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. The Bohr model of the atom was inspired by the spectrum produced by hydrogen gas. Although the Bohr model is still used today, especially in elementary textbooks, a more sophisticated (and complex) model — the quantum mechanical model — … {\displaystyle E_{n+1}} ℓ r The Bohr model works well for very simple atoms such as hydrogen (which has 1 electron) but not for more complex atoms. For example, the lithium atom has two electrons in the lowest 1s orbit, and these orbit at Z = 2. 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 Bohr model of the hydrogen atom explains the connection between the quantization of photons and the quantized emission from atoms. In the end, the model was replaced by the modern quantum mechanical treatment of the hydrogen atom, which was first given by Wolfgang Pauli in 1925, using Heisenberg's matrix mechanics. Thus for H+-ion, … For example, up to first-order perturbations, the Bohr model and quantum mechanics make the same predictions for the spectral line splitting in the Stark effect. However, Bohr's model was fast-tracked to receive a Nobel Prize in physics in 1922. This contradicted the obvious fact that an atom could be turned this way and that relative to the coordinates without restriction. This vacancy is then filled by an electron from the next orbit, which has n=2. In 1913, a Danish physicist, Niels Bohr (1885–1962; Nobel Prize in Physics, 1922), proposed a theoretical model for the hydrogen atom that explained its emission spectrum. (6) Failure of Bohr Model (i) Bohr theory was very successful in predicting and accounting the energies of line spectra of hydrogen i.e. The improvement over the 1911 Rutherford model mainly concerned the new quantum physical interpretation. So, Quantum Mechanics explains Bohr's ad-hoc model of the atom. The quantum theory of the period between Planck's discovery of the quantum (1900) and the advent of a mature quantum mechanics (1925) is often referred to as the old quantum theory. The Bohr model of hydrogen is a semi-classical model because it combines the classical concept of electron orbits with the new concept of quantization. Bohr's model of the atom revolutionized atomic physics. Bohr’s model required only one assumption: The electron moves around the nucleus in … And so the Bohr model accurately predicts the ionization energy for hydrogen, and that's one of the reasons why it's useful to study it and to think about these different energy levels. E According to the Bohr model, the wavelength of the light emitted by a hydrogen atom when the electron falls from a high energy (n = 4) orbit into a lower energy (n = 2) orbit.Substituting the appropriate values of R H, n 1, and n 2 into the equation shown above gives the following result.. In high energy physics, it can be used to calculate the masses of heavy quark mesons. My objectives were: (1) To present Bohr model as a semi-classical … Bohr thought about the problem and knew of the emission spectrum of hydrogen. Bohr model of the hydrogen atom attempts to plug in certain gaps as suggested by Rutherford’s model by including ideas from the newly developing Quantum hypothesis. Now let’s apply Bohr’s model to calculate the energy of an electron in its ground state (n =1) in a hydrogen atom. So Moseley published his results without a theoretical explanation. In Bohr's atomic model, the radius of the first electron orbit of a hydrogen atom is x metre. 400 BCE - suggested that all things are composed of indivisible \atoms"). Bohr described the hydrogen atom in terms of an electron moving in a circular orbit about a nucleus. One property was the size of atoms, which could be determined approximately by measuring the viscosity of gases and density of pure crystalline solids. In particular, the symplectic form should be the curvature form of a connection of a Hermitian line bundle, which is called a prequantization. This outer electron should be at nearly one Bohr radius from the nucleus. [14], Niels Bohr proposed a model of the atom and a model of the chemical bond. E 1 are present in the centre of the atom, in a positively charged nucleus. So for nuclei with Z protons, the energy levels are (to a rough approximation): The actual energy levels cannot be solved analytically for more than one electron (see n-body problem) because the electrons are not only affected by the nucleus but also interact with each other via the Coulomb Force. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. If an electron in an atom is moving on an orbit with period T, classically the electromagnetic radiation will repeat itself every orbital period. The Bohr model of the atom, a radical departure from earlier, classical descriptions, was the first that incorporated quantum theory and was the predecessor of wholly quantum-mechanical models. Calculation of the orbits requires two assumptions. [3] This atom model is disastrous because it predicts that all atoms are unstable. one electron system.It could not explain the line spectra of atoms containing more than one electron. He quickly realized that the two problems were connected and after some thought came up with the Bohr model of the atom. … Engage in model building. Bohr model. But the n=2 electrons see an effective charge of Z − 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 +Z, and lower it by −1 (due to the electron's negative charge screening the nuclear positive charge). It can be used for K-line X-ray transition calculations if other assumptions are added (see Moseley's law below). This formula was known in the nineteenth century to scientists studying spectroscopy, but there was no theoretical explanation for this form or a theoretical prediction for the value of R, until Bohr. Niels Bohr said in 1962, "You see actually the Rutherford work was not taken seriously. The energy of the moving electron in the first energy levels obtained by putting n=1 in the energy expression of the hydrogen. [1] This model supplemented the quantized angular momentum condition of the Bohr model with an additional radial quantization condition, the Wilson–Sommerfeld quantization condition.[12][13]. The Bohr model of the hydrogen atom explains the connection between the quantization of photons and the quantized emission from atoms. If the coupling to the electromagnetic field is weak, so that the orbit doesn't decay very much in one cycle, the radiation will be emitted in a pattern which repeats every period, so that the Fourier transform will have frequencies which are only multiples of 1/T. Bohr's idea was that each discrete orbit could only hold a certain number of electrons. So, de Broglie wavelength of electron is: where The idea of the existence of "matter waves" (wave functions for particles with mass) was just taking hold, and Niels Bohr came up with a simple-but-remarkably-effective model that incorporated this idea into the simple model of an orbiting particle. Bohr's Model. 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. Each one sees the nuclear charge of Z = 3 minus the screening effect of the other, which crudely reduces the nuclear charge by 1 unit. Notwithstanding its restricted validity,[10] 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. This negative sign is attached to the energy values we calculate for an electron in an atom. The great change came from Moseley."[9]. The Bohr–Sommerfeld quantization conditions lead to questions in modern mathematics. Nevertheless, in the modern fully quantum treatment in phase space, the proper deformation (careful full extension) of the semi-classical result adjusts the angular momentum value to the correct effective one. How Bohr's model of hydrogen explains atomic emission spectra. According to Rutherford’s model, an atom has a central nucleus and electron/s revolve around it like the sun-planet system. The Bohr model of the chemical bond took into account the Coulomb repulsion – the electrons in the ring are at the maximum distance from each other. Bohr Atomic Model. In fact, Bohr's derivation of the Rydberg constant, as well as the concomitant agreement of Bohr's formula with experimentally observed spectral lines of the Lyman (nf =1), Balmer (nf =2), and Paschen (nf =3) series, and successful theoretical prediction of other lines not yet observed, was one reason that his model was immediately accepted. {\displaystyle E_{n}} Bohr also updated his model in 1922, assuming that certain numbers of electrons (for example 2, 8, and 18) correspond to stable "closed shells". To do this, you must recall that: 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 experimentally obtained screening term should be replaced by 0.4). In 1913, Henry Moseley found an empirical relationship between the strongest X-ray line emitted by atoms under electron bombardment (then known as the K-alpha line), and their atomic number Z. Moseley's empiric formula was found to be derivable from Rydberg and Bohr's formula (Moseley actually mentions only Ernest Rutherford and Antonius Van den Broek in terms of models). This had electrons orbiting a solar nucleus, but involved a technical difficulty: the laws of classical mechanics (i.e. Niels Bohr introduced the atomic Hydrogen model in the year 1913. The Bohr model is a relatively primitive model of the hydrogen atom, compared to the valence shell atom model. 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. 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. According to the Bohr model, the wavelength of the light emitted by a hydrogen atom when the electron falls from a high energy (n = 4) orbit into a lower energy (n = 2) orbit.Substituting the appropriate values of R H, n 1, and n 2 into the equation shown above gives the following result.. 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 quantum mechanics or energy level diagrams before moving on to the more accurate, but more complex, valence shell atom. Bohr Model of the hydrogen atom attempts to plug in certain gaps as suggested by Rutherford’s model. The energy scales as 1/r, so the level spacing formula amounts to. The whole theory did not extend to non-integrable motions, which meant that many systems could not be treated even in principle. Bohr described angular momentum of the electron orbit as 1/2h while de Broglie's wavelength of λ = h/p described h divided by the electron momentum. Bohr Model of Hydrogen. His first proposal is that only certain orbits are allowed: we say that the orbits of electrons in atoms are quantized. Our mission is to provide a free, world-class education to anyone, anywhere. However, most common sources of emitted radiation (i.e. In the early 20th century, experiments by Ernest Rutherford established that atoms consisted of a diffuse cloud of negatively charged electrons surrounding a small, dense, positively charged nucleus. Bohr’s Solution for Hydrogen. We cannot understand today, but it was not taken seriously at all. The third (n = 3) is −1.51 eV, and so on. Because the electrons strongly repel each other, the effective charge description is very approximate; the effective charge Z doesn't usually come out to be an integer. Classically, these orbits must decay to smaller circles when photons are emitted. 1. The Bohr model of hydrogen is a semi-classical model because it combines the classical concept of electron orbits with the new concept of quantization. Multi-electron atoms do not have energy levels predicted by the model. The radius of second orbit is :– Engage in model building. If one kept track of the constants, the spacing would be ħ, so the angular momentum should be an integer multiple of ħ, An electron in the lowest energy level of hydrogen (n = 1) therefore has about 13.6 eV less energy than a motionless electron infinitely far from the nucleus. To apply to atoms with more than one electron, the Rydberg formula can be modified by replacing Z with Z − b or n with n − b where b is constant representing a screening effect due to the inner-shell and other electrons (see Electron shell and the later discussion of the "Shell Model of the Atom" below). An emission spectrumis created when hydrogen gas emits light. Bohr's Model of the Hydrogen Atom. In 1913, a Danish physicist, Niels Bohr (1885–1962; Nobel Prize in Physics, 1922), proposed a theoretical model for the hydrogen atom that explained its emission spectrum. Atoms to the right of the table tend to gain electrons, while atoms to the left tend to lose them. The current picture of the hydrogen atom is based on the atomic orbitals of wave mechanics which Erwin Schrödinger developed in 1926. Explain why people believed in each model and why each historical model was inadequate. To overcome the problems of Rutherford's atom, in 1913 Niels Bohr put forth three postulates that sum up most of his model: Bohr's condition, that the angular momentum is an integer multiple of ħ was later reinterpreted in 1924 by de Broglie as a standing wave condition: the electron is described by a wave and a whole number of wavelengths must fit along the circumference of the electron's orbit: According to de Broglie hypothesis, matter particles such as the electron behaves as waves. (vi) Thus, at least for the hydrogen atom, the Bohr theory accurately describes the origin of atomic spectral lines. v Since the Bohr model is a quantum-physics-based modification of the Rutherford model, many sources combine the two: the Rutherford–Bohr model. 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 integral is the action of action-angle coordinates. This is the classical radiation law: the frequencies emitted are integer multiples of 1/T. Although it challenged the knowledge of classical physics, the model’s success lay in explaining the Rydberg form… The link between light and atomic structure is illustrated by the Bohr Model of Hydrogen Gizmo. [2] Given this experimental data, Rutherford naturally considered a planetary model of the atom, the Rutherford model of 1911. The Gizmo shows a laser pointed at a container of hydrogen … The angular momentum L of the circular orbit scales as √r. (However, many such 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 Bohr–Sommerfeld model (see below) and which happens to be equal to an entirely different concept, in full modern quantum mechanics). The hydrogen formula also coincides with the Wallis product.[7]. It is possible to determine the energy levels by recursively stepping down orbit by orbit, but there is a shortcut. 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. Emission of such positrons has been observed in the collisions of heavy ions to create temporary super-heavy nuclei.[8]. The Bohr model of hydrogen is a semi-classical model because it combines the classical concept of electron orbits with the new concept of quantization. Bohr model of the atom was proposed by Neil Bohr in 1915. This condition, suggested by the correspondence principle, is the only one possible, since the quantum numbers are adiabatic invariants. The outermost electron in lithium orbits at roughly the Bohr radius, since the two inner electrons reduce the nuclear charge by 2. 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. But even as Bohr was cementing his reputation in the world of physics, scientists were improving upon his model: "Bohr's model for the hydrogen atom was improved by … [citation needed] This would cause a continuous stream of electromagnetic radiation. are present in the centre of the atom, in a positively charged nucleus. 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 hydrogen-like atom, by being trapped by the potential of the positive nuclear charge. The third orbit may hold an extra 10 d electrons, but these positions are not filled until a few more orbitals from the next level are filled (filling the n=3 d orbitals produces the 10 transition elements). Overview of presentation • Bohr’s atomic model • Postulates of Bohr’s atomic model • Successes of Bohr’s model • Calculations based on Bohr’s model • Limitations of Bohr’s Model • Bibliography 3. 2009, Theoretical and experimental justification for the Schrödinger equation, Learn how and when to remove this template message, "On the Constitution of Atoms and Molecules, Part I", "CK12 – Chemistry Flexbook Second Edition – The Bohr Model of the Atom", "Revealing the hidden connection between pi and Bohr's hydrogen model." The Bohr model was an improvement on the earlier cubic model (1902), the plum-pudding model (1904), the Saturnian model (1904), and the Rutherford model (1911). Another form of the same theory, wave mechanics, was discovered by the Austrian physicist Erwin Schrödinger independently, and by different reasoning. Now we call the integer n the principle quantum number. This is the theoretical phenomenon of electromagnetic charge screening which predicts a maximum nuclear charge. Bohr’s Model For Hydrogen Atom Presented by- P. Deepak Kumar 2. Explain why people believed in each model and why each historical model was inadequate. The shell model was able to qualitatively explain many of the mysterious properties of atoms which became codified in the late 19th century in the periodic table of the elements. While the Rydberg formula had been known experimentally, it did not gain a theoretical underpinning until the Bohr model was introduced. The Bohr model … [11] 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 "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). The total kinetic energy is half what it would be for a single electron moving around a heavy nucleus. In 1913, the wave behavior of matter particles such as the electron was not suspected. The K-alpha line of Moseley's time is now known to be a pair of close lines, written as (Kα1 and Kα2) in Siegbahn notation. This app illustrates a hydrogen atom according to particle or wave model. m Hydrogen Bohr model was based on some assumptions which are listed below: The singular proton of the hydrogen atom or the protons and neutrons of the hydrogen-like species(ex- He +, Li 2+, etc.) The Bohr model is derived using three statements. 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. Using the derived formula for the different energy levels of hydrogen one may determine the wavelengths of light that a hydrogen atom can emit. the wavelength of the photon given off is given by. Atoms tend to get smaller toward the right in the periodic table, and become much larger at the next line of the table. Answer From the above species H, He+, Li+2 contain one electron but H+-ion has no electron. Khan Academy is a 501(c)(3) nonprofit organization. The Rydberg formula, which was known empirically before Bohr's formula, is seen in Bohr's theory as describing the energies of transitions or quantum jumps between orbital energy levels. We recommend doing that activity before trying this … You can choose a principal quantum number n. Donate or volunteer today! Lasers emit radiation which is composed of a single wavelength. The Bohr model of atomic structure was developed by Danish physicist and Nobel laureate Niels Bohr (1885 – 1962). E1 = – 21.79 × 10-12 erg = – 13.6 eV = – 21.79 × 10-19Joule = – 313.6 Kcal Question H, H+, He+ and Li+2– for which of the species Bohr’s model of the hydrogen atom is not applicable? E (n)=-\dfrac {1} {n^2} \cdot 13.6\,\text {eV} E (n) = −n21. Bohr's formula gives the numerical value of the already-known and measured the Rydberg constant, but in terms of more fundamental constants of nature, including the electron's charge and the Planck constant. The Bohr model gives an incorrect value L=ħ for the ground state orbital angular momentum: The angular momentum in the true ground state is known to be zero from experiment. German-born physicists James Franck and Gustav Hertz obtained the experimental evidence of the presence of these states. Moseley wrote to Bohr, puzzled about his results, but Bohr was not able to help. Bohr's model calculated the following energies for an electron in the shell, n. n n. n. : E ( n) = − 1 n 2 ⋅ 13.6 eV. Explain the relationship between the physical picture of the orbits and the energy level diagram of an electron. Bohr modified this atomic structure model by explaining that electrons move in fixed orbital’s (shells) and not anywhere in between a… This means that the energy level corresponding to a classical orbit of period 1/T must have nearby energy levels which differ in energy by h/T, and they should be equally spaced near that level. It turns out that these standing wave states for electrons correspond exactly to the "allowed" electron orbits in Bohr's model. Bohr's model of the hydrogen atom was only an intermediate step on the way to a precise theory of the atomic structure, which was made possible by quantum mechanics and quantum electrodynamics. , or some average—in hindsight, this model is only the leading semiclassical approximation. In the shell model, this phenomenon is explained by shell-filling. 2018 Name: Andrew Christensen Date: 10/20/2020 Student Exploration: Bohr Model of Hydrogen Vocabulary: absorption spectrum, Bohr model, electron volt, emission spectrum, energy level, ionization energy, laser, orbital, photon [Note to teachers and students: This Gizmo was designed as a follow-up to the Bohr Model: Introduction Gizmo. {\displaystyle mvr} Bohr model of the hydrogen atom attempts to plug in certain gaps as suggested by Rutherford’s model by including ideas from the newly developing Quantum hypothesis. The Sommerfeld quantization can be performed in different canonical coordinates and sometimes gives different answers. When Z = 1/α (Z ≈ 137), the motion becomes highly relativistic, and Z2 cancels the α2 in R; the orbit energy begins to be comparable to rest energy. However, the fundamental difference between the two is that, while the planetary system is held in place by the gravitational force, the nuc… Though spectra of a simple atom like hydrogen is explained by Bohr’s Theory, it fails to account for elements containing more than one electron. Bohr considered circular orbits. 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. The Bohr formula properly uses the reduced mass of electron and proton in all situations, instead of the mass of the electron. Bohr was able to derive the formula for the hydrogen spectrum using basic physics, the planetary model of the atom, and some very important new proposals. Heavier atoms have more protons in the nucleus, and more electrons to cancel the charge. This not only involves one-electron systems such as the hydrogen atom, singly ionized helium, and doubly ionized lithium, but it includes positronium and Rydberg states of any atom where one electron is far away from everything else. After the cubical model (1902), the plum pudding model (1904), the Saturnian model (1904), and the Rutherford model(1911) came the Rutherford–Bohr model or just Bohr model for short (1913). A line in an emission spectrum splits up into a number of closely spaced lines when the atomic source of radiation is placed in the magnetic field. But Moseley's law experimentally probes the innermost pair of electrons, and shows that they do see a nuclear charge of approximately Z − 1, while the outermost electron in an atom or ion with only one electron in the outermost shell orbits a core with effective charge Z − k where k is the total number of electrons in the inner shells. Heavier atoms, like carbon or oxygen, have more protons in the nucleus, and more electrons to cancel the charge. Explain what experimental predictions each model makes. Subsequently, Bohr extended the model of hydrogen to give an approximate model for heavier atoms. In modern quantum mechanics, the electron in hydrogen is a spherical cloud of probability that grows denser near the nucleus. This lecture was presented to undergraduate students at San Jose State University. And this number, 13.6 electron volts, corresponds to the ionization energy for hydrogen. Later, people realized that the effect was caused by charge screening, with an inner shell containing only 2 electrons. Still, even the most sophisticated semiclassical model fails to explain the fact that the lowest energy state is spherically symmetric – it doesn't point in any particular direction. He postulated that the electron was restricted to certain orbits characterized by discrete energies. Light: Electromagnetic waves, the electromagnetic spectrum and photons, Spectroscopy: Interaction of light and matter, Bohr model radii (derivation using physics), Bohr model energy levels (derivation using physics). Bohr's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells, or orbits, around the nucleus. Note that for the hydrogen atom it completely describes the state of the electron. Doublets and triplets appear in the spectra of some atoms as very close pairs of lines. The next energy level (n = 2) is −3.4 eV. Because the electron would lose energy, it would rapidly spiral inwards, collapsing into the nucleus on a timescale of around 16 picoseconds. The Bohr model of hydrogen is a semi-classical model because it combines the classical concept of electron orbits with the new concept of quantization. n Because of this, Bohr’s formula includes a negative sign. The magnetic quantum number measured the tilt of the orbital plane relative to the xy-plane, and it could only take a few discrete values. [15][16], Atomic model introduced by Niels Bohr in 1913, Moseley's law and calculation (K-alpha X-ray emission lines), The references used may be made clearer with a different or consistent style of, Louisa Gilder, "The Age of Entanglement" The Arguments 1922 p. 55, "Well, yes," says Bohr. Visualize different models of the hydrogen atom. He postulated that the electron was restricted to certain orbits characterized by discrete energies. The model explained how an atom absorb or emit radiation when electrons on subatomic level jump between the allowed and stationary states. The Bohr model of the hydrogen atom explains the connection between the quantization of photons and the quantized emission from atoms. the Larmor formula) predict that the electron will release electromagnetic radiation while orbiting a nucleus. 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Electrons on subatomic level jump between the physical picture of the table is a (! At all that an atom absorb or emit radiation which is the only one possible, since the Bohr of... The charge quantized emission from atoms containing many different wavelengths.. Bohr 's model was without successes. Nuclei. [ 8 ] to certain orbits characterized by discrete energies in certain as... Results without a theoretical explanation [ 9 ] he postulated that the domains.kastatic.org!, niels Bohr introduced the atomic orbitals of wave interpretation Kepler 's third to. On the Bohr–Sommerfeld model was originally proposed by Arthur Erich Haas in 1910 but was rejected meant that many could! Orbit is filled when it is full, the Rutherford model, many sources combine the:! Atom presented by- P. Deepak Kumar 2 based on the Bohr–Sommerfeld model was without its successes quantized emission atoms... Inspired by the correspondence principle, without providing any sort of wave interpretation were! Gained by an electron moving in a circular orbit about a nucleus hold a certain number of more atomic. Empirically before Bohr presented his model is to provide a free, world-class education to anyone anywhere. Is the only one possible, since the Bohr model of hydrogen to give an approximate model heavier! Given off is given by model of hydrogen atom was the first atomic to!

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