# Bohr model The **Bohr model** is the picture of the [[Atom|atom]] that [[Niels_Bohr|Niels Bohr]] published in 1913: a small, heavy, positively charged [[Atomic_nucleus|nucleus]] with an [[Electron|electron]] circling it on one of a discrete set of allowed orbits, each orbit holding a fixed energy, and light emitted or absorbed only when the electron jumps from one orbit to another.[^bohr1913-i] For [[Hydrogen|hydrogen]] and for one-electron ions such as He⁺ and Li²⁺ the model gives the energy ladder E_n = −2.179×10⁻¹⁸ Z²/n² J and the orbit radii r_n = n²a₀/Z, and from the ladder it predicts every line in the hydrogen [[Emission_spectrum|emission spectrum]].[^b054-bohr][^openstax-bohr] In the microsim below the reader picks the starting level n_i (3 to 12) and a nuclear charge preset Z = 1, 2 or 3, watches the electron drop to n_f = 2, and reads the photon that leaves: ΔE = 2.179×10⁻¹⁸ Z² (1/n_f² − 1/n_i²) J and λ = hc/ΔE, drawn as a coloured line on a spectrum strip. On the Chemistry flagship this article serves Part II — Modern principles › Matter, at the section *Energy levels: the Bohr model* (row K4), the step between the nuclear atom and the [[Electron_configuration|electron configurations]] that the [[Aufbau_principle|Aufbau principle]] builds on it. [[Quantum_mechanics|Quantum mechanics]] replaced the model within thirteen years, but it remains the first theory in which atomic energies are quantized, and its energy formula survives unchanged in the [[Schrödinger_equation|Schrödinger equation]]'s solution for the [[Hydrogen_atom|hydrogen atom]]. ## Background By 1913 physicists knew that atoms contain electrons balanced by a positive charge, and that each element emits sharp, characteristic [[Spectral_line|spectral lines]]; what they lacked was a mechanism that could hold an atom together and explain the lines. ### Planetary models Electrons circling a central body like planets around the [[Sun|Sun]] predate the nucleus: in 1904 Hantaro Nagaoka proposed a "Saturnian" atom, a large positive centre ringed by electrons, to account for spectra and radioactivity.[^nagaoka1904] Classical [[Electromagnetic_radiation|electromagnetic]] theory objected at once: an orbiting electron is an accelerating charge and must radiate and spiral inward. ### Thomson's atom model J. J. Thomson's model of 1904 put the negative "corpuscles" inside a uniform sphere of positive electricity, arranged in concentric rings whose stable populations he hoped would explain the periodic system.[^thomson1904] The picture is now called the [[Plum_pudding_model|plum pudding model]]; it has no nucleus and gives no sharp lines. ### Rutherford nuclear model In 1911 [[Ernest_Rutherford|Ernest Rutherford]] showed from the large-angle scattering of [[Alpha_particle|alpha particles]] by thin foils that the positive charge and nearly all the mass sit in a nucleus far smaller than the atom.[^rutherford1911] The [[Rutherford_model|Rutherford model]] made the planetary picture unavoidable and the radiation problem acute. ### Atomic spectra In 1885 Johann Balmer fitted the four visible hydrogen lines with one formula in the integers 3 to 6,[^balmer1885] and in 1890 Johannes Rydberg generalised it to 1/λ = R (1/n₁² − 1/n₂²), covering the whole [[Hydrogen_spectral_series|hydrogen spectral series]].[^rydberg1890] The formula was exact and unexplained, and its constant R had no known link to the electron. ### Haas atomic model In 1910 Arthur Erich Haas first brought [[Max_Planck|Planck's]] constant into the atom: equating the quantum hν to the energy of an electron at the surface of Thomson's sphere gave an atomic radius in terms of h, the electron charge and the electron mass, with the form of the later Bohr radius.[^heilbron-kuhn] ### Influence of the Solvay Conference The first Solvay Conference, held in Brussels in the autumn of 1911 on radiation and quanta, put the [[Planck_constant|quantum hypothesis]] before the leading physicists of Europe. Rutherford attended, and the historians John Heilbron and Thomas Kuhn trace through him part of the route by which the Brussels questions reached Bohr in Manchester.[^heilbron-kuhn] ### Nicholson atom theory John William Nicholson's ring atom of 1912 was built to explain unidentified lines in the solar corona and in nebulae. The [[Angular_momentum|angular momentum]] of his rings came in integer multiples of h/2π, which Heilbron and Kuhn identify as the quantization condition Bohr adopted and as the work that turned his attention to spectra.[^heilbron-kuhn] ### Bohr's previous work Bohr's 1911 Copenhagen doctorate on the electron theory of metals had convinced him that classical mechanics failed inside the atom. He reached Cambridge in the autumn of 1911 and Rutherford's laboratory in March 1912, where his unpublished "Rutherford memorandum" of mid-1912 on the stability of the nuclear atom became the direct ancestor of the 1913 papers.[^heilbron-kuhn] ## Development Bohr's theory appeared in three parts in the *Philosophical Magazine* during 1913.[^bohr1913-i][^bohr1913-ii][^bohr1913-iii] Part I set out the postulates: an electron can occupy only certain "stationary states" in which, against classical electrodynamics, it does not radiate; the energies of the states are fixed by a quantum condition that amounts to angular momentum in whole multiples of h/2π; and radiation is emitted or absorbed only in a transition between two states, with a frequency ν given by hν = E_initial − E_final.[^bohr1913-i] From these statements Bohr derived Balmer's formula, and he obtained the Rydberg constant as a combination of the electron's charge and mass, Planck's constant and the [[Speed_of_light|speed of light]], reproducing its measured value.[^bohr1913-i] The same paper settled a puzzle: lines seen by Pickering in the star ζ Puppis and by Fowler in a discharge tube fitted a Balmer-like formula with half-integers, and Bohr showed they belong to singly ionised [[Helium|helium]], He⁺, whose doubled nuclear charge makes every energy four times the hydrogen value.[^bohr1913-i] Bohr received the Nobel Prize in Physics for 1922 "for his services in the investigation of the structure of atoms and of the radiation emanating from them".[^nobel1922] ## Refinements The theory that grew from Bohr's papers between 1913 and 1925 is now called the old quantum theory. Arnold Sommerfeld's 1916 paper generalised the circular orbits to ellipses, introduced a second [[Quantum_number|quantum number]] for the orbit's shape, and added the [[Special_relativity|relativistic]] variation of the electron's mass with speed; the relativistic correction split each hydrogen level by a small amount and reproduced the observed fine structure of the lines.[^sommerfeld1916] A third quantum number, for the orbit's orientation in a [[Magnetic_field|magnetic field]], gave the normal Zeeman splitting. Bohr's [[Correspondence_principle|correspondence principle]], the requirement that quantum results go over into classical ones for large quantum numbers, decided which transitions were allowed and how bright they should be. Each refinement rescued a class of measurements, and each added a rule that the theory could state but not justify. By 1924 the old theory had become a catalogue of such rules, and its failures on helium and on the anomalous Zeeman effect were well known. ## Replacement Between 1924 and 1926 the orbits disappeared. Louis de Broglie's thesis of 1924 proposed that a moving electron has a wavelength h/p; on that view Bohr's quantum condition says that a whole number of wavelengths fits around the orbit, so that the orbit is a [[Standing_wave|standing wave]].[^debroglie1924] [[Werner_Heisenberg|Werner Heisenberg]]'s matrix mechanics of 1925 dispensed with orbits altogether,[^heisenberg1925] and in early 1926 Wolfgang Pauli obtained the hydrogen spectrum from it.[^pauli1926] [[Erwin_Schrödinger|Erwin Schrödinger]]'s wave equation, published the same year, gave the same energy levels as Bohr's formula with the electron described by a [[Wave_function|wave function]] rather than a path.[^schrodinger1926] In the new theory the ground-state electron of hydrogen has zero orbital angular momentum, not h/2π, and the [[Uncertainty_principle|uncertainty principle]] rules out any orbit with a definite radius and a definite speed. The [[Atomic_orbital|atomic orbital]] replaced the ring, and of the model's results only the energy formula came through unchanged. ## Electron energy levels For a nucleus of charge Z with a single electron, the Bohr model gives the allowed energies E_n = −2.179×10⁻¹⁸ × Z²/n² J, n = 1, 2, 3, … where the constant 2.179×10⁻¹⁸ J is the ionization energy of hydrogen from its ground state,[^b054-bohr][^openstax-bohr] equal to 13.60 [[Electronvolt|electronvolts]] at 1 eV = 1.602×10⁻¹⁹ J, or 1,312 kJ per mole (derived). The energy released when the electron drops from level n_i to level n_f is ΔE = 2.179×10⁻¹⁸ × Z² × (1/n_f² − 1/n_i²) J, and the emitted [[Photon|photon]] has wavelength λ = hc/ΔE with h = 6.6262×10⁻³⁴ J·s and c = 2.998×10⁸ m/s.[^b054-bohr] The orbit of level n has radius r_n = n²a₀/Z with a₀ = 5.292×10⁻¹¹ m, the Bohr radius.[^b052-hydrogenic][^b054-radius] This is the equation the microsim computes; its HUD carries `dE = 2.179e-18*Z^2*(1/nf^2 - 1/ni^2) J` and `lambda = h*c/dE`. The reader has one control, n_i from 3 to 12, and three presets, Z = 1 for H, Z = 2 for He⁺ and Z = 3 for Li²⁺; the lower level is fixed at n_f = 2, so the reader is building the [[Balmer_series|Balmer series]]. Rings are drawn at r_n = n²a₀/Z, the electron drops from the outer ring to the second, and the photon appears on a 380–750 nm strip, with the series limit dashed and lines outside the visible band shown as labelled ultraviolet or infrared ticks. The drop animation and the strip colours are ILLUSTRATIVE: the model has no trajectory between states, and the colours come from an sRGB lookup, not from the sources. The textbook's worked number is the hydrogen line for n_i = 5: ΔE = 2.179×10⁻¹⁸ × (1/4 − 1/25) = 4.576×10⁻¹⁹ J = 2.856 eV, and λ = hc/ΔE = 434 nm, the violet Hγ line.[^b054-bohr] The same constants give the rest of the series (all derived): n_i = 3 releases 3.026×10⁻¹⁹ J at 656 nm, the red Hα line, the 656.3 nm photon of the book's own energy exercise;[^b054-bohr] n_i = 4 gives 486 nm, blue-green; and as n_i → ∞ the lines crowd toward the series limit at ΔE = 2.179×10⁻¹⁸/4 J, or 365 nm, just past the violet end of the strip. The Z presets show why the constant carries Z². The ground state of He⁺ lies at −8.716×10⁻¹⁸ J, four times deeper than hydrogen's, and the n = 8 level of hydrogen at −3.405×10⁻²⁰ J.[^b054-bohr] The 2 → 1 jump in Li²⁺ releases 1.471×10⁻¹⁷ J,[^b054-bohr] nine times the hydrogen value, and with Z = 2 every Balmer-like line leaves the visible strip for the ultraviolet. The [[Hydrogen-like_atom|hydrogen-like atom]] article gives the same [[Energy_level|energy levels]] in modern form. ### Derivation Two equations fix the orbits. [[Coulomb's_law|Coulomb's law]] supplies the centripetal force, k Z e²/r² = m v²/r with k = 1/(4πε₀), and Bohr's quantum condition fixes the angular momentum, m v r = n ħ with ħ = h/2π. Eliminating v gives r_n = n² ħ²/(k m Z e²) = n² a₀/Z, which defines a₀ = ħ²/(k m e²). The [[Kinetic_energy|kinetic energy]] is half the magnitude of the [[Potential_energy|potential energy]], so the total is E_n = −k Z e²/(2 r_n) = −(k² m e⁴/2ħ²) × Z²/n². With the Hartree energy E_h = k² m e⁴/ħ² = 4.360×10⁻¹⁸ J this is E_n = −(Z²/2n²) E_h, the inorganic text's form.[^b052-hydrogenic] Half of E_h is 2.180×10⁻¹⁸ J, which agrees with the bonding text's 2.179×10⁻¹⁸ J to 0.05 percent (derived); the books differ only in rounding. ## Rydberg formula Dividing ΔE by hc turns the energy ladder into Rydberg's reciprocal-wavelength formula, 1/λ = R Z² (1/n_f² − 1/n_i²), and identifies the constant Rydberg had fitted in 1890 with a combination of fundamental constants, R = k² m e⁴/(4π ħ³ c).[^rydberg1890][^bohr1913-i] Its recommended value for an infinitely heavy nucleus is R∞ = 1.097 373 1568×10⁷ m⁻¹.[^codata] The book's rounded constants give 2.179×10⁻¹⁸ J divided by hc, or 1.0969×10⁷ m⁻¹ (derived), 0.05 percent below the recommended value. For real hydrogen the electron and the [[Proton|proton]] orbit their common centre of mass, which multiplies R by 1/(1 + m_e/m_p) and lowers it by 0.054 percent, the correction that separates hydrogen from [[Deuterium|deuterium]] lines. In the [[Rydberg_formula|Rydberg formula]] each choice of n_f names a series: n_f = 1 is the Lyman series in the ultraviolet, n_f = 2 the Balmer series in the visible, and n_f = 3 the Paschen series in the infrared, each with its own limit at n_i → ∞. ## Shell model (heavier atoms) Bohr's Part II arranged the electrons of heavier atoms in concentric rings, but the rings could not be made to reproduce chemistry.[^bohr1913-ii] Irving Langmuir's 1919 paper, working from chemical valence rather than from spectra, placed electrons in shells of 2, 8, 8 and 18 and tied the closed shells to the inertness of the noble gases.[^langmuir1919] In his Nobel lecture of December 11, 1922, Bohr presented his own assignment of electrons to groups of orbits, built from the quantum numbers of the old theory and from X-ray and optical spectra, and showed how the lengths of the periods of the [[Periodic_table|periodic table]] follow from the way the groups close.[^bohr-nobel-lecture] This was the origin of the [[Electron_shell|electron shell]] picture that the Aufbau principle later formalised with the [[Pauli_exclusion_principle|Pauli exclusion principle]]. ## Moseley's law and calculation (K-alpha X-ray emission lines) In 1913 Henry Moseley measured the characteristic X-ray lines of the elements from calcium to zinc and found that the square root of the frequency of the strongest line, Kα, is linear in an integer he identified with the [[Atomic_number|atomic number]]. He wrote the K-line frequency as ν = (3/4) ν₀ (N − 1)², with ν₀ the Rydberg frequency, and noted the agreement with Bohr's theory.[^moseley1913] The Bohr reading is direct. A Kα photon is emitted when an electron falls from n = 2 to a vacancy at n = 1; the one remaining n = 1 electron screens one unit of nuclear charge, so the effective Z is Z − 1 and E(Kα) ≈ 2.179×10⁻¹⁸ J × (Z − 1)² × (1/1² − 1/2²) = 13.60 eV × (3/4) × (Z − 1)². For [[Copper|copper]], Z = 29, this gives 10.20 eV × 28² = 8.00 keV (derived), within 0.6 percent of the measured Kα₁ line at 8,047.8 eV.[^nist-xray] Moseley's measurements fixed the atomic numbers, exposed gaps in the periodic table, and showed that Z, not mass, orders the elements. ## Shortcomings The model fails as soon as a second electron is present. Bohr could not extend it to helium, and no arrangement of orbits accounts for the interaction between electrons.[^openstax-bohr] Within hydrogen it predicts the positions of lines but nothing about their intensities or widths, which the correspondence principle could only estimate, and it says nothing about how long an excited state lasts. It gives the fine structure only after Sommerfeld's relativistic patch, and it never explained the anomalous Zeeman effect, which required electron [[Spin_(physics)|spin]]. Its central object, an electron with a definite radius and speed, contradicts the uncertainty principle, and its ground-state angular momentum, ħ, is wrong: the Schrödinger solution gives zero. The bonding textbook's verdict is that the model gives the right energies for the wrong reasons.[^b054-wrong] What it gets right is the quantization of energy and the frequency condition hν = ΔE, and those two ideas passed intact into quantum mechanics. ## Model of the chemical bond Part III of the 1913 trilogy applied the ring picture to molecules. In Bohr's H₂ the two nuclei sit on an axis and the two electrons circulate together in a ring in the plane midway between them, perpendicular to the axis, held in dynamic equilibrium by the balance of attraction to the nuclei and repulsion between the electrons.[^bohr1913-iii] The picture gave a bound [[Diatomic_molecule|diatomic molecule]], but it could not be extended to other molecules and does not survive the quantum treatment of the [[Covalent_bond|covalent bond]], in which the electrons share an orbital rather than a ring. The quantity a modern model must reproduce is the bond dissociation enthalpy of H₂, 436 kJ/mol.[^b054-h2] ## Symbolism of planetary atomic models The nucleus ringed by elliptical orbits became the twentieth century's emblem of the atom and of atomic energy, decades after physics had abandoned orbits. Unicode encodes it as the character ⚛, U+269B ATOM SYMBOL in the Miscellaneous Symbols block, with the annotation that it marks a nuclear installation on maps.[^unicode] The sign shows three interlocking ellipses around a dot, a schematic of the Bohr–Sommerfeld atom rather than of any orbital, and it still marks agencies and [[Nuclear_power|nuclear power]] operators whose physics is entirely post-Bohr. ## See also - [[Hydrogen-like_atom]] - [[Energy_level]] - [[Rydberg_formula]] - [[Balmer_series]] - [[Rutherford_model]] - [[Atomic_orbital]] ## References ### Footnotes [^b054-bohr]: Blackstock, Lindsay; Brewer, Sharon; Cinel, Bruno (2022). *Chemical Bonding and Organic Chemistry*. Chapter 2, "Quantum Theory and Electronic Structure of Atoms", pp. 176–184 (photon and Bohr exercises with printed answers; E_n = −2.179×10⁻¹⁸/n² J at p. 181; H 5 → 2 = 4.576×10⁻¹⁹ J = 2.856 eV at p. 181; Li²⁺ 2 → 1 = 1.471×10⁻¹⁷ J, He⁺ n = 1 and H n = 8 at pp. 181–182; the 656.3 nm photon at pp. 177–178). Open Textbook Library record: https://open.umn.edu/opentextbooks/textbooks/chemical-bonding-and-organic-chemistry [^b054-wrong]: Blackstock, Brewer and Cinel (2022), *Chemical Bonding and Organic Chemistry*, Chapter 2, p. 183. [^b054-radius]: Blackstock, Brewer and Cinel (2022), *Chemical Bonding and Organic Chemistry*, Chapter 2, p. 184 (orbit radius; the standard form r_n = n²a₀/Z is used here). [^b054-h2]: Blackstock, Brewer and Cinel (2022), *Chemical Bonding and Organic Chemistry*, Chapter 4, "Chemical Bonding I: Basic Concepts", p. 231 (H₂ → 2 H, +436 kJ/mol). [^b052-hydrogenic]: Boyd, W. Christopher (2025). *Exploring Inorganic and Organometallic Chemistry*. Chapter 1, pp. 27–28 (E_n = −(Z²/2n²) E_h; a₀ = 5.292×10⁻¹¹ m; E_h = 4.360×10⁻¹⁸ J). Open Textbook Library record: https://open.umn.edu/opentextbooks/textbooks/exploring-inorganic-and-organometallic-chemistry [^openstax-bohr]: Flowers, Paul; Neth, Edward; Robinson, William, et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. Chapter 3, §3.2 "The Bohr Model" (E_n = −k Z²/n² with k = 2.179×10⁻¹⁸ J; r = n²a₀/Z with a₀ = 5.292×10⁻¹¹ m; the model's failure for helium). https://openstax.org/books/chemistry-atoms-first-2e/pages/3-2-the-bohr-model (PDF pp. 115–184, page to pin) [^bohr1913-i]: Bohr, N. (1913). "I. On the constitution of atoms and molecules." *Philosophical Magazine*, Series 6, 26 (151): 1–25. https://doi.org/10.1080/14786441308634955 [^bohr1913-ii]: Bohr, N. (1913). "On the constitution of atoms and molecules. Part II. Systems containing only a single nucleus." *Philosophical Magazine*, Series 6, 26: 476–502. [^bohr1913-iii]: Bohr, N. (1913). "On the constitution of atoms and molecules. Part III. Systems containing several nuclei." *Philosophical Magazine*, Series 6, 26 (155): 857–875. https://doi.org/10.1080/14786441308635031 [^rutherford1911]: Rutherford, E. (1911). "The scattering of α and β particles by matter and the structure of the atom." *Philosophical Magazine*, Series 6, 21 (125): 669–688. https://doi.org/10.1080/14786440508637080 [^thomson1904]: Thomson, J. J. (1904). "On the structure of the atom: an investigation of the stability and periods of oscillation of a number of corpuscles arranged at equal intervals around the circumference of a circle; with application of the results to the theory of atomic structure." *Philosophical Magazine*, Series 6, 7 (39): 237–265. https://doi.org/10.1080/14786440409463107 [^nagaoka1904]: Nagaoka, H. (1904). "Kinetics of a system of particles illustrating the line and the band spectrum and the phenomena of radioactivity." *Philosophical Magazine*, Series 6, 7 (41): 445–455. https://doi.org/10.1080/14786440409463141 [^balmer1885]: Balmer, J. J. (1885). "Notiz über die Spectrallinien des Wasserstoffs." *Annalen der Physik*, 261 (5): 80–87. https://doi.org/10.1002/andp.18852610506 [^rydberg1890]: Rydberg, J. R. (1890). "Recherches sur la constitution des spectres d'émission des éléments chimiques." *Kongliga Svenska Vetenskaps-Akademiens Handlingar*, 23 (11). [^heilbron-kuhn]: Heilbron, John L.; Kuhn, Thomas S. (1969). "The Genesis of the Bohr Atom." *Historical Studies in the Physical Sciences*, 1: 211–290. https://doi.org/10.2307/27757291 [^nobel1922]: The Nobel Prize in Physics 1922. NobelPrize.org. https://www.nobelprize.org/prizes/physics/1922/summary/ [^bohr-nobel-lecture]: Bohr, Niels (1922). "The Structure of the Atom." Nobel Lecture, December 11, 1922. NobelPrize.org. https://www.nobelprize.org/prizes/physics/1922/bohr/lecture/ [^sommerfeld1916]: Sommerfeld, A. (1916). "Zur Quantentheorie der Spektrallinien." *Annalen der Physik*, 356 (17): 1–94. [^debroglie1924]: de Broglie, Louis (1924). *Recherches sur la théorie des quanta*. Doctoral thesis, University of Paris; published in *Annales de Physique*, 10 (3): 22–128 (1925). [^heisenberg1925]: Heisenberg, W. (1925). "Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen." *Zeitschrift für Physik*, 33: 879–893. [^pauli1926]: Pauli, W. (1926). "Über das Wasserstoffspektrum vom Standpunkt der neuen Quantenmechanik." *Zeitschrift für Physik*, 36: 336–363. [^schrodinger1926]: Schrödinger, E. (1926). "Quantisierung als Eigenwertproblem (Erste Mitteilung)." *Annalen der Physik*, 384 (4): 361–376. https://doi.org/10.1002/andp.19263840404 [^langmuir1919]: Langmuir, Irving (1919). "The Arrangement of Electrons in Atoms and Molecules." *Journal of the American Chemical Society*, 41 (6): 868–934. https://doi.org/10.1021/ja02227a002 [^moseley1913]: Moseley, H. G. J. (1913). "The high-frequency spectra of the elements." *Philosophical Magazine*, Series 6, 26 (156): 1024–1034. https://doi.org/10.1080/14786441308635052 [^codata]: National Institute of Standards and Technology. "CODATA Internationally recommended 2022 values of the Fundamental Physical Constants." NIST Reference on Constants, Units and Uncertainty. https://physics.nist.gov/cuu/Constants/ [^nist-xray]: National Institute of Standards and Technology. *X-ray Transition Energies Database* (Cu Kα₁). https://physics.nist.gov/PhysRefData/XrayTrans/Html/search.html [^unicode]: The Unicode Standard. "Miscellaneous Symbols," code chart, range 2600–26FF (U+269B ATOM SYMBOL). https://www.unicode.org/charts/PDF/U2600.pdf ### Primary sources - Bohr's 1913 trilogy in the *Philosophical Magazine*, Series 6, volume 26: Part I (pp. 1–25), Part II (pp. 476–502) and Part III (pp. 857–875), cited above. - Rutherford (1911), Thomson (1904), Nagaoka (1904), Balmer (1885), Rydberg (1890), Moseley (1913), Sommerfeld (1916), de Broglie (1924), Heisenberg (1925), Pauli (1926) and Schrödinger (1926), cited above. ## Further reading - Blackstock, Brewer and Cinel (2022). *Chemical Bonding and Organic Chemistry*. Chapter 2, "Quantum Theory and Electronic Structure of Atoms", pp. 125–192. Portal Book 054. - Boyd (2025). *Exploring Inorganic and Organometallic Chemistry*. Chapter 1, the hydrogenic atom, pp. 10–30. Portal Book 052. - Flowers, Neth, Robinson et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. Chapter 3, "Electronic Structure and Periodic Properties of Elements", pp. 115–184 (§3.2 "The Bohr Model"). Portal Book 051. - Heilbron and Kuhn (1969). "The Genesis of the Bohr Atom." The standard account of the 1912–1913 work. ## External links - [The Bohr Model](https://openstax.org/books/chemistry-atoms-first-2e/pages/3-2-the-bohr-model), *Chemistry: Atoms First 2e*, OpenStax - [Niels Bohr's Nobel Lecture, "The Structure of the Atom"](https://www.nobelprize.org/prizes/physics/1922/bohr/lecture/), NobelPrize.org - [Fundamental Physical Constants](https://physics.nist.gov/cuu/Constants/), NIST <!-- MATTERSIM:BEGIN g24 — Matter & Energy Cluster microsim (framework build, specs/sims/Bohr_model.json); do not hand-edit inside --> **Microsim — three.js (Wikitube framework), pending deploy:** *Bohr model* will play here once `https://wikitube-3d-microsims.netlify.app/matter/Bohr_model.html` is live. <!-- pending: <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/matter/Bohr_model.html" data-title="Bohr model"></div> --> <!-- MATTERSIM:END --> ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Bohr_model) : [Wikitube](https://en.wikitube.io/wiki/Bohr_model) · pinned revision [1372525337](https://en.wikipedia.org/w/index.php?oldid=1372525337) · 2026-09-11 ## Previous hub tags Hubs: `Life_Physics`. Portals: [[PORTAL_Chemistry]]. --- *Matter & Energy Cluster child articles, wave 1 · 2026-09-11 · drafted · Chemistry row K4 · sim pending (matter/Bohr_model).*