434:. Lorentz explained that the Planck constant could be taken as determining the size of atoms, or that the size of atoms could be taken to determine the Planck constant. Lorentz included comments regarding the emission and absorption of radiation concluding that "A stationary state will be established in which the number of electrons entering their spheres is equal to the number of those leaving them." In the discussion of what could regulate energy differences between atoms, Max Planck simply stated: "The intermediaries could be the electrons." The discussions outlined the need for the quantum theory to be included in the atom and the difficulties in an atomic theory. Planck in his talk said explicitly: "In order for an oscillator to be able to provide radiation in accordance with the equation, it is necessary to introduce into the laws of its operation, as we have already said at the beginning of this Report, a particular physical hypothesis which is, on a fundamental point, in contradiction with classical Mechanics, explicitly or tacitly." Bohr's first paper on his atomic model quotes Planck almost word for word, saying: "Whatever the alteration in the laws of motion of the electrons may be, it seems necessary to introduce in the laws in question a quantity foreign to the classical electrodynamics, i.e. the Planck constant, or as it often is called the elementary quantum of action." Bohr's footnote at the bottom of the page is to the French translation of the 1911 Solvay Congress, proving he patterned his model directly on the proceedings and fundamental principles laid down by Planck, Lorentz, and the quantized Haas model of the atom which was mentioned seventeen times. Lorentz ended the discussion of Einstein's talk explaining: "The assumption that this energy must be a multiple of
5561: plane, and it could only take a few discrete values. This contradicted the obvious fact that an atom could be turned this way and that relative to the coordinates without restriction. The Sommerfeld quantization can be performed in different canonical coordinates and sometimes gives different answers. The incorporation of radiation corrections was difficult, because it required finding action-angle coordinates for a combined radiation/atom system, which is difficult when the radiation is allowed to escape. The whole theory did not extend to non-integrable motions, which meant that many systems could not be treated even in principle. In the end, the model was replaced by the modern quantum-mechanical treatment of the
5284:
experimentally obtained screening term should be replaced by 0.4). Notwithstanding its restricted validity, Moseley's law not only established the objective meaning of atomic number, but as Bohr noted, it also did more than the
Rydberg derivation to establish the validity of the Rutherford/Van den Broek/Bohr nuclear model of the atom, with atomic number (place on the periodic table) standing for whole units of nuclear charge. Van den Broek had published his model in January 1913 showing the periodic table was arranged according to charge while Bohr's atomic model was not published until July 1913.
4952:
which ... only a certain number of electronsânamely, eight in our caseâshould be arranged. As soon as one ring or shell is completed, a new one has to be started for the next element; the number of electrons, which are most easily accessible, and lie at the outermost periphery, increases again from element to element and, therefore, in the formation of each new shell the chemical periodicity is repeated." Later, chemist
Langmuir realized that the effect was caused by charge screening, with an inner shell containing only 2 electrons. In his 1919 paper,
4858: = 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
306:
338:, was the best available. Thomson proposed a model with electrons rotating in coplanar rings within an atomic-sized, positively-charged, spherical volume. Thomson showed that this model was mechanically stable by lengthy calculations and electrodynamically stable under his original assumption of thousands of electrons per atom. Moreover he suggested that the particularly stable configurations of electrons in rings was connected to chemical properties of the atoms and he developed a formula for the scattering of
4882:
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
1649:
5667:
5328:"around" the nucleus at all, but merely to go tightly around it in an ellipse with zero area (this may be pictured as "back and forth", without striking or interacting with the nucleus). This is only reproduced in a more sophisticated semiclassical treatment like Sommerfeld's. Still, even the most sophisticated semiclassical model fails to explain the fact that the lowest energy state is spherically symmetric â it doesn't point in any particular direction.
3623:; the orbit energy begins to be comparable to rest energy. Sufficiently large nuclei, if they were stable, would reduce their charge by creating a bound electron from the vacuum, ejecting the positron to infinity. This is the theoretical phenomenon of electromagnetic charge screening which predicts a maximum nuclear charge. Emission of such positrons has been observed in the collisions of heavy ions to create temporary super-heavy nuclei.
4606:< 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
5417:
7924:
7934:
49:
5345:
coincidental agreements are found between the semiclassical vs. full quantum mechanical treatment of the atom; these include identical energy levels in the hydrogen atom and the derivation of a fine-structure constant, which arises from the relativistic BohrâSommerfeld model (see below) and which happens to be equal to an entirely different concept, in full modern quantum mechanics).
5597:. At higher-order perturbations, however, the Bohr model and quantum mechanics differ, and measurements of the Stark effect under high field strengths helped confirm the correctness of quantum mechanics over the Bohr model. The prevailing theory behind this difference lies in the shapes of the orbitals of the electrons, which vary according to the energy state of the electron.
3788:
convincing
Rutherford of the importance of Bohr's model, for it explained the fact that the frequencies of lines in the spectra for singly ionized helium do not differ from those of hydrogen by a factor of exactly 4, but rather by 4 times the ratio of the reduced mass for the hydrogen vs. the helium systems, which was much closer to the experimental ratio than exactly 4.
551:. To avoid immediate collapse of this system he required that electrons come in pairs so the rotational acceleration of each electron was matched across the orbit. By 1913 Bohr had already shown from the analysis of alpha particle energy loss that hydrogen had only a single electron. Thus Bohr's atomic model would abandon classical electrodynamics.
250:. While the Rydberg formula had been known experimentally, it did not gain a theoretical basis until the Bohr model was introduced. Not only did the Bohr model explain the reasons for the structure of the Rydberg formula, it also provided a justification for the fundamental physical constants that make up the formula's empirical results.
3108:
519:." Rutherford could have outlined these points to Bohr or given him a copy of the proceedings since he quoted from them and used them as a reference. In a later interview, Bohr said it was very interesting to hear Rutherford's remarks about the Solvay Congress. But Bohr said, "I saw the actual reports" of the Solvay Congress.
5337:, the proper deformation (careful full extension) of the semi-classical result adjusts the angular momentum value to the correct effective one. As a consequence, the physical ground state expression is obtained through a shift of the vanishing quantum angular momentum expression, which corresponds to spherical symmetry.
3782:
4959:
In the
Moseley experiment, one of the innermost electrons in the atom is knocked out, leaving a vacancy in the lowest Bohr orbit, which contains a single remaining electron. This vacancy is then filled by an electron from the next orbit, which has n=2. But the n=2 electrons see an effective charge of
531:
published a model of the atom which would influence Bohr's model. Nicholson developed his model based on the analysis of astrophysical spectroscopy. He connected the observed spectral line frequencies with the orbits of electrons in his atoms. The connection he adopted associated the atomic electron
4873:
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
3787:
However, these numbers are very nearly the same, due to the much larger mass of the proton, about 1836.1 times the mass of the electron, so that the reduced mass in the system is the mass of the electron multiplied by the constant 1836.1/(1+1836.1) = 0.99946. This fact was historically important in
342:
that seemed to match experimental results. However
Thomson himself later showed that the atom had a factor of a thousand fewer electrons, challenging the stability argument and forcing the poorly understood positive sphere to have most of the atom's mass. Thomson was also unable to explain the many
5327:
for the ground state orbital angular momentum: The angular momentum in the true ground state is known to be zero from experiment. Although mental pictures fail somewhat at these levels of scale, an electron in the lowest modern "orbital" with no orbital momentum, may be thought of as not to rotate
3791:
For positronium, the formula uses the reduced mass also, but in this case, it is exactly the electron mass divided by 2. For any value of the radius, the electron and the positron are each moving at half the speed around their common center of mass, and each has only one fourth the kinetic energy.
4951:
in 1914 and in 1916 who explained that in the periodic table new elements would be created as electrons were added to the outer shell. In Kossel's paper, he writes: "This leads to the conclusion that the electrons, which are added further, should be put into concentric rings or shells, on each of
4881:
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
4590:
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
539:
The other critical influence of
Nicholson work was his detailed analysis of spectra. Before Nicholson's work Bohr thought the spectral data was not useful for understanding atoms. In comparing his work to Nicholson's, Bohr came to understand the spectral data and their value. When he then learned
409:
had shown that atoms will only emit light (that is, electromagnetic radiation) at certain discrete frequencies. By the early twentieth century, it was expected that the atom would account for the spectral lines. In 1897, Lord
Rayleigh analyzed the problem. By 1906, Rayleigh said, "The frequencies
4943:
Moseley wrote to Bohr, puzzled about his results, but Bohr was not able to help. At that time, he thought that the postulated innermost "K" shell of electrons should have at least four electrons, not the two which would have neatly explained the result. So
Moseley published his results without a
2111:
However, in quantum mechanics, the quantization of angular momentum leads to discrete energy levels of the orbits, and the emitted frequencies are quantized according to the energy differences between these levels. This discrete nature of energy levels introduces a fundamental departure from the
5344:
that grows denser near the nucleus. The rate-constant of probability-decay in hydrogen is equal to the inverse of the Bohr radius, but since Bohr worked with circular orbits, not zero area ellipses, the fact that these two numbers exactly agree is considered a "coincidence". (However, many such
536:. Whereas Planck focused on a quantum of energy, Nicholson's angular momentum quantum relates to orbital frequency. This new concept gave Planck constant an atomic meaning for the first time. In his 1913 paper Bohr cites Nicholson as finding quantized angular momentum important for the atom.
2107:
In classical mechanics, if an electron is orbiting around an atom with period T, and if its coupling to the electromagnetic field is weak, so that the orbit doesn't decay very much in one cycle, it will emit electromagnetic radiation in a pattern repeating at every period, so that the
Fourier
5600:
The BohrâSommerfeld quantization conditions lead to questions in modern mathematics. Consistent semiclassical quantization condition requires a certain type of structure on the phase space, which places topological limitations on the types of symplectic manifolds which can be quantized. In
4259:
5283:
is the Rydberg constant, in terms of frequency equal to 3.28 x 10 Hz. For values of Z between 11 and 31 this latter relationship had been empirically derived by Moseley, in a simple (linear) plot of the square root of X-ray frequency against atomic number (however, for silver, Z = 47, the
4830:
of 1904, although Kossel had already predicted a maximum of eight per shell in 1916. 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
2883:
5360:
group) can also be approximately predicted. Also, if the empiric electronânuclear screening factors for many atoms are known, many other spectral lines can be deduced from the information, in similar atoms of differing elements, via the RitzâRydberg combination principles (see
6553:
Well, yes," says Bohr. "But I can hardly imagine it will involve light quanta. Look, even if Einstein had found an unassailable proof of their existence and would want to inform me by telegram, this telegram would only reach me because of the existence and reality of radio
2115:
Bohr considered circular orbits. Classically, these orbits must decay to smaller circles when photons are emitted. The energy level spacing between circular orbits can be calculated with the correspondence formula. For a hydrogen atom, the classical orbits have a period
4812:, 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
5256:
5434:, which suggested that electrons travel in elliptical orbits around a nucleus instead of the Bohr model's circular orbits. This model supplemented the quantized angular momentum condition of the Bohr model with an additional radial quantization condition, the
1611:
divided by the electron momentum. In 1913, however, Bohr justified his rule by appealing to the correspondence principle, without providing any sort of wave interpretation. In 1913, the wave behavior of matter particles such as the electron was not suspected.
2448:
760:, of 0.0529 nm for hydrogen. Once an electron is in this lowest orbit, it can get no closer to the nucleus. Starting from the angular momentum quantum rule as Bohr admits is previously given by Nicholson in his 1912 paper, Bohr was able to calculate the
2898:
5653:
of the molecular system is achieved through the balance of forces between the forces of attraction of nuclei to the plane of the ring of electrons and the forces of mutual repulsion of the nuclei. The Bohr model of the chemical bond took into account the
5111:
5588:
However, this is not to say that the BohrâSommerfeld model was without its successes. Calculations based on the BohrâSommerfeld model were able to accurately explain a number of more complex atomic spectral effects. For example, up to first-order
4800:
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. The 1913 Bohr model did not discuss higher elements in detail and
3636:
3260:
4487:
3883:
developed increasingly accurate empirical formula matching measured atomic spectral lines. Critical for Bohr's later work, Rydberg expressed his formula in terms of wave-number, equivalent to frequency. These formula contained a constant,
554:
Nicholson's model of radiation was quantum but was attached to the orbits of the electrons. Bohr would adopt Nicholson's interpretation of frequency quantization, but associate it with differences in energy levels of his model of hydrogen.
7725:: Elektronenbahnen, QuantensprĂŒnge und Spektren, in: Charlotte Bigg & Jochen Hennig (eds.) Atombilder. Ikonografien des Atoms in Wissenschaft und Ăffentlichkeit des 20. Jahrhunderts, Göttingen: Wallstein-Verlag 2009, pp. 51â61
4099:
1808:
2624:
3387:
2732:
4894:
Niels Bohr said in 1962: "You see actually the Rutherford work was not taken seriously. We cannot understand today, but it was not taken seriously at all. There was no mention of it any place. The great change came from Moseley."
4261:
Therefore Bohr's theory gives the Rydberg formula and moreover the numerical value the Rydberg constant for hydrogen in terms of more fundamental constants of nature, including the electron's charge, the electron's mass, and the
410:
observed in the spectrum may not be frequencies of disturbance or of oscillation in the ordinary sense at all, but rather form an essential part of the original constitution of the atom as determined by conditions of stability."
1635:
independently, and by different reasoning. Schrödinger employed de Broglie's matter waves, but sought wave solutions of a three-dimensional wave equation describing electrons that were constrained to move about the nucleus of a
373:
developed a new scattering model, showing that the observed large angle scattering could be explained by a compact, highly charged mass at the center of the atom. Rutherford scattering did not involve the electrons and thus his
3473:
4886:). 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.
1924:
4968:, and lower it by â1 (due to the electron's negative charge screening the nuclear positive charge). The energy gained by an electron dropping from the second shell to the first gives Moseley's law for K-alpha lines,
3982:
4842:
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
4847:. 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.
3991:
between orbital energy levels is able to explain these formula. For the hydrogen atom Bohr starts with his derived formula for the energy released as a free electron moves into a stable circular orbit indexed by
2758:
2208:
4094:
5679:
has been widely used as a symbol for atoms and even for "atomic" energy (even though this is more properly considered nuclear energy). Examples of its use over the past century include but are not limited to:
2301:
3573:
3493:
is the atomic number. This will now give us energy levels for hydrogenic (hydrogen-like) atoms, which can serve as a rough order-of-magnitude approximation of the actual energy levels. So for nuclei with
5674:
Although Bohr's atomic model was superseded by quantum models in the 1920's, the visual image of electrons orbiting a nucleus has remained the popular concept of atoms. The concept of an atom as a tiny
5368:
The relative intensities of spectral lines; although in some simple cases, Bohr's formula or modifications of it, was able to provide reasonable estimates (for example, calculations by Kramers for the
4342:
3854:
1991:
1656:
The Bohr model gives almost exact results only for a system where two charged points orbit each other at speeds much less than that of light. This not only involves one-electron systems such as the
7611:
p. 434. (provides an elegant reformulation of the BohrâSommerfeld quantization conditions, as well as an important insight into the quantization of non-integrable (chaotic) dynamical systems.)
316:
Until the second decade of the 20th century, atomic models were generally speculative and even the concept of atoms let alone atoms with internal structure faced opposition from some scientists.
594:
suggests. These stable orbits are called stationary orbits and are attained at certain discrete distances from the nucleus. The electron cannot have any other orbit in between the discrete ones.
4920:
in terms of models as these had been published before Moseley's work and Moseley's 1913 paper was published the same month as the first Bohr model paper). The two additional assumptions that
5511:
2517:
5122:
3103:{\displaystyle E=-{\frac {Zk_{\mathrm {e} }e^{2}}{2r_{n}}}=-{\frac {Z^{2}(k_{\mathrm {e} }e^{2})^{2}m_{\mathrm {e} }}{2\hbar ^{2}n^{2}}}\approx {\frac {-13.6Z^{2}}{n^{2}}}~\mathrm {eV} .}
2339:
2095:
1517:
855:
643:
4388:
1303:
1419:
1361:
4974:
389:
The arrangement of the electrons was unknown. Some suggestions had electrons orbiting a solar nucleus, but involved a technical difficulty: the laws of classical mechanics (i.e. the
3142:, these are also the binding energies of a highly excited atom with one electron in a large circular orbit around the rest of the atom. The hydrogen formula also coincides with the
3309:
1848:. It is assumed here that the mass of the nucleus is much larger than the electron mass (which is a good assumption). This equation determines the electron's speed at any radius:
269:. However, because of its simplicity, and its correct results for selected systems (see below for application), the Bohr model is still commonly taught to introduce students to
4610:= 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:"
1248:
900:
of the electromagnetic field. Quantization of the electromagnetic field was explained by the discreteness of the atomic energy levels; Bohr did not believe in the existence of
3777:{\displaystyle m_{\text{red}}={\frac {m_{\mathrm {e} }m_{\mathrm {p} }}{m_{\mathrm {e} }+m_{\mathrm {p} }}}=m_{\mathrm {e} }{\frac {1}{1+m_{\mathrm {e} }/m_{\mathrm {p} }}}.}
734:
517:
1589:
772:. In these orbits, the electron's acceleration does not result in radiation and energy loss. The Bohr model of an atom was based upon Planck's quantum theory of radiation.
7618:
La théorie du rayonnement et les quanta : rapports et discussions de la réunion tenue à Bruxelles, du 30 octobre au 3 novembre 1911, sous les auspices de M.E. Solvay
3162:
2242:
693:
4399:
5649:, the electrons of the atoms of the molecule form a rotating ring whose plane is perpendicular to the axis of the molecule and equidistant from the atomic nuclei. The
2331:
1012:
5404:
Doublets and triplets appear in the spectra of some atoms as very close pairs of lines. Bohr's model cannot say why some energy levels should be very close together.
1199:
4964: â 1, which is the value appropriate for the charge of the nucleus, when a single electron remains in the lowest Bohr orbit to screen the nuclear charge +
4010:
1468:
1118:), the two orbits involved in the emission process have nearly the same rotation frequency, so that the classical orbital frequency is not ambiguous. But for small
979:
455:
945:
925:
793:
1551:
1448:
1718:
3902:
2539:
1609:
1156:
1136:
1112:
1092:
1072:
1052:
1032:
875:
754:
475:
3911:
3320:
2639:
3479:
Since this derivation is with the assumption that the nucleus is orbited by one electron, we can generalize this result by letting the nucleus have a charge
6566:
397:
while orbiting a nucleus. Because the electron would lose energy, it would rapidly spiral inwards, collapsing into the nucleus on a timescale of around 16
6975:
4826:
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
4015:
430:
in the discussion of Planck's lecture raised the question of the composition of the atom based on Thomson's model with the quantum modification added by
3398:
775:
Electrons can only gain and lose energy by jumping from one allowed orbit to another, absorbing or emitting electromagnetic radiation with a frequency
5352:
Much of the spectra of larger atoms. At best, it can make predictions about the K-alpha and some L-alpha X-ray emission spectra for larger atoms, if
4492:
Bohr's derivation of the Rydberg constant, as well as the concomitant agreement of Bohr's formula with experimentally observed spectral lines of the
4254:{\displaystyle h\nu =W_{\tau _{2}}-W_{\tau _{1}}={\frac {2\pi ^{2}me^{4}}{h^{2}}}\left({\frac {1}{\tau _{2}^{2}}}-{\frac {1}{\tau _{1}^{2}}}\right)}
1853:
378:
was incomplete. Bohr begins his first paper on his atomic model by describing Rutherford's atom as consisting of a small, dense, positively charged
7140:
Dahl, Jens Peder; Springborg, Michael (10 December 1982). "Wigner's phase space function and atomic structure: I. The hydrogen atom ground state".
4865:
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
7819:
6150:
5685:
597:
The stationary orbits are attained at distances for which the angular momentum of the revolving electron is an integer multiple of the reduced
4269:
7972:
7738:
7367:
6704:
6511:
On the Constitution of Atoms and Molecules ... Papers of 1913 reprinted from the Philosophical Magazine, with an introduction by L. Rosenfeld
6446:
6277:
6033:
5961:
2878:{\displaystyle r_{1}={\frac {\hbar ^{2}}{k_{\mathrm {e} }e^{2}m_{\mathrm {e} }}}\approx 5.29\times 10^{-11}~\mathrm {m} =52.9~\mathrm {pm} .}
4531:=3) series, and successful theoretical prediction of other lines not yet observed, was one reason that his model was immediately accepted.
1209:
condition: the electron is described by a wave and a whole number of wavelengths must fit along the circumference of the electron's orbit:
5383:
in spectral lines, which are known to be due to a variety of relativistic and subtle effects, as well as complications from electron spin.
2138:
2250:
4956:
postulated the existence of "cells" which could each only contain two electrons each, and these were arranged in "equidistant layers".
4805:
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.
7258:
5696:
4912:. Moseley's empiric formula was found to be derivable from Rydberg's formula and later Bohr's formula (Moseley actually mentions only
7713:
7694:
7664:
5801:
5435:
4576:
and the later discussion of the "Shell Model of the Atom" below). This was established empirically before Bohr presented his model.
3504:
352:
281:
in 1910 but was rejected until the 1911 Solvay Congress where it was thoroughly discussed. The quantum theory of the period between
540:
from a friend about Balmer's compact formula for the spectral line data, Bohr quickly realized his model would match it in detail.
5623:
Bohr also updated his model in 1922, assuming that certain numbers of electrons (for example, 2, 8, and 18) correspond to stable "
426:'s lecture ended with this remark: "... atoms or electrons subject to the molecular bond would obey the laws of quantum theory".
405:
becoming shorter, resulting in electromagnetic radiation with a continuous spectrum. However, late 19th-century experiments with
4902:
found an empirical relationship between the strongest X-ray line emitted by atoms under electron bombardment (then known as the
7616:
5642:
5636:
1174:
543:
Nicholson's model was based on classical electrodynamics with negative electron orbiting a positive nucleus along the lines of
3798:
4866:
1935:
4822:
who corrected Bohr's work to show that electrons interacted through the outer rings, and Kossel called the rings: "shells".
2213:
It is possible to determine the energy level spacings by recursively stepping down orbit by orbit, but there is a shortcut.
31:
590:
The electron is able to revolve in certain stable orbits around the nucleus without radiating any energy, contrary to what
2005:, the energy is zero, corresponding to a motionless electron infinitely far from the proton. The total energy is half the
7358:
Schirrmacher, Arne (2009). "Bohr's Atomic Model". In Greenberger, Daniel M.; Hentschel, Klaus; Weinert, Friedel (eds.).
7033:(Interview). Interviewed by Thomas S. Kuhn; Leon Rosenfeld; Aage Petersen; Erik Rudinger. American Institute of Physics.
6371:(Interview). Interviewed by Thomas S. Kuhn; Leon Rosenfeld; Aage Petersen; Erik Rudinger. American Institute of Physics.
6353:(Interview). Interviewed by Thomas S. Kuhn; Leon Rosenfeld; Aage Petersen; Erik Rudinger. American Institute of Physics.
5788:
5394:; these are also due to more complicated quantum principles interacting with electron spin and orbital magnetic fields.
309:
Bohr model in 1921 after Sommerfeld expansion of 1913 model showing maximum electrons per shell with shells labeled in
7987:
7812:
7069:
5401:
in that it considers electrons to have known orbits and locations, two things which cannot be measured simultaneously.
5251:{\displaystyle f=\nu =R_{\mathrm {v} }\left({\frac {3}{4}}\right)(Z-1)^{2}=(2.46\times 10^{15}~{\text{Hz}})(Z-1)^{2}.}
277:
before moving on to the more accurate, but more complex, valence shell atom. A related quantum model was proposed by
7794:âAn interactive simulation to intuitively explain the quantization condition of standing waves in Bohr's atomic mode
7748:
Kragh, Helge (November 2011). "Conceptual objections to the Bohr atomic theory â do electrons have a 'free will'?".
7116:
5448:
5356:
additional ad hoc assumptions are made. Emission spectra for atoms with a single outer-shell electron (atoms in the
2467:
2443:{\displaystyle \Delta E\propto {\frac {1}{(L+\Delta L)^{2}}}-{\frac {1}{L^{2}}}\approx -{\frac {2\Delta L}{L^{3}}}.}
954:
at integer multiples of this frequency. This result is obtained from the Bohr model for jumps between energy levels
265:
of the hydrogen atom using the broader and much more accurate quantum mechanics and thus may be considered to be an
5751:
3988:
591:
266:
6762:
Bohr, N. (1913). "On the Constitution of Atoms and Molecules, Part II. Systems containing only a Single Nucleus".
5782:
5425:
563:
Next, Bohr was told by his friend, Hans Hansen, that the Balmer series is calculated using the Balmer formula, an
7977:
7850:
7791:
7121:
2053:
394:
7030:
6944:
6368:
6350:
5106:{\displaystyle E=h\nu =E_{i}-E_{f}=R_{\mathrm {E} }(Z-1)^{2}\left({\frac {1}{1^{2}}}-{\frac {1}{2^{2}}}\right),}
2453:
This is as desired for equally spaced angular momenta. If one kept track of the constants, the spacing would be
1476:
802:
604:
7962:
7828:
5606:
5543:
5539:
4352:
1267:
1159:
696:
300:
247:
99:
1372:
1314:
1258:
5407:
Multi-electron atoms do not have energy levels predicted by the model. It does not work for (neutral) helium.
2001:. This means that it takes energy to pull the orbiting electron away from the proton. For infinite values of
235:
interpretation introduced by Haas and Nicholson, but forsaking any attempt to explain radiation according to
7967:
5578:
5554:
5332:
3390:
2009:, the difference being the kinetic energy of the electron. This is also true for noncircular orbits by the
1628:
262:
3275:
7805:
7222:
7112:
7045:
5624:
5617:
4917:
4836:
4802:
1170:
897:
528:
305:
228:
195:
In the history of atomic physics, it followed, and ultimately replaced, several earlier models, including
1162:, requiring quantum theory to agree with the classical theory only in the limit of large quantum numbers.
231:'s nuclear quantum model (1912). The improvement over the 1911 Rutherford model mainly concerned the new
5735:
5707:
5593:, the Bohr model and quantum mechanics make the same predictions for the spectral line splitting in the
5398:
768:
atoms and ions. These orbits are associated with definite energies and are also called energy shells or
6022:
John L, Heilbron (1985). "Bohr's First Theories of the Atom". In French, A. P.; Kennedy, P. J. (eds.).
3792:
The total kinetic energy is half what it would be for a single electron moving around a heavy nucleus.
1215:
571:
in 1885 that described wavelengths of some spectral lines of hydrogen. This was further generalized by
6023:
5365:). All these techniques essentially make use of Bohr's Newtonian energy-potential picture of the atom.
1648:
7757:
7565:
7524:
7491:
7458:
7425:
7312:
7190:
7078:
6914:
6833:
6794:
6599:
6143:
6116:
5868:
5842:
5777:
5710:
5582:
4813:
1632:
886:
83:
6587:
5666:
3255:{\displaystyle R_{\mathrm {E} }={\frac {(k_{\mathrm {e} }e^{2})^{2}m_{\mathrm {e} }}{2\hbar ^{2}}}.}
1158:), the radiation frequency has no unambiguous classical interpretation. This marks the birth of the
702:
586:
put forth three postulates to provide an electron model consistent with Rutherford's nuclear model:
401:. Also, as the electron spirals inward, the emission would rapidly increase in frequency due to the
90:). The orbits in which the electron may travel are shown as grey circles; their radius increases as
7982:
7067:
M.A.B. Whitaker (1999). "The BohrâMoseley synthesis and a simple model for atomic x-ray energies".
5743:
5650:
5590:
5547:
5380:
4883:
480:
330:
When Bohr began his work on a new atomic theory in the summer of 1912 the atomic model proposed by
7933:
4482:{\displaystyle {\frac {1}{\lambda }}=R\left({\frac {1}{n_{f}^{2}}}-{\frac {1}{n_{i}^{2}}}\right).}
1560:
7908:
7871:
7773:
7581:
7540:
7302:
7181:
7157:
7094:
6967:
6849:
6657:
6623:
6414:
6406:
6240:
6078:
6001:
5929:
5431:
2223:
1637:
648:
548:
406:
335:
325:
287:
216:
158:
4534:
To apply to atoms with more than one electron, the Rydberg formula can be modified by replacing
422:
in 1911 on the subject of Radiation and Quanta, at which Bohr's mentor, Rutherford was present.
7251:
The Life of Stars: The Controversial Inception and Emergence of the Theory of Stellar Structure
6724:
4923:
this X-ray line came from a transition between energy levels with quantum numbers 1 and 2, and
4869:. One property was the size of atoms, which could be determined approximately by measuring the
3124:
less energy than a motionless electron infinitely far from the nucleus. The next energy level (
82:
and where an electron jumps between orbits, is accompanied by an emitted or absorbed amount of
7734:
7709:
7690:
7660:
7622:
7363:
7340:
7254:
6959:
6744:
6700:
6677:
6615:
6514:
6488:
6442:
6273:
6232:
6070:
6029:
5957:
5795:
5721:
5655:
5646:
5439:
5306:
4913:
3984:
Despite many attempts, no theory of the atom could reproduce these relatively simple formula.
2313:
1826:
1706:
1624:
1616:
431:
419:
370:
278:
270:
236:
232:
150:
17:
984:
7941:
7877:
7765:
7573:
7532:
7499:
7466:
7433:
7330:
7320:
7231:
7198:
7149:
7086:
7008:
6922:
6880:
6841:
6802:
6736:
6669:
6607:
6478:
6398:
6265:
6224:
6180:
6124:
6062:
5993:
5921:
5850:
5676:
5570:
5535:
4844:
4835:, after that the orbit is full, the next level would have to be used. This gives the atom a
4572:
is constant representing a screening effect due to the inner-shell and other electrons (see
3905:
3876:
3312:
2026:
2006:
1837:
1620:
1184:
572:
258:
224:
185:
165:
only to be replaced by the quantum atomic model in the 1920s. It consists of a small, dense
154:
4850:
For example, the lithium atom has two electrons in the lowest 1s orbit, and these orbit at
3995:
1803:{\displaystyle {\frac {m_{\mathrm {e} }v^{2}}{r}}={\frac {Zk_{\mathrm {e} }e^{2}}{r^{2}}},}
1453:
957:
437:
7864:
7722:
6992:
5772:
5689:
5610:
5574:
5362:
4953:
4823:
4263:
3866:
2619:{\displaystyle m_{\text{e}}{\sqrt {\dfrac {k_{\text{e}}Ze^{2}}{m_{\text{e}}r}}}r=n\hbar ,}
2112:
classical radiation law, giving rise to distinct spectral lines in the emitted radiation.
930:
910:
796:
778:
598:
576:
533:
427:
375:
369:
occasionally scatter at large angles, a result inconsistent with Thomson's model. In 1911
243:
208:
4839:
designed by Kossel, Langmuir, and Bury, in which each shell corresponds to a Bohr orbit.
3149:
The combination of natural constants in the energy formula is called the Rydberg energy (
1528:
1427:
7761:
7569:
7528:
7495:
7462:
7429:
7316:
7194:
7082:
6918:
6837:
6798:
6603:
6259:
6120:
5846:
5553:
The BohrâSommerfeld model was fundamentally inconsistent and led to many paradoxes. The
4932:
when used in the formula for atoms heavier than hydrogen, should be diminished by 1, to
3382:{\displaystyle {\frac {k_{\mathrm {e} }e^{2}}{\hbar c}}=\alpha \approx {\frac {1}{137}}}
2727:{\displaystyle r_{n}={\frac {n^{2}\hbar ^{2}}{Zk_{\mathrm {e} }e^{2}m_{\mathrm {e} }}}.}
7937:
7927:
7902:
7653:
7335:
7290:
5602:
5566:
5391:
5376:
5341:
4948:
4819:
4809:
4585:
4573:
4519:
4393:
these results can be expressed in terms of the the wavelength of the photon given off:
3887:
3586:
3579:
3578:
The actual energy levels cannot be solved analytically for more than one electron (see
3143:
2010:
1677:
1673:
1619:, in which Bohr's model of electrons traveling in quantized orbits was extended into a
1594:
1141:
1121:
1097:
1077:
1057:
1037:
1017:
860:
739:
460:
402:
390:
379:
366:
362:
310:
285:(1900) and the advent of a mature quantum mechanics (1925) is often referred to as the
166:
130:
79:
1253:
According to de Broglie's hypothesis, matter particles such as the electron behave as
7956:
7777:
7098:
7090:
6571:
6418:
6389:
McCormmach, Russell (1 January 1966). "The atomic theory of John William Nicholson".
5888:
5886:
5758:
5562:
5387:
4899:
4506:
3872:
3590:
3266:
1845:
1681:
1657:
1206:
1115:
568:
254:
196:
107:
53:
38:
7544:
6971:
6627:
1676:
of any atom where one electron is far away from everything else. It can be used for
7857:
7585:
7383:
7289:
Svidzinsky, Anatoly A.; Scully, Marlan O.; Herschbach, Dudley R. (23 August 2005).
7161:
6853:
6641:
Bohr, N. (1985). "Rydberg's discovery of the spectral laws". In Kalckar, J. (ed.).
6244:
5872:
5717:
5594:
5416:
5369:
4493:
3880:
3627:
3121:
2121:
769:
544:
274:
204:
181:
75:
5833:
Lakhtakia, Akhlesh; Salpeter, Edwin E. (1996). "Models and Modelers of Hydrogen".
7769:
6740:
3468:{\displaystyle R_{\mathrm {E} }={\frac {1}{2}}(m_{\mathrm {e} }c^{2})\alpha ^{2}}
7843:
6269:
5613:
2749:
2108:
transform of the pattern will only have frequencies which are multiples of 1/T.
1710:
1669:
1554:
1254:
757:
358:
331:
220:
200:
162:
42:
7484:
The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science
7451:
The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science
7418:
The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science
7295:
Proceedings of the National Academy of Sciences of the United States of America
6787:
The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science
6662:
The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science
6261:
Old Quantum Theory and Early Quantum Mechanics. Challenges in Physics Education
6173:
The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science
6109:
The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science
3630:
of electron and proton in all situations, instead of the mass of the electron,
3265:
This expression is clarified by interpreting it in combinations that form more
7626:
7615:
de Broglie, Maurice; Langevin, Paul; Solvay, Ernest; Einstein, Albert (1912).
7503:
7470:
7437:
7235:
7153:
7026:
6806:
6673:
6586:
MĂŒller, U.; de Reus, T.; Reinhardt, J.; MĂŒller, B.; Greiner, W. (1988-03-01).
6364:
6346:
6184:
6128:
4827:
1919:{\displaystyle v={\sqrt {\frac {Zk_{\mathrm {e} }e^{2}}{m_{\mathrm {e} }r}}}.}
1652:
Models depicting electron energy levels in hydrogen, helium, lithium, and neon
1202:
1169:(BKS theory) is a failed attempt to extend the Bohr model, which violates the
1166:
583:
423:
398:
339:
282:
146:
118:
48:
7360:
Compendium of quantum physics: concepts, experiments, history, and philosophy
7202:
6963:
6926:
6748:
6681:
6611:
6518:
6492:
6483:
6466:
6074:
5954:
Niels Bohr and the Quantum Atom: The Bohr Model of Atomic Structure 1913â1925
5291:
line of Moseley's time is now known to be a pair of close lines, written as (
1631:
of the same theory, wave mechanics, was discovered by the Austrian physicist
192:, and with the electron energies quantized (assuming only discrete values).
7325:
4875:
4870:
951:
564:
122:
7344:
7117:"Die Radioelemente, das periodische System und die Konstitution der. Atome"
6236:
5984:
Heilbron, John L.; Kuhn, Thomas S. (1969). "The Genesis of the Bohr Atom".
4808:
In 1921, following the work of chemists and others involved in work on the
6869:"Langmuir's Theory of the Arrangement of Electrons in Atoms and Molecules"
6619:
1705:
The electron is held in a circular orbit by electrostatic attraction. The
1684:
below). In high energy physics, it can be used to calculate the masses of
893:
amount of energy is radiated. However, unlike Einstein, Bohr stuck to the
6534:
Quantum Reality, Relativistic Causality, and Closing the Epistemic Circle
5658:â the electrons in the ring are at the maximum distance from each other.
4591:
electrons in a shell is eight, writing: "We see, further, that a ring of
3977:{\displaystyle \nu =R\left({\frac {1}{m^{2}}}-{\frac {1}{n^{2}}}\right).}
383:
173:
71:
7307:
7012:
6884:
6410:
6082:
6050:
6005:
5933:
6402:
6066:
5806:
Theoretical and experimental justification for the Schrödinger equation
5732:
5725:
5430:
Several enhancements to the Bohr model were proposed, most notably the
5357:
5288:
4903:
2892:-th level for any atom is determined by the radius and quantum number:
1665:
189:
177:
6567:"Revealing the hidden connection between pi and Bohr's hydrogen model"
1181:
Bohr's condition, that the angular momentum be an integer multiple of
7607:, A. Engel translator, (1997) Princeton University Press, Princeton.
7577:
7536:
6845:
5997:
5925:
5420:
Elliptical orbits with the same energy and quantized angular momentum
4832:
1661:
1177:
in quantum jumps, with the conservation laws only holding on average.
901:
212:
7553:
7512:
7479:
7446:
7413:
7217:
7176:
6996:
6905:[On molecular formation as a question of atomic structure].
6902:
6868:
6821:
6782:
6645:. Vol. 10. Amsterdam: North-Holland Publ. Cy. pp. 373â379.
6228:
6168:
6104:
5912:
Kragh, Helge (1 January 1979). "Niels Bohr's Second Atomic Theory".
5854:
5738:
code point U+269B (â) for an atom looks like a planetary atom model.
2203:{\displaystyle \Delta E\propto {\frac {1}{r^{3/2}}}\propto E^{3/2}.}
1640:, by being trapped by the potential of the positive nuclear charge.
756:
is 1; this gives the smallest possible orbital radius, known as the
418:
The outline of Bohr's atom came during the proceedings of the first
6258:
Giliberti, Marco; Lovisetti, Luisa (2024). "Bohr's Hydrogen Atom".
5688:, which was in part responsible for its later usage in relation to
5348:
The Bohr model also has difficulty with, or else fails to explain:
4595:
electrons cannot rotate in a single ring round a nucleus of charge
4089:{\displaystyle W_{\tau }={\frac {2\pi ^{2}me^{4}}{h^{2}\tau ^{2}}}}
2525:
Substituting the expression for the velocity gives an equation for
795:
determined by the energy difference of the levels according to the
7593:
A. Einstein (1917). "Zum Quantensatz von Sommerfeld und Epstein".
5700:
5665:
5415:
4889:
2296:{\displaystyle E\propto {\frac {1}{r}}\propto {\frac {1}{L^{2}}}.}
1688:
1685:
1680:
X-ray transition calculations if other assumptions are added (see
1647:
304:
170:
7797:
6328:
6316:
6304:
6292:
6197:
6169:"VII. On electrical vibrations and the constitution of the atom"
5892:
5713:' logo shows baseballs as electrons orbiting a large letter "A".
142:
7801:
7687:
Atomic and Molecular Structure: the development of our concepts
6215:
Heilbron, John L. (June 2013). "The path to the quantum atom".
5523:
is the radial momentum canonically conjugate to the coordinate
6725:"Early atomic models â from mechanical to quantum (1904â1913)"
3568:{\displaystyle E_{n}=-{\frac {Z^{2}R_{\mathrm {E} }}{n^{2}}}.}
1930:
It also determines the electron's total energy at any radius:
6588:"Positron production in crossed beams of bare uranium nuclei"
2244:. The energy in terms of the angular momentum then obeys to:
6509:
Bohr, Niels; Rosenfeld, LĂ©on Jacques Henri Constant (1963).
5828:
5826:
4890:
Moseley's law and calculation (K-alpha X-ray emission lines)
6051:"The Scattering of α and ÎČ Particles and Rutherford's Atom"
5573:. The current picture of the hydrogen atom is based on the
5340:
In modern quantum mechanics, the electron in hydrogen is a
3987:
In Bohr's theory describing the energies of transitions or
3498:
protons, the energy levels are (to a rough approximation):
2457:, so the angular momentum should be an integer multiple of
1997:
The total energy is negative and inversely proportional to
5979:
5977:
5975:
5973:
5546:, is the only one possible, since the quantum numbers are
1450:
is the angular momentum of the orbiting electron. Writing
927:
of classical radiation is equal to the rotation frequency
1525:
Bohr described angular momentum of the electron orbit as
1470:
for this angular momentum, the previous equation becomes
6945:"Lars Vegard, atomic structure, and the periodic system"
6439:
Inward bound: of matter and forces in the physical world
4337:{\displaystyle cR_{H}={\frac {2\pi ^{2}me^{4}}{h^{3}}}.}
3849:{\displaystyle E_{n}={\frac {R_{\mathrm {E} }}{2n^{2}}}}
579:. After this, Bohr declared, "everything became clear".
106:
transition depicted here produces the first line of the
7595:
Verhandlungen der Deutschen Physikalischen Gesellschaft
5557:
measured the tilt of the orbital plane relative to the
4096:
The energy difference between two such levels is then:
1986:{\displaystyle E=-{\frac {1}{2}}m_{\mathrm {e} }v^{2}.}
6699:(Impression: 3 ed.). Oxford: Oxford Univ. Press.
5947:
5945:
5943:
889:, Bohr's formula assumes that during a quantum jump a
253:
The Bohr model is a relatively primitive model of the
7645:(3rd ed.). San Francisco: W.H. Freeman & Co.
6997:"The Arrangement of Electrons in Atoms and Molecules"
5451:
5125:
4977:
4402:
4355:
4272:
4102:
4018:
3998:
3914:
3890:
3801:
3639:
3585:) because the electrons are not only affected by the
3507:
3401:
3323:
3278:
3165:
3138:
3) is â1.51 eV, and so on. For larger values of
2901:
2761:
2642:
2555:
2542:
2470:
2342:
2333:, the spacing between neighboring energies obeys to;
2316:
2253:
2226:
2141:
2056:
1938:
1856:
1721:
1597:
1563:
1531:
1479:
1456:
1430:
1375:
1317:
1270:
1218:
1187:
1144:
1124:
1100:
1080:
1060:
1040:
1020:
987:
960:
933:
913:
863:
805:
781:
742:
705:
651:
607:
483:
463:
440:
7480:"LXXIII. On the constitution of atoms and molecules"
7447:"XXXVII. On the constitution of atoms and molecules"
6783:"LXXIII. On the constitution of atoms and molecules"
4854: = 2. Each one sees the nuclear charge of
3113:
An electron in the lowest energy level of hydrogen (
1694:
Calculation of the orbits requires two assumptions.
7894:
7835:
5798:
is adequately explained by means of the Bohr model.
5699:is a "crest-and-spinning-atom emblem", enclosed in
4818:Bohr's partner in research during 1914 to 1916 was
1623:of electron motion. The new theory was proposed by
7652:
7218:"The quantum theory of radiation and line spectra"
6547:Gilder, Louisa (2009). "The Arguments 1909â1935".
6432:
6430:
6428:
5505:
5250:
5105:
4481:
4382:
4336:
4253:
4088:
4004:
3976:
3896:
3848:
3776:
3567:
3467:
3381:
3303:
3254:
3102:
2877:
2726:
2618:
2511:
2442:
2325:
2295:
2236:
2202:
2089:
1985:
1918:
1802:
1603:
1583:
1545:
1511:
1462:
1442:
1413:
1355:
1297:
1242:
1193:
1150:
1130:
1106:
1086:
1066:
1046:
1026:
1006:
973:
939:
919:
869:
849:
787:
748:
728:
687:
637:
511:
469:
449:
6471:Monthly Notices of the Royal Astronomical Society
6384:
6382:
6380:
6378:
30:"Bohr's law" redirects here. For other uses, see
7729:Steven and Susan Zumdahl (2010). "Chapter 7.4".
6504:
6502:
6460:
6458:
5534:is one full orbital period. The integral is the
2132:, so the energy level spacing formula obeys to:
765:
7414:"I. On the constitution of atoms and molecules"
6658:"I. On the constitution of atoms and molecules"
6210:
6208:
6206:
6105:"I. On the constitution of atoms and molecules"
3611:), the motion becomes highly relativistic, and
1615:In 1925, a new kind of mechanics was proposed,
575:in 1888, resulting in what is now known as the
242:The model's key success lies in explaining the
6017:
6015:
5747:uses a planetary-like image in its print logo.
5601:particular, the symplectic form should be the
5506:{\displaystyle \int _{0}^{T}p_{r}\,dq_{r}=nh,}
2512:{\displaystyle L={\frac {nh}{2\pi }}=n\hbar .}
2306:Assuming, with Bohr, that quantized values of
907:According to the Maxwell theory the frequency
7813:
6896:
6894:
6532:Stachel, John (2009). "Bohr and the Photon".
6441:(Reprint ed.). Oxford: Clarendon Press
6028:. Cambridge, Mass: Harvard University Press.
1054:. These jumps reproduce the frequency of the
27:Atomic model introduced by Niels Bohr in 1913
8:
7046:"The high-frequency spectra of the elements"
6938:
6936:
6903:"Ăber MolekĂŒlbildung als Frage des Atombaus"
6718:
6716:
5757:On maps, it is generally used to indicate a
5641:Niels Bohr proposed a model of the atom and
5390:â changes in spectral lines due to external
3908:and a pair of integers indexing the lines:
6142:Olsen, James D.; McDonald, Kirk T. (2005).
5986:Historical Studies in the Physical Sciences
5914:Historical Studies in the Physical Sciences
5907:
5905:
5903:
5901:
5670:Shield of the U.S. Atomic Energy Commission
4862:doesn't usually come out to be an integer.
2090:{\displaystyle m_{\mathrm {e} }vr=n\hbar .}
761:
261:model. As a theory, it can be derived as a
7820:
7806:
7798:
7641:Linus Carl Pauling (1970). "Chapter 5-1".
7276:ĐзбŃĐ°ĐœĐœŃĐ” ĐœĐ°ŃŃĐœŃĐ” ŃŃŃĐŽŃ (ŃŃĐ°ŃŃĐž 1909â1925)
6697:The quantum story: a history in 40 moments
6467:"The Constitution of the Solar Corona. IL"
6341:
6339:
6337:
5791:provided early support for the Bohr model.
3589:but also interact with each other via the
1512:{\displaystyle \ell ={\frac {nh}{2\pi }},}
850:{\displaystyle \Delta E=E_{2}-E_{1}=h\nu }
638:{\displaystyle m_{\mathrm {e} }vr=n\hbar }
7334:
7324:
7306:
6822:"The Constitution of Atoms and Molecules"
6482:
5724:, and has come to be used as a symbol of
5485:
5477:
5471:
5461:
5456:
5450:
5239:
5215:
5206:
5184:
5154:
5143:
5142:
5124:
5087:
5078:
5067:
5058:
5047:
5024:
5023:
5010:
4997:
4976:
4463:
4458:
4449:
4438:
4433:
4424:
4403:
4401:
4383:{\displaystyle E={\frac {hc}{\lambda }},}
4362:
4354:
4323:
4312:
4299:
4289:
4280:
4271:
4238:
4233:
4224:
4213:
4208:
4199:
4186:
4175:
4162:
4152:
4141:
4136:
4121:
4116:
4101:
4077:
4067:
4055:
4042:
4032:
4023:
4017:
3997:
3958:
3949:
3938:
3929:
3913:
3889:
3837:
3822:
3821:
3815:
3806:
3800:
3761:
3760:
3751:
3744:
3743:
3727:
3720:
3719:
3702:
3701:
3687:
3686:
3673:
3672:
3661:
3660:
3653:
3644:
3638:
3554:
3542:
3541:
3531:
3524:
3512:
3506:
3459:
3446:
3435:
3434:
3417:
3407:
3406:
3400:
3369:
3343:
3332:
3331:
3324:
3322:
3295:
3284:
3283:
3277:
3240:
3224:
3223:
3213:
3203:
3192:
3191:
3181:
3171:
3170:
3164:
3089:
3078:
3067:
3054:
3042:
3032:
3016:
3015:
3005:
2995:
2984:
2983:
2970:
2963:
2948:
2933:
2922:
2921:
2911:
2900:
2864:
2850:
2838:
2815:
2814:
2804:
2793:
2792:
2781:
2775:
2766:
2760:
2711:
2710:
2700:
2689:
2688:
2673:
2663:
2656:
2647:
2641:
2587:
2575:
2562:
2553:
2547:
2541:
2477:
2469:
2429:
2412:
2398:
2389:
2377:
2352:
2341:
2315:
2282:
2273:
2260:
2252:
2227:
2225:
2187:
2183:
2164:
2160:
2151:
2140:
2062:
2061:
2055:
1974:
1963:
1962:
1948:
1937:
1899:
1898:
1886:
1875:
1874:
1863:
1855:
1789:
1778:
1767:
1766:
1756:
1741:
1730:
1729:
1722:
1720:
1596:
1573:
1562:
1535:
1530:
1486:
1478:
1455:
1429:
1376:
1374:
1318:
1316:
1298:{\displaystyle \lambda ={\frac {h}{mv}},}
1277:
1269:
1217:
1186:
1143:
1123:
1099:
1079:
1059:
1039:
1019:
992:
986:
965:
959:
932:
912:
862:
832:
819:
804:
780:
741:
715:
704:
650:
613:
612:
606:
491:
482:
462:
439:
393:) predict that the electron will release
7704:Paul Tipler and Ralph Llewellyn (2002).
7685:Walter J. Lehmann (1972). "Chapter 18".
7278:. Vol. 1. Đ.: «ĐĐ°ŃĐșа». p. 133.
7001:Journal of the American Chemical Society
6873:Journal of the American Chemical Society
5317:The Bohr model gives an incorrect value
4612:
2629:so that the allowed orbit radius at any
1414:{\displaystyle {\frac {nh}{2\pi }}=mvr,}
1356:{\displaystyle {\frac {nh}{mv}}=2\pi r,}
47:
7605:The Collected Papers of Albert Einstein
7291:"Bohr's 1913 molecular model revisited"
7177:"Zur Quantentheorie der Spektrallinien"
6513:. Copenhagen; W.A. Benjamin: New York.
6477:(8). Oxford University Press: 677â693.
6098:
6096:
6094:
6092:
5956:. Oxford University Press. p. 18.
5822:
3351:
3237:
3029:
2778:
2670:
2610:
2522:This is how Bohr arrived at his model.
2503:
2081:
1188:
706:
632:
5754:uses planetary-like image as its logo.
5686:United States Atomic Energy Commission
5334:fully quantum treatment in phase space
457:leads to the following formula, where
141:was the first successful model of the
78:encircles a small, positively charged
7792:Standing waves in Bohr's atomic model
6952:Bulletin for the History of Chemistry
6391:Archive for History of Exact Sciences
6264:. Cham: Springer Nature Switzerland.
6055:Archive for History of Exact Sciences
3304:{\displaystyle m_{\mathrm {e} }c^{2}}
1201:, was later reinterpreted in 1924 by
7:
7513:"The Spectra of Helium and Hydrogen"
5662:Symbolism of planetary atomic models
5530:, which is the radial position, and
5432:Sommerfeld or BohrâSommerfeld models
4614:Bohr's 1913 proposed configurations
6144:"Classical lifetime of a bohr atom"
5720:, was chosen as the symbol for the
5542:. This condition, suggested by the
3626:The Bohr formula properly uses the
1094:. For sufficiently large values of
950:of the electron in its orbit, with
7676:George Gamow (1985). "Chapter 2".
6536:. Dordrecht: Springer. p. 79.
5697:International Atomic Energy Agency
5144:
5025:
4874:of the table is chemically inert (
3823:
3762:
3745:
3721:
3703:
3688:
3674:
3662:
3543:
3436:
3408:
3333:
3285:
3225:
3193:
3172:
3093:
3090:
3017:
2985:
2923:
2868:
2865:
2851:
2816:
2794:
2712:
2690:
2418:
2367:
2343:
2317:
2142:
2063:
1964:
1900:
1876:
1768:
1731:
1522:which is Bohr's second postulate.
806:
614:
532:orbital angular momentum with the
414:Influence of the Solvay Conference
248:hydrogen's spectral emission lines
184:, but with attraction provided by
145:. Developed from 1911 to 1918 by
25:
7362:. Heidelberg New York: Springer.
6465:Nicholson, J. W. (14 June 1912).
5802:Introduction to quantum mechanics
1243:{\displaystyle n\lambda =2\pi r.}
353:Rutherford scattering experiments
283:Planck's discovery of the quantum
7932:
7923:
7922:
7659:. New York: Dover Publications.
6981:from the original on 2022-10-09.
6156:from the original on 2022-10-09.
4346:Since the energy of a photon is
3120:) therefore has about 13.6
2220:of the circular orbit scales as
70:), where the negatively charged
7750:The European Physical Journal H
7708:(4th ed.). W. H. Freeman.
7678:Thirty Years That Shook Physics
7621:(in French). Gauthier-Villars.
6729:The European Physical Journal H
6167:Rayleigh, Lord (January 1906).
5645:. According to his model for a
5637:Bohr model of the chemical bond
4906:line), and their atomic number
3315:of the electron (511 keV),
2737:The smallest possible value of
764:of the hydrogen atom and other
6867:Bury, Charles R. (July 1921).
6025:Niels Bohr: a centenary volume
5342:spherical cloud of probability
5236:
5223:
5220:
5193:
5181:
5168:
5044:
5031:
4867:periodic table of the elements
3452:
3427:
3210:
3184:
3131:) is â3.4 eV. The third (
3002:
2976:
2374:
2358:
885:Like Einstein's theory of the
762:energies of the allowed orbits
729:{\displaystyle \hbar =h/2\pi }
382:attracting negatively charged
199:'s Solar System model (1897),
18:SommerfeldâWilson quantization
1:
7733:(8th ed.). Brooks/Cole.
6820:Nicholson, J. W. (May 1914).
5873:"Les HypothÚses moléculaires"
512:{\displaystyle qv^{2}=nh\nu }
223:'s quantum model (1910), the
7973:Foundational quantum physics
7911:(relativistic quantum model)
7478:Bohr, N. (1 November 1913).
6781:Bohr, N. (1 November 1913).
5643:a model of the chemical bond
5569:in 1925, using Heisenberg's
5397:The model also violates the
5331:Nevertheless, in the modern
1584:{\displaystyle \lambda =h/p}
117:) it results in a photon of
7445:Bohr, N. (September 1913).
7070:European Journal of Physics
6270:10.1007/978-3-031-57934-9_6
5835:American Journal of Physics
5565:, which was first given by
4580:Shell model (heavier atoms)
2237:{\displaystyle {\sqrt {r}}}
688:{\displaystyle n=1,2,3,...}
32:Bohr's law (disambiguation)
8004:
7770:10.1140/epjh/e2011-20031-x
7091:10.1088/0143-0807/20/3/312
6741:10.1140/epjh/e2012-30009-7
6351:"Niels Bohr â Session III"
6049:Heilbron, John L. (1968).
5634:
5631:Model of the chemical bond
5423:
4583:
3864:
2044:is an integer multiple of
1167:BohrâKramersâSlater theory
592:classical electromagnetism
350:
323:
319:
298:
267:obsolete scientific theory
63:) or a hydrogen-like ion (
36:
29:
7918:
7851:vortex theory of the atom
7511:Bohr, N. (October 1913).
7504:10.1080/14786441308635031
7471:10.1080/14786441308634993
7438:10.1080/14786441308634955
7253:. Springer. p. 203.
7236:10.1080/14786440608635362
7154:10.1080/00268978200100752
7122:Physikalische Zeitschrift
6807:10.1080/14786441308635031
6674:10.1080/14786441308634955
6369:"Niels Bohr â Session II"
6185:10.1080/14786440609463428
6129:10.1080/14786441308634955
5692:technology in particular.
4944:theoretical explanation.
4926:, that the atomic number
3871:Beginning in late 1860s,
2128:. The energy scales as 1/
395:electromagnetic radiation
343:lines in atomic spectra.
263:first-order approximation
7203:10.1002/andp.19163561702
7044:Moseley, H.G.J. (1913).
7031:"Niels Bohr â Session I"
6927:10.1002/andp.19163540302
6723:Baily, C. (2013-01-01).
6612:10.1103/PhysRevA.37.1449
5544:correspondence principle
5540:action-angle coordinates
2326:{\displaystyle \Delta L}
1821:is the electron's mass,
1160:correspondence principle
697:principal quantum number
347:Rutherford nuclear model
301:History of atomic theory
180:to the structure of the
100:principal quantum number
37:Not to be confused with
7689:. John Wiley and Sons.
7552:Bohr, N. (March 1921).
7384:"Logo Usage Guidelines"
7326:10.1073/pnas.0505778102
7113:van den Broek, Antonius
6695:Baggott, J. E. (2013).
6549:The Age of Entanglement
5789:FranckâHertz experiment
5750:The JavaScript library
5555:magnetic quantum number
5442:quantization condition
3391:fine-structure constant
1555:de Broglie's wavelength
1007:{\displaystyle E_{n-k}}
877:is the Planck constant.
567:equation discovered by
52:The Bohr model of the
7651:Linus Pauling (1988).
7412:Bohr, N. (July 1913).
7249:Shaviv, Glora (2010).
7223:Philosophical Magazine
7175:A. Sommerfeld (1916).
7050:Philosophical Magazine
6764:Philosophical Magazine
6656:Bohr, N. (July 1913).
6484:10.1093/mnras/72.8.677
6437:Pais, Abraham (2002).
6329:de Broglie et al. 1912
6317:de Broglie et al. 1912
6305:de Broglie et al. 1912
6293:de Broglie et al. 1912
6198:de Broglie et al. 1912
6103:Bohr, N. (July 1913).
5893:de Broglie et al. 1912
5716:A similar symbol, the
5671:
5507:
5421:
5252:
5107:
4918:Antonius Van den Broek
4803:John William Nicholson
4483:
4384:
4338:
4255:
4090:
4006:
3978:
3898:
3850:
3778:
3569:
3469:
3383:
3305:
3256:
3104:
2879:
2741:in the hydrogen atom (
2728:
2620:
2513:
2444:
2327:
2310:are equally spaced by
2297:
2238:
2204:
2091:
1987:
1920:
1804:
1653:
1644:Electron energy levels
1605:
1585:
1547:
1513:
1464:
1444:
1415:
1357:
1299:
1244:
1195:
1194:{\displaystyle \hbar }
1171:conservation of energy
1152:
1132:
1108:
1088:
1074:-th harmonic of orbit
1068:
1048:
1028:
1008:
975:
941:
921:
871:
851:
789:
750:
736:. The lowest value of
730:
689:
639:
529:John William Nicholson
513:
471:
451:
313:
229:John William Nicholson
126:
84:electromagnetic energy
7846:(billiard ball model)
7680:. Dover Publications.
6943:Kragh, Helge (2012).
5952:Kragh, Helge (2012).
5877:La Revue scientifique
5783:BohrâSommerfeld model
5736:Miscellaneous Symbols
5708:minor league baseball
5669:
5508:
5426:BohrâSommerfeld model
5419:
5399:uncertainty principle
5253:
5108:
4484:
4385:
4339:
4256:
4091:
4007:
4005:{\displaystyle \tau }
3979:
3899:
3856: (positronium).
3851:
3779:
3570:
3470:
3384:
3306:
3257:
3105:
2880:
2729:
2621:
2514:
2445:
2328:
2298:
2239:
2216:The angular momentum
2205:
2092:
1988:
1921:
1805:
1664:, and doubly ionized
1651:
1606:
1586:
1548:
1514:
1465:
1463:{\displaystyle \ell }
1445:
1416:
1358:
1300:
1259:de Broglie wavelength
1245:
1196:
1153:
1133:
1109:
1089:
1069:
1049:
1034:is much smaller than
1029:
1009:
976:
974:{\displaystyle E_{n}}
942:
922:
872:
852:
790:
751:
731:
690:
640:
523:Nicholson atom theory
514:
472:
452:
450:{\displaystyle h\nu }
308:
275:energy level diagrams
203:'s model (1901), the
139:RutherfordâBohr model
51:
7903:electron cloud model
7860:(cubical atom model)
6575:. November 17, 2015.
5741:The television show
5711:Albuquerque Isotopes
5616:, which is called a
5548:adiabatic invariants
5449:
5123:
4975:
4814:Charles Rugeley Bury
4634:Electrons per shell
4400:
4353:
4270:
4100:
4016:
3996:
3912:
3888:
3799:
3637:
3505:
3399:
3321:
3276:
3163:
2899:
2759:
2640:
2540:
2468:
2340:
2314:
2251:
2224:
2139:
2054:
1936:
1854:
1719:
1595:
1561:
1529:
1477:
1454:
1428:
1373:
1315:
1268:
1216:
1185:
1142:
1122:
1098:
1078:
1058:
1038:
1018:
985:
958:
940:{\displaystyle \nu }
931:
920:{\displaystyle \nu }
911:
887:photoelectric effect
861:
803:
788:{\displaystyle \nu }
779:
740:
703:
649:
605:
481:
461:
438:
320:Thomson's atom model
157:, it supplanted the
110:, and for hydrogen (
7887:(old quantum model)
7762:2011EPJH...36..327K
7570:1921Natur.107..104B
7529:1913Natur..92..231B
7496:1913PMag...26..857B
7463:1913PMag...26..476B
7430:1913PMag...26....1B
7317:2005PNAS..10211985S
7301:(34): 11985â11988.
7195:1916AnP...356....1S
7083:1999EJPh...20..213W
7029:(31 October 1962).
7013:10.1021/ja02227a002
6919:1916AnP...354..229K
6901:Kossel, W. (1916).
6885:10.1021/ja01440a023
6838:1914Natur..93..268N
6799:1913PMag...26..857B
6604:1988PhRvA..37.1449M
6367:(1 November 1962).
6349:(7 November 1962).
6121:1913PMag...26....1B
5895:, pp. 122â123.
5847:1997AmJPh..65..933L
5744:The Big Bang Theory
5651:dynamic equilibrium
5585:developed in 1926.
5466:
5381:hyperfine structure
4884:transition elements
4628:Electrons per shell
4622:Electrons per shell
4615:
4468:
4443:
4243:
4218:
1699:Classical mechanics
1621:more accurate model
1546:{\displaystyle 2/h}
1443:{\displaystyle mvr}
1308:which implies that
407:electric discharges
334:, now known as the
186:electrostatic force
7988:Old quantum theory
7909:DiracâGordon model
7872:plum pudding model
7554:"Atomic Structure"
7216:W. Wilson (1915).
7182:Annalen der Physik
6907:Annalen der Physik
6403:10.1007/BF00357268
6067:10.1007/BF00411591
5672:
5503:
5452:
5422:
5248:
5103:
4613:
4479:
4454:
4429:
4380:
4334:
4251:
4229:
4204:
4086:
4002:
3974:
3894:
3846:
3774:
3565:
3465:
3379:
3301:
3252:
3100:
2888:The energy of the
2875:
2724:
2616:
2598:
2509:
2440:
2323:
2293:
2234:
2200:
2122:Kepler's third law
2087:
1983:
1916:
1800:
1668:, but it includes
1654:
1638:hydrogen-like atom
1601:
1581:
1543:
1509:
1460:
1440:
1411:
1353:
1295:
1261:of an electron is
1240:
1191:
1148:
1128:
1104:
1084:
1064:
1044:
1024:
1004:
971:
937:
917:
881:Other points are:
867:
847:
785:
746:
726:
685:
635:
549:plum pudding model
509:
467:
447:
365:demonstrated that
336:Plum pudding model
326:Plum pudding model
314:
288:old quantum theory
257:, compared to the
233:quantum mechanical
217:plum pudding model
215:model (1904), the
159:plum pudding model
127:
7950:
7949:
7880:(planetary model)
7867:(Saturnian model)
7740:978-0-495-82992-8
7655:General Chemistry
7643:General Chemistry
7564:(2682): 104â107.
7523:(2295): 231â232.
7369:978-3-540-70626-7
7142:Molecular Physics
6832:(2324): 268â269.
6706:978-0-19-965597-7
6592:Physical Review A
6448:978-0-19-851997-3
6279:978-3-031-57933-2
6035:978-0-674-62415-3
5963:978-0-19-163046-0
5796:inert-pair effect
5778:Balmer's Constant
5722:American Atheists
5656:Coulomb repulsion
5647:diatomic molecule
5583:Erwin Schrödinger
5375:The existence of
5307:Siegbahn notation
5218:
5214:
5162:
5093:
5073:
4914:Ernest Rutherford
4798:
4797:
4469:
4444:
4411:
4375:
4329:
4244:
4219:
4192:
4084:
3964:
3944:
3897:{\displaystyle R}
3844:
3769:
3710:
3647:
3560:
3425:
3377:
3358:
3247:
3088:
3084:
3049:
2955:
2863:
2849:
2823:
2752:and is equal to:
2719:
2599:
2597:
2590:
2565:
2550:
2495:
2435:
2404:
2384:
2288:
2268:
2232:
2174:
1956:
1911:
1910:
1827:elementary charge
1795:
1751:
1707:centripetal force
1660:, singly ionized
1633:Erwin Schrödinger
1625:Werner Heisenberg
1617:quantum mechanics
1604:{\displaystyle h}
1504:
1394:
1336:
1290:
1151:{\displaystyle k}
1131:{\displaystyle n}
1107:{\displaystyle n}
1087:{\displaystyle n}
1067:{\displaystyle k}
1047:{\displaystyle n}
1027:{\displaystyle k}
870:{\displaystyle h}
749:{\displaystyle n}
470:{\displaystyle n}
432:Arthur Erich Haas
420:Solvay Conference
376:model of the atom
371:Ernest Rutherford
279:Arthur Erich Haas
271:quantum mechanics
237:classical physics
151:Ernest Rutherford
16:(Redirected from
7995:
7978:Hydrogen physics
7936:
7926:
7925:
7878:Rutherford model
7822:
7815:
7808:
7799:
7781:
7744:
7719:
7700:
7681:
7670:
7658:
7646:
7630:
7602:
7589:
7578:10.1038/107104a0
7548:
7537:10.1038/092231d0
7507:
7490:(155): 857â875.
7474:
7457:(153): 476â502.
7441:
7399:
7398:
7396:
7395:
7380:
7374:
7373:
7355:
7349:
7348:
7338:
7328:
7310:
7286:
7280:
7279:
7271:
7265:
7264:
7246:
7240:
7239:
7230:(174): 795â802.
7213:
7207:
7206:
7172:
7166:
7165:
7148:(5): 1001â1019.
7137:
7131:
7130:
7115:(January 1913).
7109:
7103:
7102:
7064:
7058:
7057:
7041:
7035:
7034:
7023:
7017:
7016:
6993:Langmuir, Irving
6989:
6983:
6982:
6980:
6949:
6940:
6931:
6930:
6898:
6889:
6888:
6879:(7): 1602â1609.
6864:
6858:
6857:
6846:10.1038/093268a0
6817:
6811:
6810:
6793:(155): 857â875.
6778:
6772:
6771:
6759:
6753:
6752:
6720:
6711:
6710:
6692:
6686:
6685:
6653:
6647:
6646:
6638:
6632:
6631:
6598:(5): 1449â1455.
6583:
6577:
6576:
6563:
6557:
6556:
6544:
6538:
6537:
6529:
6523:
6522:
6506:
6497:
6496:
6486:
6462:
6453:
6452:
6434:
6423:
6422:
6386:
6373:
6372:
6361:
6355:
6354:
6343:
6332:
6326:
6320:
6314:
6308:
6302:
6296:
6290:
6284:
6283:
6255:
6249:
6248:
6212:
6201:
6195:
6189:
6188:
6164:
6158:
6157:
6155:
6148:
6139:
6133:
6132:
6100:
6087:
6086:
6046:
6040:
6039:
6019:
6010:
6009:
5998:10.2307/27757291
5981:
5968:
5967:
5949:
5938:
5937:
5926:10.2307/27757389
5909:
5896:
5890:
5881:
5880:
5865:
5859:
5858:
5830:
5695:The flag of the
5684:The logo of the
5677:planetary system
5571:matrix mechanics
5512:
5510:
5509:
5504:
5490:
5489:
5476:
5475:
5465:
5460:
5326:
5257:
5255:
5254:
5249:
5244:
5243:
5219:
5216:
5212:
5211:
5210:
5189:
5188:
5167:
5163:
5155:
5149:
5148:
5147:
5112:
5110:
5109:
5104:
5099:
5095:
5094:
5092:
5091:
5079:
5074:
5072:
5071:
5059:
5052:
5051:
5030:
5029:
5028:
5015:
5014:
5002:
5001:
4939:
4931:
4911:
4616:
4571:
4565:
4555:
4549:
4539:
4530:
4517:
4504:
4488:
4486:
4485:
4480:
4475:
4471:
4470:
4467:
4462:
4450:
4445:
4442:
4437:
4425:
4412:
4404:
4389:
4387:
4386:
4381:
4376:
4371:
4363:
4343:
4341:
4340:
4335:
4330:
4328:
4327:
4318:
4317:
4316:
4304:
4303:
4290:
4285:
4284:
4260:
4258:
4257:
4252:
4250:
4246:
4245:
4242:
4237:
4225:
4220:
4217:
4212:
4200:
4193:
4191:
4190:
4181:
4180:
4179:
4167:
4166:
4153:
4148:
4147:
4146:
4145:
4128:
4127:
4126:
4125:
4095:
4093:
4092:
4087:
4085:
4083:
4082:
4081:
4072:
4071:
4061:
4060:
4059:
4047:
4046:
4033:
4028:
4027:
4011:
4009:
4008:
4003:
3983:
3981:
3980:
3975:
3970:
3966:
3965:
3963:
3962:
3950:
3945:
3943:
3942:
3930:
3906:Rydberg constant
3904:, now known the
3903:
3901:
3900:
3895:
3877:Johannes Rydberg
3855:
3853:
3852:
3847:
3845:
3843:
3842:
3841:
3828:
3827:
3826:
3816:
3811:
3810:
3783:
3781:
3780:
3775:
3770:
3768:
3767:
3766:
3765:
3755:
3750:
3749:
3748:
3728:
3726:
3725:
3724:
3711:
3709:
3708:
3707:
3706:
3693:
3692:
3691:
3680:
3679:
3678:
3677:
3667:
3666:
3665:
3654:
3649:
3648:
3645:
3610:
3574:
3572:
3571:
3566:
3561:
3559:
3558:
3549:
3548:
3547:
3546:
3536:
3535:
3525:
3517:
3516:
3488:
3474:
3472:
3471:
3466:
3464:
3463:
3451:
3450:
3441:
3440:
3439:
3426:
3418:
3413:
3412:
3411:
3388:
3386:
3385:
3380:
3378:
3370:
3359:
3357:
3349:
3348:
3347:
3338:
3337:
3336:
3325:
3313:rest mass energy
3310:
3308:
3307:
3302:
3300:
3299:
3290:
3289:
3288:
3261:
3259:
3258:
3253:
3248:
3246:
3245:
3244:
3231:
3230:
3229:
3228:
3218:
3217:
3208:
3207:
3198:
3197:
3196:
3182:
3177:
3176:
3175:
3137:
3130:
3119:
3109:
3107:
3106:
3101:
3096:
3086:
3085:
3083:
3082:
3073:
3072:
3071:
3055:
3050:
3048:
3047:
3046:
3037:
3036:
3023:
3022:
3021:
3020:
3010:
3009:
3000:
2999:
2990:
2989:
2988:
2975:
2974:
2964:
2956:
2954:
2953:
2952:
2939:
2938:
2937:
2928:
2927:
2926:
2912:
2884:
2882:
2881:
2876:
2871:
2861:
2854:
2847:
2846:
2845:
2824:
2822:
2821:
2820:
2819:
2809:
2808:
2799:
2798:
2797:
2786:
2785:
2776:
2771:
2770:
2748:) is called the
2747:
2733:
2731:
2730:
2725:
2720:
2718:
2717:
2716:
2715:
2705:
2704:
2695:
2694:
2693:
2679:
2678:
2677:
2668:
2667:
2657:
2652:
2651:
2625:
2623:
2622:
2617:
2600:
2596:
2592:
2591:
2588:
2581:
2580:
2579:
2567:
2566:
2563:
2556:
2554:
2552:
2551:
2548:
2518:
2516:
2515:
2510:
2496:
2494:
2486:
2478:
2449:
2447:
2446:
2441:
2436:
2434:
2433:
2424:
2413:
2405:
2403:
2402:
2390:
2385:
2383:
2382:
2381:
2353:
2332:
2330:
2329:
2324:
2302:
2300:
2299:
2294:
2289:
2287:
2286:
2274:
2269:
2261:
2243:
2241:
2240:
2235:
2233:
2228:
2209:
2207:
2206:
2201:
2196:
2195:
2191:
2175:
2173:
2172:
2168:
2152:
2096:
2094:
2093:
2088:
2068:
2067:
2066:
2043:
2027:angular momentum
2007:potential energy
1992:
1990:
1989:
1984:
1979:
1978:
1969:
1968:
1967:
1957:
1949:
1925:
1923:
1922:
1917:
1912:
1909:
1905:
1904:
1903:
1892:
1891:
1890:
1881:
1880:
1879:
1865:
1864:
1838:Coulomb constant
1809:
1807:
1806:
1801:
1796:
1794:
1793:
1784:
1783:
1782:
1773:
1772:
1771:
1757:
1752:
1747:
1746:
1745:
1736:
1735:
1734:
1723:
1709:is equal to the
1610:
1608:
1607:
1602:
1590:
1588:
1587:
1582:
1577:
1552:
1550:
1549:
1544:
1539:
1518:
1516:
1515:
1510:
1505:
1503:
1495:
1487:
1469:
1467:
1466:
1461:
1449:
1447:
1446:
1441:
1420:
1418:
1417:
1412:
1395:
1393:
1385:
1377:
1362:
1360:
1359:
1354:
1337:
1335:
1327:
1319:
1304:
1302:
1301:
1296:
1291:
1289:
1278:
1249:
1247:
1246:
1241:
1200:
1198:
1197:
1192:
1157:
1155:
1154:
1149:
1137:
1135:
1134:
1129:
1113:
1111:
1110:
1105:
1093:
1091:
1090:
1085:
1073:
1071:
1070:
1065:
1053:
1051:
1050:
1045:
1033:
1031:
1030:
1025:
1013:
1011:
1010:
1005:
1003:
1002:
980:
978:
977:
972:
970:
969:
946:
944:
943:
938:
926:
924:
923:
918:
876:
874:
873:
868:
856:
854:
853:
848:
837:
836:
824:
823:
794:
792:
791:
786:
755:
753:
752:
747:
735:
733:
732:
727:
719:
694:
692:
691:
686:
644:
642:
641:
636:
619:
618:
617:
573:Johannes Rydberg
518:
516:
515:
510:
496:
495:
476:
474:
473:
468:
456:
454:
453:
448:
225:Rutherford model
149:and building on
116:
105:
69:
62:
21:
8003:
8002:
7998:
7997:
7996:
7994:
7993:
7992:
7963:1913 in science
7953:
7952:
7951:
7946:
7914:
7890:
7836:Historic models
7831:
7826:
7788:
7747:
7741:
7728:
7723:Klaus Hentschel
7716:
7703:
7697:
7684:
7675:
7667:
7650:
7640:
7637:
7635:Further reading
7614:
7592:
7551:
7510:
7477:
7444:
7411:
7408:
7406:Primary sources
7403:
7402:
7393:
7391:
7382:
7381:
7377:
7370:
7357:
7356:
7352:
7308:physics/0508161
7288:
7287:
7283:
7274:ĐĐŸŃ Đ. (1970).
7273:
7272:
7268:
7261:
7248:
7247:
7243:
7215:
7214:
7210:
7174:
7173:
7169:
7139:
7138:
7134:
7111:
7110:
7106:
7066:
7065:
7061:
7043:
7042:
7038:
7025:
7024:
7020:
6991:
6990:
6986:
6978:
6947:
6942:
6941:
6934:
6900:
6899:
6892:
6866:
6865:
6861:
6819:
6818:
6814:
6780:
6779:
6775:
6761:
6760:
6756:
6722:
6721:
6714:
6707:
6694:
6693:
6689:
6655:
6654:
6650:
6643:Collected works
6640:
6639:
6635:
6585:
6584:
6580:
6565:
6564:
6560:
6546:
6545:
6541:
6531:
6530:
6526:
6508:
6507:
6500:
6464:
6463:
6456:
6449:
6436:
6435:
6426:
6388:
6387:
6376:
6363:
6362:
6358:
6345:
6344:
6335:
6327:
6323:
6315:
6311:
6303:
6299:
6291:
6287:
6280:
6257:
6256:
6252:
6229:10.1038/498027a
6223:(7452): 27â30.
6214:
6213:
6204:
6196:
6192:
6179:(61): 117â123.
6166:
6165:
6161:
6153:
6146:
6141:
6140:
6136:
6102:
6101:
6090:
6048:
6047:
6043:
6036:
6021:
6020:
6013:
5983:
5982:
5971:
5964:
5951:
5950:
5941:
5911:
5910:
5899:
5891:
5884:
5867:
5866:
5862:
5855:10.1119/1.18691
5832:
5831:
5824:
5819:
5814:
5809:
5773:1913 in science
5768:
5690:nuclear fission
5664:
5639:
5633:
5618:prequantization
5575:atomic orbitals
5528:
5521:
5481:
5467:
5447:
5446:
5428:
5414:
5392:magnetic fields
5363:Rydberg formula
5318:
5315:
5303:
5296:
5277:
5268:
5235:
5202:
5180:
5150:
5138:
5121:
5120:
5083:
5063:
5057:
5053:
5043:
5019:
5006:
4993:
4973:
4972:
4954:Irving Langmuir
4938: â 1)
4933:
4927:
4907:
4892:
4837:shell structure
4824:Irving Langmuir
4600:
4588:
4582:
4567:
4557:
4551:
4541:
4535:
4528:
4523:
4515:
4510:
4502:
4497:
4423:
4419:
4398:
4397:
4364:
4351:
4350:
4319:
4308:
4295:
4291:
4276:
4268:
4267:
4264:Planck constant
4198:
4194:
4182:
4171:
4158:
4154:
4137:
4132:
4117:
4112:
4098:
4097:
4073:
4063:
4062:
4051:
4038:
4034:
4019:
4014:
4013:
3994:
3993:
3954:
3934:
3928:
3924:
3910:
3909:
3886:
3885:
3869:
3867:Rydberg formula
3863:
3861:Rydberg formula
3833:
3829:
3817:
3802:
3797:
3796:
3756:
3739:
3732:
3715:
3697:
3682:
3681:
3668:
3656:
3655:
3640:
3635:
3634:
3605:
3550:
3537:
3527:
3526:
3508:
3503:
3502:
3480:
3455:
3442:
3430:
3402:
3397:
3396:
3350:
3339:
3327:
3326:
3319:
3318:
3291:
3279:
3274:
3273:
3236:
3232:
3219:
3209:
3199:
3187:
3183:
3166:
3161:
3160:
3155:
3132:
3125:
3114:
3074:
3063:
3056:
3038:
3028:
3024:
3011:
3001:
2991:
2979:
2966:
2965:
2944:
2940:
2929:
2917:
2913:
2897:
2896:
2834:
2810:
2800:
2788:
2787:
2777:
2762:
2757:
2756:
2742:
2706:
2696:
2684:
2680:
2669:
2659:
2658:
2643:
2638:
2637:
2583:
2582:
2571:
2558:
2557:
2543:
2538:
2537:
2487:
2479:
2466:
2465:
2425:
2414:
2394:
2373:
2357:
2338:
2337:
2312:
2311:
2278:
2249:
2248:
2222:
2221:
2179:
2156:
2137:
2136:
2105:
2057:
2052:
2051:
2039:
2029:
1970:
1958:
1934:
1933:
1894:
1893:
1882:
1870:
1866:
1852:
1851:
1835:
1820:
1785:
1774:
1762:
1758:
1737:
1725:
1724:
1717:
1716:
1646:
1593:
1592:
1559:
1558:
1527:
1526:
1496:
1488:
1475:
1474:
1452:
1451:
1426:
1425:
1386:
1378:
1371:
1370:
1328:
1320:
1313:
1312:
1282:
1266:
1265:
1214:
1213:
1183:
1182:
1140:
1139:
1120:
1119:
1096:
1095:
1076:
1075:
1056:
1055:
1036:
1035:
1016:
1015:
988:
983:
982:
961:
956:
955:
949:
929:
928:
909:
908:
859:
858:
828:
815:
801:
800:
797:Planck relation
777:
776:
738:
737:
701:
700:
647:
646:
608:
603:
602:
599:Planck constant
577:Rydberg formula
561:
534:Planck constant
525:
487:
479:
478:
477:is an integer:
459:
458:
436:
435:
428:Hendrik Lorentz
416:
355:
349:
328:
322:
303:
297:
244:Rydberg formula
209:Hantaro Nagaoka
111:
103:
74:confined to an
64:
57:
46:
35:
28:
23:
22:
15:
12:
11:
5:
8001:
7999:
7991:
7990:
7985:
7980:
7975:
7970:
7968:Atomic physics
7965:
7955:
7954:
7948:
7947:
7945:
7944:
7938:Portal:Physics
7930:
7928:Category:Atoms
7919:
7916:
7915:
7913:
7912:
7905:
7898:
7896:
7895:Current models
7892:
7891:
7889:
7888:
7881:
7874:
7868:
7861:
7854:
7847:
7839:
7837:
7833:
7832:
7827:
7825:
7824:
7817:
7810:
7802:
7796:
7795:
7787:
7786:External links
7784:
7783:
7782:
7756:(3): 327â352.
7745:
7739:
7726:
7720:
7714:
7706:Modern Physics
7701:
7695:
7682:
7673:
7672:
7671:
7665:
7636:
7633:
7632:
7631:
7612:
7590:
7549:
7508:
7475:
7442:
7407:
7404:
7401:
7400:
7375:
7368:
7350:
7281:
7266:
7260:978-3642020872
7259:
7241:
7208:
7167:
7132:
7104:
7077:(3): 213â220.
7059:
7052:. 6th series.
7036:
7018:
7007:(6): 868â934.
6984:
6932:
6913:(3): 229â362.
6890:
6859:
6812:
6773:
6754:
6712:
6705:
6687:
6648:
6633:
6578:
6558:
6551:. p. 55.
6539:
6524:
6498:
6454:
6447:
6424:
6397:(2): 160â184.
6374:
6356:
6333:
6331:, p. 447.
6321:
6319:, p. 109.
6309:
6307:, p. 127.
6297:
6295:, p. 124.
6285:
6278:
6250:
6202:
6200:, p. 114.
6190:
6159:
6134:
6088:
6061:(4): 247â307.
6041:
6034:
6011:
5969:
5962:
5939:
5897:
5882:
5860:
5821:
5820:
5818:
5815:
5813:
5810:
5808:
5807:
5804:
5799:
5792:
5785:
5780:
5775:
5769:
5767:
5764:
5763:
5762:
5755:
5748:
5739:
5729:
5714:
5704:
5693:
5663:
5660:
5635:Main article:
5632:
5629:
5603:curvature form
5579:wave mechanics
5567:Wolfgang Pauli
5526:
5519:
5514:
5513:
5502:
5499:
5496:
5493:
5488:
5484:
5480:
5474:
5470:
5464:
5459:
5455:
5424:Main article:
5413:
5410:
5409:
5408:
5405:
5402:
5395:
5384:
5377:fine structure
5373:
5366:
5314:
5311:
5301:
5294:
5275:
5266:
5259:
5258:
5247:
5242:
5238:
5234:
5231:
5228:
5225:
5222:
5209:
5205:
5201:
5198:
5195:
5192:
5187:
5183:
5179:
5176:
5173:
5170:
5166:
5161:
5158:
5153:
5146:
5141:
5137:
5134:
5131:
5128:
5114:
5113:
5102:
5098:
5090:
5086:
5082:
5077:
5070:
5066:
5062:
5056:
5050:
5046:
5042:
5039:
5036:
5033:
5027:
5022:
5018:
5013:
5009:
5005:
5000:
4996:
4992:
4989:
4986:
4983:
4980:
4949:Walther Kossel
4891:
4888:
4820:Walther Kossel
4810:periodic table
4796:
4795:
4794:8, 8, 4, 2, 2
4792:
4789:
4786:
4783:
4780:
4776:
4775:
4772:
4769:
4766:
4763:
4760:
4756:
4755:
4752:
4749:
4746:
4743:
4740:
4736:
4735:
4732:
4729:
4726:
4723:
4720:
4716:
4715:
4712:
4709:
4706:
4703:
4700:
4696:
4695:
4692:
4689:
4686:
4683:
4680:
4676:
4675:
4672:
4669:
4666:
4663:
4660:
4656:
4655:
4652:
4649:
4646:
4643:
4640:
4636:
4635:
4632:
4629:
4626:
4623:
4620:
4598:
4586:Electron shell
4584:Main article:
4581:
4578:
4574:Electron shell
4526:
4513:
4500:
4490:
4489:
4478:
4474:
4466:
4461:
4457:
4453:
4448:
4441:
4436:
4432:
4428:
4422:
4418:
4415:
4410:
4407:
4391:
4390:
4379:
4374:
4370:
4367:
4361:
4358:
4333:
4326:
4322:
4315:
4311:
4307:
4302:
4298:
4294:
4288:
4283:
4279:
4275:
4249:
4241:
4236:
4232:
4228:
4223:
4216:
4211:
4207:
4203:
4197:
4189:
4185:
4178:
4174:
4170:
4165:
4161:
4157:
4151:
4144:
4140:
4135:
4131:
4124:
4120:
4115:
4111:
4108:
4105:
4080:
4076:
4070:
4066:
4058:
4054:
4050:
4045:
4041:
4037:
4031:
4026:
4022:
4001:
3973:
3969:
3961:
3957:
3953:
3948:
3941:
3937:
3933:
3927:
3923:
3920:
3917:
3893:
3865:Main article:
3862:
3859:
3858:
3857:
3840:
3836:
3832:
3825:
3820:
3814:
3809:
3805:
3785:
3784:
3773:
3764:
3759:
3754:
3747:
3742:
3738:
3735:
3731:
3723:
3718:
3714:
3705:
3700:
3696:
3690:
3685:
3676:
3671:
3664:
3659:
3652:
3643:
3576:
3575:
3564:
3557:
3553:
3545:
3540:
3534:
3530:
3523:
3520:
3515:
3511:
3477:
3476:
3462:
3458:
3454:
3449:
3445:
3438:
3433:
3429:
3424:
3421:
3416:
3410:
3405:
3394:
3376:
3373:
3368:
3365:
3362:
3356:
3353:
3346:
3342:
3335:
3330:
3316:
3298:
3294:
3287:
3282:
3263:
3262:
3251:
3243:
3239:
3235:
3227:
3222:
3216:
3212:
3206:
3202:
3195:
3190:
3186:
3180:
3174:
3169:
3153:
3144:Wallis product
3111:
3110:
3099:
3095:
3092:
3081:
3077:
3070:
3066:
3062:
3059:
3053:
3045:
3041:
3035:
3031:
3027:
3019:
3014:
3008:
3004:
2998:
2994:
2987:
2982:
2978:
2973:
2969:
2962:
2959:
2951:
2947:
2943:
2936:
2932:
2925:
2920:
2916:
2910:
2907:
2904:
2886:
2885:
2874:
2870:
2867:
2860:
2857:
2853:
2844:
2841:
2837:
2833:
2830:
2827:
2818:
2813:
2807:
2803:
2796:
2791:
2784:
2780:
2774:
2769:
2765:
2735:
2734:
2723:
2714:
2709:
2703:
2699:
2692:
2687:
2683:
2676:
2672:
2666:
2662:
2655:
2650:
2646:
2627:
2626:
2615:
2612:
2609:
2606:
2603:
2595:
2586:
2578:
2574:
2570:
2561:
2546:
2520:
2519:
2508:
2505:
2502:
2499:
2493:
2490:
2485:
2482:
2476:
2473:
2451:
2450:
2439:
2432:
2428:
2423:
2420:
2417:
2411:
2408:
2401:
2397:
2393:
2388:
2380:
2376:
2372:
2369:
2366:
2363:
2360:
2356:
2351:
2348:
2345:
2322:
2319:
2304:
2303:
2292:
2285:
2281:
2277:
2272:
2267:
2264:
2259:
2256:
2231:
2211:
2210:
2199:
2194:
2190:
2186:
2182:
2178:
2171:
2167:
2163:
2159:
2155:
2150:
2147:
2144:
2120:determined by
2104:
2101:
2100:
2099:
2098:
2097:
2086:
2083:
2080:
2077:
2074:
2071:
2065:
2060:
2037:
2022:
2021:
2019:A quantum rule
2015:
2014:
2011:virial theorem
1995:
1994:
1993:
1982:
1977:
1973:
1966:
1961:
1955:
1952:
1947:
1944:
1941:
1928:
1927:
1926:
1915:
1908:
1902:
1897:
1889:
1885:
1878:
1873:
1869:
1862:
1859:
1844:is the atom's
1833:
1818:
1812:
1811:
1810:
1799:
1792:
1788:
1781:
1777:
1770:
1765:
1761:
1755:
1750:
1744:
1740:
1733:
1728:
1702:
1701:
1674:Rydberg states
1645:
1642:
1600:
1580:
1576:
1572:
1569:
1566:
1542:
1538:
1534:
1520:
1519:
1508:
1502:
1499:
1494:
1491:
1485:
1482:
1459:
1439:
1436:
1433:
1422:
1421:
1410:
1407:
1404:
1401:
1398:
1392:
1389:
1384:
1381:
1364:
1363:
1352:
1349:
1346:
1343:
1340:
1334:
1331:
1326:
1323:
1306:
1305:
1294:
1288:
1285:
1281:
1276:
1273:
1251:
1250:
1239:
1236:
1233:
1230:
1227:
1224:
1221:
1190:
1179:
1178:
1163:
1147:
1127:
1116:Rydberg states
1103:
1083:
1063:
1043:
1023:
1001:
998:
995:
991:
968:
964:
947:
936:
916:
905:
898:Maxwell theory
879:
878:
866:
846:
843:
840:
835:
831:
827:
822:
818:
814:
811:
808:
784:
773:
745:
725:
722:
718:
714:
711:
708:
695:is called the
684:
681:
678:
675:
672:
669:
666:
663:
660:
657:
654:
634:
631:
628:
625:
622:
616:
611:
595:
560:
557:
524:
521:
508:
505:
502:
499:
494:
490:
486:
466:
446:
443:
415:
412:
403:orbital period
391:Larmor formula
367:alpha particle
363:Ernest Marsden
351:Main article:
348:
345:
340:beta particles
324:Main article:
321:
318:
311:X-ray notation
299:Main article:
296:
293:
169:surrounded by
131:atomic physics
80:atomic nucleus
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
8000:
7989:
7986:
7984:
7981:
7979:
7976:
7974:
7971:
7969:
7966:
7964:
7961:
7960:
7958:
7943:
7939:
7935:
7931:
7929:
7921:
7920:
7917:
7910:
7906:
7904:
7900:
7899:
7897:
7893:
7886:
7882:
7879:
7875:
7873:
7869:
7866:
7865:Nagaoka model
7862:
7859:
7855:
7852:
7848:
7845:
7841:
7840:
7838:
7834:
7830:
7829:Atomic models
7823:
7818:
7816:
7811:
7809:
7804:
7803:
7800:
7793:
7790:
7789:
7785:
7779:
7775:
7771:
7767:
7763:
7759:
7755:
7751:
7746:
7742:
7736:
7732:
7727:
7724:
7721:
7717:
7715:0-7167-4345-0
7711:
7707:
7702:
7698:
7696:0-471-52440-9
7692:
7688:
7683:
7679:
7674:
7668:
7666:0-486-65622-5
7662:
7657:
7656:
7648:
7647:
7644:
7639:
7638:
7634:
7628:
7624:
7620:
7619:
7613:
7610:
7606:
7603:Reprinted in
7600:
7596:
7591:
7587:
7583:
7579:
7575:
7571:
7567:
7563:
7559:
7555:
7550:
7546:
7542:
7538:
7534:
7530:
7526:
7522:
7518:
7514:
7509:
7505:
7501:
7497:
7493:
7489:
7485:
7481:
7476:
7472:
7468:
7464:
7460:
7456:
7452:
7448:
7443:
7439:
7435:
7431:
7427:
7424:(151): 1â25.
7423:
7419:
7415:
7410:
7409:
7405:
7389:
7385:
7379:
7376:
7371:
7365:
7361:
7354:
7351:
7346:
7342:
7337:
7332:
7327:
7322:
7318:
7314:
7309:
7304:
7300:
7296:
7292:
7285:
7282:
7277:
7270:
7267:
7262:
7256:
7252:
7245:
7242:
7237:
7233:
7229:
7225:
7224:
7219:
7212:
7209:
7204:
7200:
7196:
7192:
7188:
7185:(in German).
7184:
7183:
7178:
7171:
7168:
7163:
7159:
7155:
7151:
7147:
7143:
7136:
7133:
7128:
7125:(in German).
7124:
7123:
7118:
7114:
7108:
7105:
7100:
7096:
7092:
7088:
7084:
7080:
7076:
7072:
7071:
7063:
7060:
7055:
7051:
7047:
7040:
7037:
7032:
7028:
7022:
7019:
7014:
7010:
7006:
7002:
6998:
6995:(June 1919).
6994:
6988:
6985:
6977:
6973:
6969:
6965:
6961:
6957:
6953:
6946:
6939:
6937:
6933:
6928:
6924:
6920:
6916:
6912:
6909:(in German).
6908:
6904:
6897:
6895:
6891:
6886:
6882:
6878:
6874:
6870:
6863:
6860:
6855:
6851:
6847:
6843:
6839:
6835:
6831:
6827:
6823:
6816:
6813:
6808:
6804:
6800:
6796:
6792:
6788:
6784:
6777:
6774:
6769:
6765:
6758:
6755:
6750:
6746:
6742:
6738:
6734:
6730:
6726:
6719:
6717:
6713:
6708:
6702:
6698:
6691:
6688:
6683:
6679:
6675:
6671:
6668:(151): 1â25.
6667:
6663:
6659:
6652:
6649:
6644:
6637:
6634:
6629:
6625:
6621:
6617:
6613:
6609:
6605:
6601:
6597:
6593:
6589:
6582:
6579:
6574:
6573:
6572:Physics World
6568:
6562:
6559:
6555:
6550:
6543:
6540:
6535:
6528:
6525:
6520:
6516:
6512:
6505:
6503:
6499:
6494:
6490:
6485:
6480:
6476:
6472:
6468:
6461:
6459:
6455:
6450:
6444:
6440:
6433:
6431:
6429:
6425:
6420:
6416:
6412:
6408:
6404:
6400:
6396:
6392:
6385:
6383:
6381:
6379:
6375:
6370:
6366:
6360:
6357:
6352:
6348:
6342:
6340:
6338:
6334:
6330:
6325:
6322:
6318:
6313:
6310:
6306:
6301:
6298:
6294:
6289:
6286:
6281:
6275:
6271:
6267:
6263:
6262:
6254:
6251:
6246:
6242:
6238:
6234:
6230:
6226:
6222:
6218:
6211:
6209:
6207:
6203:
6199:
6194:
6191:
6186:
6182:
6178:
6174:
6170:
6163:
6160:
6152:
6145:
6138:
6135:
6130:
6126:
6122:
6118:
6115:(151): 1â25.
6114:
6110:
6106:
6099:
6097:
6095:
6093:
6089:
6084:
6080:
6076:
6072:
6068:
6064:
6060:
6056:
6052:
6045:
6042:
6037:
6031:
6027:
6026:
6018:
6016:
6012:
6007:
6003:
5999:
5995:
5991:
5987:
5980:
5978:
5976:
5974:
5970:
5965:
5959:
5955:
5948:
5946:
5944:
5940:
5935:
5931:
5927:
5923:
5919:
5915:
5908:
5906:
5904:
5902:
5898:
5894:
5889:
5887:
5883:
5878:
5874:
5870:
5864:
5861:
5856:
5852:
5848:
5844:
5840:
5836:
5829:
5827:
5823:
5816:
5811:
5805:
5803:
5800:
5797:
5793:
5790:
5786:
5784:
5781:
5779:
5776:
5774:
5771:
5770:
5765:
5761:installation.
5760:
5759:nuclear power
5756:
5753:
5749:
5746:
5745:
5740:
5737:
5734:
5730:
5727:
5723:
5719:
5715:
5712:
5709:
5705:
5702:
5698:
5694:
5691:
5687:
5683:
5682:
5681:
5678:
5668:
5661:
5659:
5657:
5652:
5648:
5644:
5638:
5630:
5628:
5626:
5625:closed shells
5621:
5619:
5615:
5612:
5608:
5604:
5598:
5596:
5592:
5591:perturbations
5586:
5584:
5580:
5576:
5572:
5568:
5564:
5563:hydrogen atom
5560:
5556:
5551:
5549:
5545:
5541:
5537:
5533:
5529:
5522:
5500:
5497:
5494:
5491:
5486:
5482:
5478:
5472:
5468:
5462:
5457:
5453:
5445:
5444:
5443:
5441:
5437:
5433:
5427:
5418:
5411:
5406:
5403:
5400:
5396:
5393:
5389:
5388:Zeeman effect
5385:
5382:
5378:
5374:
5371:
5367:
5364:
5359:
5355:
5351:
5350:
5349:
5346:
5343:
5338:
5336:
5335:
5329:
5325:
5321:
5312:
5310:
5308:
5304:
5297:
5290:
5285:
5282:
5281:
5274:
5269:
5265:
5245:
5240:
5232:
5229:
5226:
5207:
5203:
5199:
5196:
5190:
5185:
5177:
5174:
5171:
5164:
5159:
5156:
5151:
5139:
5135:
5132:
5129:
5126:
5119:
5118:
5117:
5100:
5096:
5088:
5084:
5080:
5075:
5068:
5064:
5060:
5054:
5048:
5040:
5037:
5034:
5020:
5016:
5011:
5007:
5003:
4998:
4994:
4990:
4987:
4984:
4981:
4978:
4971:
4970:
4969:
4967:
4963:
4957:
4955:
4950:
4945:
4941:
4937:
4930:
4925:
4922:
4919:
4915:
4910:
4905:
4901:
4900:Henry Moseley
4896:
4887:
4885:
4879:
4877:
4872:
4868:
4863:
4861:
4857:
4853:
4848:
4846:
4840:
4838:
4834:
4829:
4825:
4821:
4816:
4815:
4811:
4806:
4804:
4793:
4790:
4787:
4784:
4781:
4778:
4777:
4773:
4770:
4767:
4764:
4761:
4758:
4757:
4753:
4750:
4747:
4744:
4741:
4738:
4737:
4733:
4730:
4727:
4724:
4721:
4718:
4717:
4713:
4710:
4707:
4704:
4701:
4698:
4697:
4693:
4690:
4687:
4684:
4681:
4678:
4677:
4673:
4670:
4667:
4664:
4661:
4658:
4657:
4653:
4650:
4647:
4644:
4641:
4638:
4637:
4633:
4630:
4627:
4624:
4621:
4618:
4617:
4611:
4609:
4605:
4601:
4594:
4587:
4579:
4577:
4575:
4570:
4564:
4561: â
4560:
4554:
4548:
4545: â
4544:
4538:
4532:
4529:
4521:
4516:
4508:
4503:
4495:
4476:
4472:
4464:
4459:
4455:
4451:
4446:
4439:
4434:
4430:
4426:
4420:
4416:
4413:
4408:
4405:
4396:
4395:
4394:
4377:
4372:
4368:
4365:
4359:
4356:
4349:
4348:
4347:
4344:
4331:
4324:
4320:
4313:
4309:
4305:
4300:
4296:
4292:
4286:
4281:
4277:
4273:
4265:
4247:
4239:
4234:
4230:
4226:
4221:
4214:
4209:
4205:
4201:
4195:
4187:
4183:
4176:
4172:
4168:
4163:
4159:
4155:
4149:
4142:
4138:
4133:
4129:
4122:
4118:
4113:
4109:
4106:
4103:
4078:
4074:
4068:
4064:
4056:
4052:
4048:
4043:
4039:
4035:
4029:
4024:
4020:
3999:
3990:
3989:quantum jumps
3985:
3971:
3967:
3959:
3955:
3951:
3946:
3939:
3935:
3931:
3925:
3921:
3918:
3915:
3907:
3891:
3882:
3878:
3874:
3873:Johann Balmer
3868:
3860:
3838:
3834:
3830:
3818:
3812:
3807:
3803:
3795:
3794:
3793:
3789:
3771:
3757:
3752:
3740:
3736:
3733:
3729:
3716:
3712:
3698:
3694:
3683:
3669:
3657:
3650:
3641:
3633:
3632:
3631:
3629:
3624:
3622:
3618:
3614:
3608:
3603:
3599:
3594:
3592:
3591:Coulomb force
3588:
3584:
3583:-body problem
3582:
3562:
3555:
3551:
3538:
3532:
3528:
3521:
3518:
3513:
3509:
3501:
3500:
3499:
3497:
3492:
3487:
3483:
3460:
3456:
3447:
3443:
3431:
3422:
3419:
3414:
3403:
3395:
3392:
3374:
3371:
3366:
3363:
3360:
3354:
3344:
3340:
3328:
3317:
3314:
3296:
3292:
3280:
3272:
3271:
3270:
3268:
3267:natural units
3249:
3241:
3233:
3220:
3214:
3204:
3200:
3188:
3178:
3167:
3159:
3158:
3157:
3152:
3147:
3145:
3141:
3135:
3128:
3123:
3117:
3097:
3079:
3075:
3068:
3064:
3060:
3057:
3051:
3043:
3039:
3033:
3025:
3012:
3006:
2996:
2992:
2980:
2971:
2967:
2960:
2957:
2949:
2945:
2941:
2934:
2930:
2918:
2914:
2908:
2905:
2902:
2895:
2894:
2893:
2891:
2872:
2858:
2855:
2842:
2839:
2835:
2831:
2828:
2825:
2811:
2805:
2801:
2789:
2782:
2772:
2767:
2763:
2755:
2754:
2753:
2751:
2745:
2740:
2721:
2707:
2701:
2697:
2685:
2681:
2674:
2664:
2660:
2653:
2648:
2644:
2636:
2635:
2634:
2632:
2613:
2607:
2604:
2601:
2593:
2584:
2576:
2572:
2568:
2559:
2544:
2536:
2535:
2534:
2532:
2528:
2523:
2506:
2500:
2497:
2491:
2488:
2483:
2480:
2474:
2471:
2464:
2463:
2462:
2460:
2456:
2437:
2430:
2426:
2421:
2415:
2409:
2406:
2399:
2395:
2391:
2386:
2378:
2370:
2364:
2361:
2354:
2349:
2346:
2336:
2335:
2334:
2320:
2309:
2290:
2283:
2279:
2275:
2270:
2265:
2262:
2257:
2254:
2247:
2246:
2245:
2229:
2219:
2214:
2197:
2192:
2188:
2184:
2180:
2176:
2169:
2165:
2161:
2157:
2153:
2148:
2145:
2135:
2134:
2133:
2131:
2127:
2123:
2119:
2113:
2109:
2102:
2084:
2078:
2075:
2072:
2069:
2058:
2050:
2049:
2047:
2042:
2036:
2032:
2028:
2024:
2023:
2020:
2017:
2016:
2012:
2008:
2004:
2000:
1996:
1980:
1975:
1971:
1959:
1953:
1950:
1945:
1942:
1939:
1932:
1931:
1929:
1913:
1906:
1895:
1887:
1883:
1871:
1867:
1860:
1857:
1850:
1849:
1847:
1846:atomic number
1843:
1839:
1832:
1828:
1824:
1817:
1813:
1797:
1790:
1786:
1779:
1775:
1763:
1759:
1753:
1748:
1742:
1738:
1726:
1715:
1714:
1712:
1711:Coulomb force
1708:
1704:
1703:
1700:
1697:
1696:
1695:
1692:
1690:
1687:
1683:
1682:Moseley's law
1679:
1675:
1671:
1667:
1663:
1659:
1658:hydrogen atom
1650:
1643:
1641:
1639:
1634:
1630:
1626:
1622:
1618:
1613:
1598:
1578:
1574:
1570:
1567:
1564:
1556:
1540:
1536:
1532:
1523:
1506:
1500:
1497:
1492:
1489:
1483:
1480:
1473:
1472:
1471:
1457:
1437:
1434:
1431:
1408:
1405:
1402:
1399:
1396:
1390:
1387:
1382:
1379:
1369:
1368:
1367:
1350:
1347:
1344:
1341:
1338:
1332:
1329:
1324:
1321:
1311:
1310:
1309:
1292:
1286:
1283:
1279:
1274:
1271:
1264:
1263:
1262:
1260:
1256:
1237:
1234:
1231:
1228:
1225:
1222:
1219:
1212:
1211:
1210:
1208:
1207:standing wave
1204:
1176:
1172:
1168:
1164:
1161:
1145:
1125:
1117:
1101:
1081:
1061:
1041:
1021:
999:
996:
993:
989:
966:
962:
953:
934:
914:
906:
903:
899:
896:
892:
888:
884:
883:
882:
864:
844:
841:
838:
833:
829:
825:
820:
816:
812:
809:
798:
782:
774:
771:
770:energy levels
767:
766:hydrogen-like
763:
759:
743:
723:
720:
716:
712:
709:
698:
682:
679:
676:
673:
670:
667:
664:
661:
658:
655:
652:
629:
626:
623:
620:
609:
600:
596:
593:
589:
588:
587:
585:
580:
578:
574:
570:
569:Johann Balmer
566:
558:
556:
552:
550:
546:
541:
537:
535:
530:
522:
520:
506:
503:
500:
497:
492:
488:
484:
464:
444:
441:
433:
429:
425:
421:
413:
411:
408:
404:
400:
396:
392:
387:
385:
381:
377:
372:
368:
364:
360:
354:
346:
344:
341:
337:
333:
327:
317:
312:
307:
302:
294:
292:
290:
289:
284:
280:
276:
272:
268:
264:
260:
259:valence shell
256:
255:hydrogen atom
251:
249:
245:
240:
238:
234:
230:
226:
222:
218:
214:
210:
206:
205:cubical model
202:
198:
197:Joseph Larmor
193:
191:
187:
183:
179:
175:
172:
168:
164:
160:
156:
152:
148:
144:
140:
136:
132:
124:
120:
114:
109:
108:Balmer series
101:
97:
93:
89:
85:
81:
77:
73:
67:
60:
55:
54:hydrogen atom
50:
44:
40:
39:Bohr equation
33:
19:
7884:
7853:(knot model)
7844:Dalton model
7753:
7749:
7730:
7705:
7686:
7677:
7654:
7642:
7617:
7608:
7604:
7598:
7594:
7561:
7557:
7520:
7516:
7487:
7483:
7454:
7450:
7421:
7417:
7392:. Retrieved
7390:. 2021-11-23
7388:www.iaea.org
7387:
7378:
7359:
7353:
7298:
7294:
7284:
7275:
7269:
7250:
7244:
7227:
7221:
7211:
7189:(17): 1â94.
7186:
7180:
7170:
7145:
7141:
7135:
7126:
7120:
7107:
7074:
7068:
7062:
7056:: 1024â1034.
7053:
7049:
7039:
7021:
7004:
7000:
6987:
6958:(1): 42â49.
6955:
6951:
6910:
6906:
6876:
6872:
6862:
6829:
6825:
6815:
6790:
6786:
6776:
6767:
6763:
6757:
6732:
6728:
6696:
6690:
6665:
6661:
6651:
6642:
6636:
6595:
6591:
6581:
6570:
6561:
6552:
6548:
6542:
6533:
6527:
6510:
6474:
6470:
6438:
6394:
6390:
6359:
6324:
6312:
6300:
6288:
6260:
6253:
6220:
6216:
6193:
6176:
6172:
6162:
6137:
6112:
6108:
6058:
6054:
6044:
6024:
5989:
5985:
5953:
5917:
5913:
5876:
5869:Perrin, Jean
5863:
5838:
5834:
5742:
5718:atomic whirl
5673:
5640:
5622:
5599:
5595:Stark effect
5587:
5558:
5552:
5531:
5524:
5517:
5515:
5429:
5370:Stark effect
5353:
5347:
5339:
5333:
5330:
5323:
5319:
5316:
5313:Shortcomings
5299:
5292:
5286:
5279:
5272:
5271:
5263:
5262:
5260:
5115:
4965:
4961:
4958:
4946:
4942:
4935:
4928:
4924:
4921:
4908:
4897:
4893:
4880:
4864:
4859:
4855:
4851:
4849:
4841:
4817:
4807:
4799:
4607:
4603:
4596:
4592:
4589:
4568:
4562:
4558:
4552:
4546:
4542:
4536:
4533:
4524:
4511:
4498:
4491:
4392:
4345:
3986:
3881:Walther Ritz
3870:
3790:
3786:
3628:reduced mass
3625:
3620:
3616:
3615:cancels the
3612:
3606:
3601:
3597:
3595:
3580:
3577:
3495:
3490:
3485:
3481:
3478:
3264:
3150:
3148:
3139:
3133:
3126:
3115:
3112:
2889:
2887:
2743:
2738:
2736:
2630:
2628:
2530:
2529:in terms of
2526:
2524:
2521:
2458:
2454:
2452:
2307:
2305:
2217:
2215:
2212:
2129:
2125:
2124:to scale as
2117:
2114:
2110:
2106:
2045:
2040:
2034:
2030:
2018:
2002:
1998:
1841:
1830:
1822:
1815:
1698:
1693:
1655:
1629:Another form
1614:
1524:
1521:
1423:
1365:
1307:
1252:
1180:
894:
890:
880:
581:
562:
553:
545:J.J. Thomson
542:
538:
526:
417:
388:
356:
329:
315:
286:
252:
241:
227:(1911), and
194:
188:rather than
182:Solar System
138:
134:
128:
125:(red light).
112:
95:
91:
87:
76:atomic shell
65:
58:
7858:Lewis model
7027:Bohr, Niels
6735:(1): 1â38.
6365:Bohr, Niels
6347:Bohr, Niels
5920:: 123â186.
5728:in general.
5614:line bundle
5412:Refinements
4774:8, 8, 4, 3
4754:8, 8, 2, 4
4734:8, 8, 2, 3
4714:8, 8, 2, 2
4694:8, 8, 2, 1
4654:8, 4, 4, 1
2750:Bohr radius
1686:heavy quark
1670:positronium
1114:(so-called
758:Bohr radius
559:Development
399:picoseconds
359:Hans Geiger
332:J J Thomson
221:Arthur Haas
201:Jean Perrin
163:J J Thomson
153:'s nuclear
104:3 → 2
43:Bohr effect
7983:Niels Bohr
7957:Categories
7885:Bohr model
7627:1048217622
7394:2024-09-04
6770:: 476â502.
5992:: viâ290.
5841:(9): 933.
5812:References
5607:connection
5440:Sommerfeld
4828:octet rule
4788:8, 4, 2, 2
3875:and later
2103:Derivation
1591:described
1203:de Broglie
1138:(or large
584:Niels Bohr
424:Max Planck
295:Background
147:Niels Bohr
135:Bohr model
119:wavelength
7942:Chemistry
7778:120859582
7731:Chemistry
7649:Reprint:
7099:250901403
6964:797965772
6749:2102-6467
6682:1941-5982
6519:557599205
6493:0035-8711
6419:120797894
6075:0003-9519
5817:Footnotes
5703:branches.
5611:Hermitian
5454:∫
5230:−
5200:×
5175:−
5133:ν
5076:−
5038:−
5004:−
4988:ν
4898:In 1913,
4876:noble gas
4871:viscosity
4845:screening
4518:=2), and
4447:−
4409:λ
4373:λ
4297:π
4231:τ
4222:−
4206:τ
4160:π
4139:τ
4130:−
4119:τ
4107:ν
4075:τ
4040:π
4025:τ
4000:τ
3947:−
3916:ν
3522:−
3457:α
3367:≈
3364:α
3352:ℏ
3238:ℏ
3058:−
3052:≈
3030:ℏ
2961:−
2909:−
2840:−
2832:×
2826:≈
2779:ℏ
2671:ℏ
2611:ℏ
2504:ℏ
2492:π
2419:Δ
2410:−
2407:≈
2387:−
2368:Δ
2350:∝
2344:Δ
2318:Δ
2271:∝
2258:∝
2177:∝
2149:∝
2143:Δ
2082:ℏ
1946:−
1565:λ
1501:π
1481:ℓ
1458:ℓ
1391:π
1345:π
1272:λ
1232:π
1223:λ
1189:ℏ
997:−
952:harmonics
935:ν
915:ν
895:classical
845:ν
826:−
807:Δ
783:ν
724:π
707:ℏ
633:ℏ
565:empirical
507:ν
445:ν
384:electrons
357:In 1908,
213:Saturnian
178:analogous
174:electrons
121:656
7601:: 82â92.
7545:11988018
7345:16103360
7129:: 32â41.
6976:Archived
6972:53520045
6628:35364965
6411:41133258
6237:23739408
6151:Archived
6083:41133273
6006:27757291
5934:27757389
5871:(1901).
5766:See also
5581:, which
4674:8, 8, 2
3489:, where
1175:momentum
891:discrete
857:, where
645:, where
582:In 1913
527:In 1911
219:(1904),
207:(1902),
176:. It is
171:orbiting
94:, where
72:electron
7758:Bibcode
7586:4035652
7566:Bibcode
7525:Bibcode
7492:Bibcode
7459:Bibcode
7426:Bibcode
7336:1186029
7313:Bibcode
7191:Bibcode
7162:9628509
7079:Bibcode
6915:Bibcode
6854:3977652
6834:Bibcode
6795:Bibcode
6620:9899816
6600:Bibcode
6245:4355108
6117:Bibcode
5843:Bibcode
5733:Unicode
5726:atheism
5706:The US
5358:lithium
5289:K-alpha
4947:It was
4904:K-alpha
4782:4, 2, 2
4768:8, 4, 3
4748:8, 2, 4
4728:8, 2, 3
4708:8, 2, 2
4688:8, 2, 1
4648:4, 4, 1
4631:Element
4625:Element
4619:Element
4602:unless
4520:Paschen
3587:nucleus
3389:is the
3311:is the
1836:is the
1825:is the
1666:lithium
902:photons
380:nucleus
190:gravity
167:nucleus
98:is the
88:hν
7776:
7737:
7712:
7693:
7663:
7625:
7584:
7558:Nature
7543:
7517:Nature
7366:
7343:
7333:
7257:
7160:
7097:
6970:
6962:
6852:
6826:Nature
6747:
6703:
6680:
6626:
6618:
6554:waves.
6517:
6491:
6445:
6417:
6409:
6276:
6243:
6235:
6217:Nature
6081:
6073:
6032:
6004:
5960:
5932:
5879:: 463.
5536:action
5516:where
5436:Wilson
5261:Here,
5213:
4833:Kossel
4566:where
4507:Balmer
3087:
2862:
2848:
1814:where
1689:mesons
1678:K-line
1662:helium
1553:while
1424:where
1257:. The
699:, and
133:, the
102:. The
68:> 1
7907:1928
7901:1926
7883:1913
7876:1911
7870:1904
7863:1904
7856:1902
7849:1867
7842:1804
7774:S2CID
7582:S2CID
7541:S2CID
7303:arXiv
7158:S2CID
7095:S2CID
6979:(PDF)
6968:S2CID
6948:(PDF)
6850:S2CID
6624:S2CID
6415:S2CID
6407:JSTOR
6241:S2CID
6154:(PDF)
6147:(PDF)
6079:JSTOR
6002:JSTOR
5930:JSTOR
5752:React
5701:olive
5609:of a
5605:of a
5305:) in
4556:with
4540:with
4505:=1),
4494:Lyman
3609:â 137
3596:When
1255:waves
1205:as a
1014:when
155:model
7735:ISBN
7710:ISBN
7691:ISBN
7661:ISBN
7623:OCLC
7364:ISBN
7341:PMID
7255:ISBN
6960:OCLC
6745:ISSN
6701:ISBN
6678:ISSN
6616:PMID
6515:OCLC
6489:ISSN
6443:ISBN
6274:ISBN
6233:PMID
6071:ISSN
6030:ISBN
5958:ISBN
5794:The
5787:The
5731:The
5386:The
5379:and
5298:and
5287:The
5197:2.46
4916:and
4762:4, 3
4742:2, 4
4722:2, 3
4702:2, 2
4682:2, 1
4668:8, 2
3879:and
3600:= 1/
3061:13.6
2859:52.9
2829:5.29
2025:The
1840:and
1672:and
1173:and
1165:The
981:and
361:and
246:for
143:atom
7766:doi
7574:doi
7562:107
7533:doi
7500:doi
7467:doi
7434:doi
7331:PMC
7321:doi
7299:102
7232:doi
7199:doi
7150:doi
7087:doi
7009:doi
6923:doi
6911:354
6881:doi
6842:doi
6803:doi
6737:doi
6670:doi
6608:doi
6479:doi
6399:doi
6266:doi
6225:doi
6221:498
6181:doi
6125:doi
6063:doi
5994:doi
5922:doi
5851:doi
5627:".
5577:of
5538:of
5354:two
5116:or
4878:).
4550:or
3646:red
3619:in
3375:137
3156:):
3129:= 2
3118:= 1
2746:= 1
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