from 1926 to 1927.{{sfn|Pais|1991|pp=272–275}}

Bohr became convinced that light behaved like both waves and particles and, in 1927, experiments confirmed the [[de Broglie hypothesis]] that matter (like electrons) also behaved like waves.{{sfn|Pais|1991|p=301}} He conceived the philosophical principle of [[Complementarity (physics)|complementarity]]: that items could have apparently mutually exclusive properties, such as being a wave or a stream of particles, depending on the experimental framework.{{sfn|MacKinnon|1985|pp=112–113}} He felt that it was not fully understood by professional philosophers.{{sfn|MacKinnon|1985|p=101}}

In February 1927, Heisenberg developed the first version of the [[uncertainty principle]], presenting it using a [[thought experiment]] where an electron was observed through a [[gamma-ray microscope]]. Bohr was dissatisfied with Heisenberg's argument, since it required only that a measurement disturb properties that already existed, rather than the more radical idea that the electron's properties could not be discussed at all apart from the context they were measured in. In a paper presented at the [[Como Conference]] in September 1927, Bohr emphasised that Heisenberg's uncertainty relations could be derived from classical considerations about the resolving power of optical instruments.{{sfn|Pais|1991|pp=304–309}} Understanding the true meaning of complementarity would, Bohr believed, require "closer investigation".{{sfn|Bohr|1928|p=582}} Einstein preferred the determinism of classical physics over the probabilistic new quantum physics to which he himself had contributed. Philosophical issues that arose from the novel aspects of quantum mechanics became widely celebrated subjects of discussion. Einstein and Bohr had [[Bohr–Einstein debates|good-natured arguments]] over such issues throughout their lives.{{sfn|Dialogue|1985|pp=121–140}}

In 1914 [[Carl Jacobsen]], the heir to [[Carlsberg Group|Carlsberg breweries]], bequeathed his mansion (the Carlsberg Honorary Residence, currently known as Carlsberg Academy) to be used for life by the Dane who had made the most prominent contribution to science, literature or the arts, as an honorary residence ({{langx|da|Æresbolig|links=no}}). Harald Høffding had been the first occupant, and upon his death in July 1931, the Royal Danish Academy of Sciences and Letters gave Bohr occupancy. He and his family moved there in 1932.{{sfn|Pais|1991|pp=332–333}} He was elected president of the Academy on 17 March 1939.{{sfn|Pais|1991|pp=464–465}}

By 1929 the phenomenon of [[beta decay]] prompted Bohr to again suggest that the [[law of conservation of energy]] be abandoned, but [[Wolfgang Pauli]]'s hypothetical [[neutrino]] and the subsequent 1932 discovery of the [[neutron]] provided another explanation. This prompted Bohr to create a new theory of the [[compound nucleus]] in 1936, which explained how neutrons could be captured by the nucleus. In this model, the nucleus could be deformed like a drop of liquid. He worked on this with a new collaborator, the Danish physicist Fritz Kalckar, who died suddenly in 1938.{{sfn|Pais|1991|pp=337–340, 368–370}}<ref>{{cite journal |title=Transmutations of Atomic Nuclei |last=Bohr |first=Niels |journal=[[Science (journal)|Science]] |date=20 August 1937 |volume=86 |issue=2225 |pages=161–165 |doi=10.1126/science.86.2225.161 |bibcode = 1937Sci....86..161B |pmid=17751630}}</ref>

The discovery of [[nuclear fission]] by [[Otto Hahn]] in December 1938 (and its theoretical explanation by [[Lise Meitner]]) generated intense interest among physicists. Bohr brought the news to the United States where he opened the fifth [[Washington Conference on Theoretical Physics]] with Fermi on 26 January 1939.{{sfn|Stuewer|1985|pp=211–216}} When Bohr told [[George Placzek]] that this resolved all the mysteries of [[transuranic elements]], Placzek told him that one remained: the neutron capture energies of uranium did not match those of its decay. Bohr thought about it for a few minutes and then announced to Placzek, [[Léon Rosenfeld]] and [[John Archibald Wheeler|John Wheeler]] that "I have understood everything."{{sfn|Pais|1991|p=456}} Based on his [[liquid drop model]] of the nucleus, Bohr concluded that it was the [[uranium-235]] isotope and not the more abundant [[uranium-238]] that was primarily responsible for fission with thermal neutrons. In April 1940, [[John R. Dunning]] demonstrated that Bohr was correct.{{sfn|Stuewer|1985|pp=211–216}} In the meantime, Bohr and Wheeler developed a theoretical treatment, which they published in a September 1939 paper on "The Mechanism of Nuclear Fission".<ref>{{cite journal |last1=Bohr |first1=Niels |last2=Wheeler |first2=John Archibald |author-link2=John Archibald Wheeler |title=The Mechanism of Nuclear Fission |journal=[[Physical Review]] |volume=56 |issue=5 |pages=426–450 |date=September 1939 |doi=10.1103/PhysRev.56.426 |url=http://www.pugetsound.edu/files/resources/7579_Bohr%20liquid%20drop.pdf |bibcode=1939PhRv...56..426B |doi-access=free |access-date=22 October 2013 |archive-date=24 September 2015 |archive-url=https://web.archive.org/web/20150924083202/http://www.pugetsound.edu/files/resources/7579_Bohr%20liquid%20drop.pdf |url-status=live }}</ref>