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Journal articles on the topic 'Bohr model'

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Published: 5 June 2025
Last updated: 24 June 2025

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1

Nanni, Luca. "Relativistic Bohr model." Physics Essays 32, no. 1 (2019): 73–76. http://dx.doi.org/10.4006/0836-1398-32.1.73.

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2

Malte, Hans, and Gunnar Lykkeboe. "The Bohr/Haldane effect: a model-based uncovering of the full extent of its impact on O2 delivery to and CO2 removal from tissues." Journal of Applied Physiology 125, no. 3 (2018): 916–22. http://dx.doi.org/10.1152/japplphysiol.00140.2018.

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For a century, the influence of the Bohr effect on the utilization of blood-borne oxygen has been deemed secondary to its influence on the uptake of carbon dioxide by the blood. Here, we show that the opposite is the case. Using a simple two-ligand, two-state formulation, we modeled the simultaneous oxygen and proton binding to hemoglobin, as well as the resulting acid-base changes of the surrounding solution. Blocking of the Bohr effect in this model system results in a dramatic increase in the oxygen affinity, as expressed by the oxygen partial pressure at half saturation, the P50. It also becomes clear that the P50 and the Bohr factor (a measure of the size of the Bohr effect) are not independent but directly related. Thus, everything else being equal, varying the number of Bohr groups from 0 to 8 per tetramer results in an increase in the Bohr factor from 0 to −0.9 and an increase in P50 from 6 to 46 mmHg at a constant Pco2 of 40 mmHg. Therefore, changes in hemoglobin structure that lead to changes in the Bohr factor will inevitably also change hemoglobin oxygen affinity. NEW & NOTEWORTHY Using a mathematical model, we show that the Bohr effect has a more profound effect on gas exchange than is evident when comparing oxygen equilibrium curves measured in the laboratory at different constant values of Pco2 or pH. Protons preloaded on the Bohr groups, as well as the protons taken up during oxygen unloading, dramatically decrease oxygen affinity of the physiological oxygen equilibrium curve. Therefore, the Bohr effect is instrumental in setting the oxygen affinity.
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3

Khare, Avinash. "One hundred years of Bohr model." Resonance 18, no. 10 (2013): 885–96. http://dx.doi.org/10.1007/s12045-013-0115-2.

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4

KRUPIŃSKI, KRZYSZTOF, and ANAND PILLAY. "Generalised Bohr compactification and model-theoretic connected components." Mathematical Proceedings of the Cambridge Philosophical Society 163, no. 2 (2016): 219–49. http://dx.doi.org/10.1017/s0305004116000967.

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AbstractFor a group G first order definable in a structure M, we continue the study of the “definable topological dynamics” of G (from [9] for example). The special case when all subsets of G are definable in the given structure M is simply the usual topological dynamics of the discrete group G; in particular, in this case, the words “externally definable” and “definable” can be removed in the results described below.Here we consider the mutual interactions of three notions or objects: a certain model-theoretic invariant G*/(G*)000M of G, which appears to be “new” in the classical discrete case and of which we give a direct description in the paper; the [externally definable] generalised Bohr compactification of G; [externally definable] strong amenability. Among other things, we essentially prove: (i) the “new” invariant G*/(G*)000M lies in between the externally definable generalised Bohr compactification and the definable Bohr compactification, and these all coincide when G is definably strongly amenable and all types in SG(M) are definable; (ii) the kernel of the surjective homomorphism from G*/(G*)000M to the definable Bohr compactification has naturally the structure of the quotient of a compact (Hausdorff) group by a dense normal subgroup; (iii) when Th(M) is NIP, then G is [externally] definably amenable iff it is externally definably strongly amenable.In the situation when all types in SG(M) are definable, one can just work with the definable (instead of externally definable) objects in the above results.
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5

Borrelli, Arianna. "Niels Bohr and the Quantum Atom: The Bohr Model of Atomic Structure 1913–1925." International Studies in the Philosophy of Science 27, no. 2 (2013): 222–24. http://dx.doi.org/10.1080/02698595.2013.813250.

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6

Rapoport, D. M., R. G. Norman, and R. M. Goldring. "CO2 homeostasis during periodic breathing: predictions from a computer model." Journal of Applied Physiology 75, no. 5 (1993): 2302–9. http://dx.doi.org/10.1152/jappl.1993.75.5.2302.

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The Bohr/Riley model of CO2 homeostasis describes the relationship between CO2 production, ventilation, and arterial PCO2 and assumes that ventilation and CO2 delivery to the lung are both anatomically and temporally well matched. In contrast to normal breathing, periodic patterns of ventilation show temporal mismatch of ventilation to CO2 delivery. We developed a computer model of lung CO2 clearance that uses CO2 transfer equations to generate iterative solutions for PCO2 in multiple body compartments as a function of time. During continuous ventilatory patterns our model predicts steady-state arterial PCO2 identical to that of the Bohr model. During periodic ventilation, we predict mean PCO2 will be elevated unless mean ventilation is increased above that required by the Bohr model. Waxing and waning tidal volumes, low functional residual capacity, and low capillary blood volume potentiate the hypercapnia. However, if cardiac output oscillates in phase with breathing, hypercapnia is minimized. This analysis suggests a new mechanism for the development of sustained hypercapnia, separate from absolute hypoventilation or the presence of lung disease.
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7

Gong-ou, Xu, Li Fu-li, and Fu De-ji. "Microscopic aspects of the Bohr-Mottelson model." Physical Review C 43, no. 3 (1991): 1216–24. http://dx.doi.org/10.1103/physrevc.43.1216.

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8

Chen, Goong, Zhonghai Ding, Sze-Bi Hsu, Moochan Kim, and Jianxin Zhou. "Mathematical analysis of a Bohr atom model." Journal of Mathematical Physics 47, no. 2 (2006): 022107. http://dx.doi.org/10.1063/1.2168396.

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9

Bloom, Danning, and Dan W. Bloom. "Vibrating Wire Loop and the Bohr Model." Physics Teacher 41, no. 5 (2003): 292–94. http://dx.doi.org/10.1119/1.1571265.

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10

Bonatsos, Dennis, D. Lenis, D. Petrellis, and P. A. Terziev. "W(5): Wobbling Mode in the Framework of the X(5) Model." HNPS Proceedings 13 (February 20, 2020): 214. http://dx.doi.org/10.12681/hnps.2971.

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Using in the Bohr Hamiltonian the approximations leading to the Bohr and Mot- telson description of wobbling motion in even nuclei, a W(5) model for wobbling bands, coexisting with a X(5) ground state band, is obtained. Separation of vari­ ables is achieved by assuming that the relevant potential has a sharp minimum at 70, which is the only parameter entering in the spectra and B(E2) transition rates (up to overall scale factors). B(E2) transition rates exhibit the features expected in the wobbling case.
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11

Roche Allred, Zahilyn D., and Stacey Lowery Bretz. "University chemistry students’ interpretations of multiple representations of the helium atom." Chemistry Education Research and Practice 20, no. 2 (2019): 358–68. http://dx.doi.org/10.1039/c8rp00296g.

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Multiple chemistry education research studies at the secondary level have characterized students’ difficulties regarding a conceptual understanding of the quantum model of the atom. This research explores undergraduate students’ interpretations of multiple representations of the atom. Semi-structured interviews were conducted with first-year university chemistry students (n= 26) and second-semester physical chemistry students (n= 8) after they were taught and tested on the quantum model of the atom in their respective courses. During the interview, students were asked to interpret four representations of the atom (an electron cloud model, a probability representation, a boundary surface representation, and the Bohr model) and to rank each of the representations from most preferred to the least preferred. Nearly two-thirds of the students ranked the electron cloud and Bohr-model as their two most preferred representations. Students invoked ideas from classical mechanics to interpret the electron cloud model and used probabilistic language to describe the Bohr model of the atom.
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12

KRUPIŃSKI, KRZYSZTOF. "DEFINABLE TOPOLOGICAL DYNAMICS." Journal of Symbolic Logic 82, no. 3 (2017): 1080–105. http://dx.doi.org/10.1017/jsl.2017.32.

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AbstractFor a group G definable in a first order structure M we develop basic topological dynamics in the category of definable G-flows. In particular, we give a description of the universal definable G-ambit and of the semigroup operation on it. We find a natural epimorphism from the Ellis group of this flow to the definable Bohr compactification of G, that is to the quotient ${G^{\rm{*}}}/G_M^{{\rm{*}}00}$ (where G* is the interpretation of G in a monster model). More generally, we obtain these results locally, i.e., in the category of Δ-definable G-flows for any fixed set Δ of formulas of an appropriate form. In particular, we define local connected components $G_{{\rm{\Delta }},M}^{{\rm{*}}00}$ and $G_{{\rm{\Delta }},M}^{{\rm{*}}000}$, and show that ${G^{\rm{*}}}/G_{{\rm{\Delta }},M}^{{\rm{*}}00}$ is the Δ-definable Bohr compactification of G. We also note that some deeper arguments from [14] can be adapted to our context, showing for example that our epimorphism from the Ellis group to the Δ-definable Bohr compactification factors naturally yielding a continuous epimorphism from the Δ-definable generalized Bohr compactification to the Δ-definable Bohr compactification of G. Finally, we propose to view certain topological-dynamic and model-theoretic invariants as Polish structures which leads to some observations and questions.
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13

KRIVE, I. V., and A. A. ZVYAGIN. "AHARONOV–CASHER EFFECT IN HALF-INTEGER SPIN ANTIFERROMAGNETS." Modern Physics Letters B 06, no. 14 (1992): 871–78. http://dx.doi.org/10.1142/s0217984992001721.

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The manifestation of the Aharonov–Casher effect in condensed media is considered. In the one-dimensional Hubbard model with arbitrary band filling we derived analytical expressions for the oscillating part of the ground state energy of mesoscopic ring with twisted boundary conditions which model the influence of Aharonov–Bohn (AB) and/or Aharonov–Casher (AC) fields. It is shown that in the limit of strong on-site repulsion AB-oscillations disappear for half-filled band, but the amplitude of the AC-oscillations, on the contrary, attains its maximum. The period of the AC-oscillations in this case equals hc/2 μ B (μ B is the Bohr magneton).
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14

Olszewski, Stanisław. "The Bohr Model of the Hydrogen Atom Revisited." Reviews in Theoretical Science 4, no. 4 (2016): 336–52. http://dx.doi.org/10.1166/rits.2016.1066.

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15

Stein, Wolf-Dieter R. "Quantized Magnetic Flux in the Bohr–Sommerfeld Model." Journal of Russian Laser Research 34, no. 6 (2013): 553–64. http://dx.doi.org/10.1007/s10946-013-9387-y.

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16

Gulshani, P. "Derivation of microscopic unified Bohr–Mottelson rotational model." Nuclear Physics A 852, no. 1 (2011): 109–26. http://dx.doi.org/10.1016/j.nuclphysa.2011.01.013.

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17

Faessler, Amand, G. Kyrchev, and R. Nojarov. "Boson quasispin in the generalised Bohr-Mottelson model." Nuclear Physics A 487, no. 1 (1988): 37–61. http://dx.doi.org/10.1016/0375-9474(88)90128-5.

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18

Lahkar, Jugal, D. K. Choudhury, S. Roy, and N. S. Bordoloi. "A model of mesons in finite extra-dimension." Canadian Journal of Physics 96, no. 5 (2018): 524–28. http://dx.doi.org/10.1139/cjp-2017-0658.

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Recently, the problem of stability of the H atom has been reported in extra-finite dimension, and found out that it is stable in extra-finite dimension of size R ≤ a0/4, where a0 is the Bohr radius. Assuming that heavy flavoured mesons also have such stability controlled by the scale of the coupling constant, we obtain corresponding QCD Bohr radius, and it is found to be well within the present theoretical and experimental limit of higher dimension. We then study its consequences in their masses using effective string-inspired potential model in higher dimension. Our analysis suggests that an extra-dimension of size 0.007 × 10−15 m ≤ L ≤ 0.13 × 10−15 m can account for the masses of heavy flavoured mesons under study within their experimental uncertainty without confinement effects. This range is well below the present theoretical and experimental limits on the size of extra-dimension.
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19

Hijab, Sarah A., and Saeed N. Turki Al-Rashid. "Study of Electrical Properties of Nano TiO2 Coatings Based on the Characteristic Matrix Theory and the Brus Model." 2, no. 2 (June 2, 2022): 80–84. http://dx.doi.org/10.26565/2312-4334-2022-2-09.

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Electrical properties of Nano TiO2 coatings as a function of the nanoparticle size have been studied. In addition, this study explores how to calculate the quantum confinement energy of TiO2. The results confirm the effect of particle size on electrical properties especially when the size becomes close to the exciton Bohr radius. The electrical properties are not effected when the size becomes close to 40 nm. The Bohr radius of Nano TiO2 coatings has been found to be 1.4 nm. While the confinement energy was 0.43 eV. The program depends on the Characteristic Matrix Theory and The Brus Model.
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20

Shorter, R. S. "Niels Bohr and the Quantum Atom: The Bohr Model of Atomic Structure 1913–1925, by Helge Kragh." Contemporary Physics 54, no. 2 (2013): 133. http://dx.doi.org/10.1080/00107514.2013.800588.

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21

Putra, Fima Ardianto. "On the Ehrenfest Paradox in the Bohr Atomic Model toward the Quantization of Gravitation." Jurnal Fisika Indonesia 22, no. 1 (2020): 7. http://dx.doi.org/10.22146/jfi.v22i1.34275.

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Ehrenfest Paradox has been studied in the Bohr Atomic Model as the theoretical procedure such a way that we can express the coordinate curvature i.e. gravitational aspect in the electromagnetic coupling constant. The strength of the curvature depends on the principal quantum number which shows that the value of curvature is quantized. For , the value is . The curvature value in the Bohr atomic model can be a standard to measure how strong the curvature of all system are, by comparing them with this value. We also get the understanding that the change of the curvature will manifest the curvature propagation in the form of quantum energy, i.e. . This theory can be considered to enlarge the unification theory between quantum and gravitation. Another consequence of this theory is the quantization of Equivalence Principle.
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22

Kharitonov, Vladimir Vitalievich. "At the 100 years anniversary of Bohr atom model." Izvestiya Wysshikh Uchebnykh Zawedeniy, Yadernaya Energetika 2013, no. 3 (2013): 48–51. http://dx.doi.org/10.26583/npe.2013.3.06.

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23

Boilley, David, Yasuhisa Abe, Sakir Ayik, and Eric Suraud. "A Bohr-Mottelson model of nuclei at finite temperature." Zeitschrift f�r Physik A Hadrons and Nuclei 349, no. 2 (1994): 119–27. http://dx.doi.org/10.1007/bf01291169.

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24

Hewitt, Paul G. "Focus on Physics: The Bohr Model of the Atom." Science Teacher 88, no. 3 (2021): 14–16. http://dx.doi.org/10.1080/00368555.2021.12293579.

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25

Anwar, Budiman, Rd R. Srie Ernawati, Rahmat Setiadi, and Ms Wiji. "PENGEMBANGAN REPRESENTASI KIMIA SEKOLAH BERBASIS INTERTEKSTUAL PADA SUB-KONSEP KONFIGURASI ELEKTRON MODEL ATOM BOHR YANG DIPERLUAS DALAM BENTUK MULTIMEDIA." Jurnal Pengajaran Matematika dan Ilmu Pengetahuan Alam 17, no. 2 (2015): 278. http://dx.doi.org/10.18269/jpmipa.v17i2.272.

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Telah dilakukan penelitian yang menghasilkan representasi kimia berbasis intertekstual berupa multimedia pada sub-konsep konfigurasi elektron berdasarkan model atom Bohr yang diperluas. Dalam penelitian ini digunakan metode deskriptif dan evaluatif yang merupakan bagian dari Penelitian dan Pengembangan (R & D). Prosedur penelitian dilakukan melalui beberapa tahapan kerja, yaitu: (1) penentuan materi subjek, (2) kajian standar kompetensi dan kompetensi dasar yang terdapat pada standar isi serta contoh silabus BSNP untuk menentukan indikator dan konsep, (3) pengumpulan multimedia existing, (4) analisis multimedia existing berdasarkan kajian aspek konten, pedagogi, dan multimedia, (5) pembuatan script dan storyboard yang divalidasi berdasarkan aspek konten dan pedagogi, (6) revisi script dan storyboard, (7) pembuatan multimedia yang kemudian di validasi pada aspek multimedia. Multimedia ini kemudian ditanggapi oleh guru dan siswa untuk mengetahui kualitas multimedia berdasarkan kriteria/ indikator yang telah ditentukan melalui angket. Hasilnya diolah secara deskriptif persentase. Angket diberikan kepada lima orang guru mata pelajaran Kimia dan 30 orang siswa SMA kelas XI dan XII yang telah mempelajari mengenai sub-konsep konfigurasi elektron berdasarkan model atom Bohr yang diperluas. Berdasarkan data angket guru diperoleh hasil bahwa tingkat persetujuan terhadap: (1) kualitas multimedia adalah 84%, (2) kejelasan penyampaian materi/ konsep adalah 96%, (3) peran multimedia adalah 100%, dan (4) pengembangan multimedia adalah 100%. Secara keseluruhan respon guru terhadap multimedia terletak pada daerah positif. Berdasarkan data angket siswa diperoleh hasil bahwa tingkat persetujuan terhadap: (1) motivasi pada multimedia adalah 85.31%, (2) konten pada multimedia adalah 84.7%, (3) navigasi pada multimedia adalah 86%, (4) multimedia dan interaktivitasnya adalah 90.84%, dan (5) tampilan multimedia adalah 86.77%. Secara keseluruhan respon siswa terhadap multimedia terletak pada daerah setuju. Dengan demikian representasi kimia sekolah berbasis intertekstual pada sub-konsep konfigurasi elektron model atom Bohr yang diperluas dalam bentuk multimedia yang telah dikembangkan dapat digunakan.Kata kunci: intertekstual, konfigurasi elektron, model atom Bohr, multimedia, representasi kimia
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26

Bonatsos, D., P. E. Georgoudis, D. Lenis, N. Minkov, and C. Quesne. "The Deformation Dependent Mass Davidson Model." HNPS Proceedings 19 (January 1, 2020): 22. http://dx.doi.org/10.12681/hnps.2511.

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The Deformation Dependent Mass Davidson Model is an extension of the well known Bohr-Mottelson Hamiltonian for the atomic nuclei. It primarily refers to the mass dependence on the deformation and secondary to the Davidson behavior for the potential of the Ø-vibration. This article will be devoted solely in the solution of the radial equation. Fitting results for the 162Dy and 238U ground state, β1 and γ1 bands are also presented.
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27

Mohammed, Maina Aliyu Adamu Mustapha Sanda Muhammad I. Bukar. "The Bohr Model of the Atom: A Critical Evaluation of its Impact and Limitations in Modern Physics." Journal of Science and Technology Research 5, no. 3 (2023): 180–93. https://doi.org/10.5281/zenodo.8330960.

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<em>This study investigated the properties and behavior of orbiting leptons, with a focus on their speed, wavelength, frequency, and energy. The research revealed the dependence of lepton speed on the size of the orbit and the magnitude of the charge of the nucleus. The speeds of electrons and muons were found to be similar, but muons being closer to the nucleus exhibited a greater sensitivity to nuclear charge. The analysis also demonstrated that the wavelengths of leptons increase linearly with the principal quantum number and the charge of the nucleus. Moreover, the comparison between Bohr and de Broglie wavelengths highlighted the influence of mass and speed on the wavelength differences. The research provided valuable insights into the relationship between speed, wavelength, frequency, and energy of orbiting leptons in atomic systems. The observations underscored the impact of relativistic motion on these parameters and highlighted the need to account for these effects in theoretical calculations. By examining computed values of lepton speed and analyzing their implications for different energy states and atoms, researchers gained a deeper understanding of lepton properties and the nature of orbital motion. The study incorporated the relativistic motion of leptons, leading to higher energies than those calculated by Niels Bohr. While the differences were small, they underscored the importance of considering relativistic corrections in energy level calculations. The findings emphasized the significance of incorporating these corrections to achieve accurate results, particularly in simple energy level calculations. The impact of the Bohr model extends beyond atomic theory and finds applications in various fields, including atomic physics, chemistry, and materials science. Therefore, this study contributed to our understanding of orbiting leptons, their properties, and their behavior within atomic systems. It highlighted the importance of incorporating relativistic corrections in energy level calculations and provided insights into the relationship between speed, wavelength, frequency, and energy. The investigation also emphasized the significance of the Bohr model in explaining atomic behavior, while acknowledging the advancements and limitations of modern theoretical frameworks like quantum mechanics.</em><strong> </strong>
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28

Ali, Ahmed H. "Investigation of the Quadrupole Moment and Form Factors of Some Ca Isotopes." Baghdad Science Journal 17, no. 2 (2020): 0502. http://dx.doi.org/10.21123/bsj.2020.17.2.0502.

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Nuclear shell model is adopted to calculate the electric quadrupole moments for some Calcium isotopes 20Ca (N = 21, 23, 25, and 27) in the fp shell. The wave function is generated using a two body effective interaction fpd6 and fp space model. The one body density matrix elements (OBDM) are calculated for these isotopes using the NuShellX@MSU code. The effect of the core-polarizations was taken through the theory microscopic by taking the set of the effective charges. The results for the quadrupole moments by using Bohr-Mottelson (B-M) effective charges are the best. The behavior of the form factors of some Calcium isotopes was studied by using Bohr-Mottelson (B-M) effective charges.
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29

Talantsev, E. F. "Quasi-classical model for real space shape of the Cooper pair probabilitydensity." Superconductivity: Fundamental and Applied Research, no. 2 (July 2024): 57–65. http://dx.doi.org/10.62539/2949-5644-2024-0-2-57-65.

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Within Bardeen-Cooper-Schrieffer theory of superconductivity, two electrons form the Cooper pair in the momentum space. However, it is a challenging task to represent the Cooper pair probability density in real space. Here we proposed a quasi-classical three dimensional model for the Cooper pair probability density shape in a real space, which is appeared as a direct consequence to describe the Meissner-Ochsenfeld critical field, Bc,MO (which is the thermodynamic critical field in Type-I superconductors, and lower critical field in Type-II superconductors) by the equation Bc,MO= 11/2μ0nμBln(1+√2ξ/λ), where μ0 is the magnetic permeability of free space, n is the Cooper pair bulk density, μB is the Bohr magneton, and λ is the London penetration depth, and ξ is the coherence length. As a result, the Meissner-Ochsenfeld field can be defined as the field at which each Cooper pair exhibits the diamagnetic moment of one Bohr magneton with a multiplicative pre-factor of 1/2ln(1+√2λ/ξ). Based on quasi-classical interpretation of this result, in this study we proposed that the probability density of the Cooper pair in real space can be represented as a toroid with an inner radius ξ and an outer radius of ξ + √2λ. This means that the superconducting transition is associated not only with the charge carrier pairing, but that the pairs exhibit a new topological state with genus 1.
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30

Freitas, Savana Dos Anjos, and Agostinho Serrano. "Use of different external mediating mechanisms of the Bohr atom model: Evidence of Meaningful Learning through verbal-gestural analysis in elementary school students." Acta Scientiae 21, no. 4 (2019): 133–48. http://dx.doi.org/10.17648/acta.scientiae.v21iss4id5253.

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The present article sought to investigate if the use of different external mediation mechanisms to teach the Bohr Atom model in elementary education with the didactic methodology of the Potentially Significant Teaching Units (PSTU) can result in Meaningful learning. Therefore, we naturally use the theoretical contribution of the Ausubelian Meaningful Learning Theory, in particular by discussing elements that indicate evidence of meaningful learning. This theory was adopted with the purpose of understanding and analyzing whether or not there is evidence of meaningful learning with elementary level students after about a year of using the didactic methodology. The didactic methodology used was the application of didactic sequences inspired by the PSTU model, modified to be applied in Elementary School. We also use different external mediation mechanisms that independently reproduce the Bohr atom model, such as model building (psychophysical mediation), teacher explanation on a blackboard (social mediation), use of textbooks (cultural mediation) and computer simulations (hypercultural mediation). Data analysis was carried out through two semi-structured interviews according to the Report Aloud protocol followed by the depictive gestural analysis, performed with an interval of almost one year, both interviews were carried out after the application of the didactic methodology, in order to assess the retention of the learning residue. We argue that the students' verbal-gestural production indicates that there was meaningful learning of the Bohr Atom model, especially related to social and hypercultural mediations.
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31

Bakhodir, Tursunbaev, and Nigmatov Khikmatulla. "THE REAL RADIUS OF THE HYDROGEN ATOM: NEW THEORETICAL AND EXPERIMENTAL APPROACHES." Deutsche internationale Zeitschrift für zeitgenössische Wissenschaft 100 (March 20, 2025): 38–41. https://doi.org/10.5281/zenodo.15061577.

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This paper presents an investigation of the real radius of the hydrogen atom based on experimental data and new theoretical models. The experimental data show that the radius of the hydrogen atom in the approximate state is 1 &micro;m, while in the excited state it is 1.4 &micro;m [1]. These data were converted into real values, which show that the radius is 1 &Aring; in the approximate state and 1.4 &Aring; in the excited state [2]. Three theoretical models were also considered: the Bohr model [3, 4], the Schr&ouml;dinger method [5] and the deterministic theory of the atom (DTA) of Bahodir Tursunbaev [6, 7]. The results show that Bahodir Tursunbaev's DTA provides more accurate predictions for the radii of the hydrogen atom than the Bohr model and the Schr&ouml;dinger method. The paper also addresses the problem of the spread of pseudoscience and proposes recommendations for popularising the new theory in the&nbsp;scientific community.
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32

Pandu, Gerda, Redi Kristian Pingak, Albert Zicko Johannes, and Zakarias Seba Ngara. "A Study on Radial Properties of Hydrogenic Ions using Laguerre Polynomials." BULETIN FISIKA 23, no. 2 (2021): 78. http://dx.doi.org/10.24843/bf.2022.v23.i02.p01.

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A preliminary study has been carried out on the radial properties of the hydrogenic systems using the Laguerre polynomial. The aims of this study were to investigate radial properties of hydrogenic ions by evaluating the radial probability density, the most probable radial distance and the average distance of electron from the nuclei of hydrogenic ions. Based on the research results for Z=1 to Z=10 with the principal quantum number (n)=1 to 5, 150 radial function forms, 150 radial probability density, 150 most probable radial distance values and 150 electron average distance values were obtained. The most probable radial distance from the nucleus was compared with the Bohr model and showed the same results as the Bohr model.
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33

Bonatsos, D., E. A. McCutchan, N. Minkov, et al. "Exactly separable version of the Bohr Hamiltonian with the Davidson potential." HNPS Proceedings 16 (January 1, 2020): 121. http://dx.doi.org/10.12681/hnps.2589.

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An exactly separable version of the Bohr Hamiltonian, is obtained by using a potential of the form V (β, γ) = u(β) + u(γ)/β2, with a Davidson potential for u(β) and a stiff harmonic oscillator potential centered around γ = 0o, for u(γ).Using two parameters (β0 and the γ-stiffness parameter) the band features and B(E2) transition rates of almost all well-deformed rare-earth and actinide nuclei are reproduced, while the spectrum of the SU(3) dynamical symmetry of the Interacting Boson Model can be obtained, for the first time using the Bohr Hamiltonian.
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34

Petrellis, D. "Critical point for the Deformation Dependent Mass model through a variational procedure." HNPS Proceedings 21 (March 8, 2019): 65. http://dx.doi.org/10.12681/hnps.2005.

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The recently introduced Deformation-Dependent Mass model is combined with a variational approach to the Bohr Hamiltonian in order to describe transitional nuclei. The results of this procedure are demon- strated for the ‘spherical to γ-unstable’ and the ‘spherical to deformed’ transitional classes, which corre- spond to the E(5) and X(5) solutions.
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35

Ganev, H. G. "Microscopic Version of the Bohr-Mottelson Model and Its Application." Bulgarian Journal of Physics 48, no. 5-6 (2021): 421–31. http://dx.doi.org/10.55318/bgjp.2021.48.5-6.421.

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36

Deutsch, Daniel H. "Bohr-Wilson-Sommerfeld Model of the Hydrogen Atom: A Reinterpretation." Physics Essays 2, no. 2 (1989): 113–17. http://dx.doi.org/10.4006/1.3035856.

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37

Iloh Udema, Ikechukwu. "Renaissance of Bohr's Model Via Derived Alternative Equation." American Journal of Modern Physics 6, no. 2 (2017): 23. http://dx.doi.org/10.11648/j.ajmp.20170602.11.

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38

Rowe, D. J., and G. Thiamova. "The many relationships between the IBM and the Bohr model." Nuclear Physics A 760, no. 1-2 (2005): 59–81. http://dx.doi.org/10.1016/j.nuclphysa.2005.06.001.

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39

Folse, Henry J. "Laudan's Model of Axiological Change and the Bohr-Einstein Debate." PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1990, no. 1 (1990): 77–88. http://dx.doi.org/10.1086/psaprocbienmeetp.1990.1.192694.

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40

Reed, B. Cameron. "Bohr’s model predicts ionization potential of two-electron atoms." Physics Education 40, no. 2 (2005): 117–18. http://dx.doi.org/10.1088/0031-9120/40/2/f02.

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41

Svidzinsky, Anatoly, Goong Chen, Siu Chin, et al. "Bohr model and dimensional scaling analysis of atoms and molecules." International Reviews in Physical Chemistry 27, no. 4 (2008): 665–723. http://dx.doi.org/10.1080/01442350802364664.

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42

Stávek, Jiří. "The Rydberg Constant Interpreted as the Gaussian Curvature, Gauss-Bohr-de Broglie Model – Two Shadow Projections of the Helix, Unlocking of the Fixed Constant c of the Speed of Light – New Tests for Old Physics." European Journal of Applied Physics 3, no. 2 (2021): 19–22. http://dx.doi.org/10.24018/ejphysics.2021.3.2.59.

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We have newly interpreted the Rydberg constant R∞ as the Gaussian curvature – the ratio of the 4π electron spin rotation to the area on the Gauss – Bohr sphere travelled by that electron. Rydberg constant for hydrogen RH was newly derived and can be experimentally tested and compared with the value RH derived from the reduced mass. The de Broglie electron on the helical path embedded on the Gauss – Bohr sphere was projected as two shadows: the real shadow Re [cos(t)] and the imaginary shadow Im [i sin(t)]. This model differs from the Schrödinger famous quantum wave description in the physical interpretation. The wave amplitude is here interpreted as the distance of the shadow from the Gauss – Bohr sphere. Moreover, we have newly inserted into the wave equation curvature and torsion of that de Broglie helix. One very interesting result of this model is the estimation of the constant c of the speed of light with three additional significant figures. We have divided the very precise CODATA 2018 value for R∞ expressed in frequency and the CODATA 1986 value for R∞ expressed in wavenumber unit. Based on these precise spectroscopic data we might increase the accuracy of the constant c of the speed of light to twelve significant figures.
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43

Rigden, John S. "Niels Bohr and the Quantum Atom: The Bohr Model of Atomic Structure 1913–1925.Niels Bohr and the Quantum Atom: The Bohr Model of Atomic Structure 1913–1925.HelgeKragh.416 pp. Oxford U.P., Oxford, UK, 2012. Price $62.99 (hardcover). ISBN 978-9-19-965498-7." American Journal of Physics 81, no. 3 (2013): 237–38. http://dx.doi.org/10.1119/1.4771884.

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44

Kupczynski, Marian. "Can we close the Bohr–Einstein quantum debate?" Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 375, no. 2106 (2017): 20160392. http://dx.doi.org/10.1098/rsta.2016.0392.

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Recent experiments allow one to conclude that Bell-type inequalities are indeed violated; thus, it is important to understand what this means and how we can explain the existence of strong correlations between outcomes of distant measurements. Do we have to announce that Einstein was wrong, Nature is non-local and non-local correlations are produced due to quantum magic and emerge, somehow, from outside space–time? Fortunately, such conclusions are unfounded because, if supplementary parameters describing measuring instruments are correctly incorporated in a theoretical model, then Bell-type inequalities may not be proved. We construct a simple probabilistic model allowing these correlations to be explained in a locally causal way. In our model, measurement outcomes are neither predetermined nor produced in an irreducibly random way. We explain why, contrary to the general belief, the introduction of setting-dependent parameters does not restrict experimenters' freedom of choice. Since the violation of Bell-type inequalities does not allow the conclusion that Nature is non-local and that quantum theory is complete, the Bohr–Einstein quantum debate may not be closed. The continuation of this debate is important not only for a better understanding of Nature but also for various practical applications of quantum phenomena. This article is part of the themed issue ‘Second quantum revolution: foundational questions’.
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Velinov, Peter, and Simeon Asenovski. "CORIMIA IONIZATION MODEL – A TWO-INTERVAL APPROXIMATION OF IONIZATION LOSS FUNCTION." Aerospace Research in Bulgaria 37 (2025): 7–15. https://doi.org/10.3897/arb.v37.e01.

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This article examines the ionization model CORIMIA (COsmic Ray Ionization Model for Ionosphere and Atmosphere) in its two-interval approximation of the ionization loss function. Increasing the number of approximation intervals is the next step in improving the model. The last stage was the introduction of a 5-interval approximation of the Bohr-Bethe-Bloch formula with an intermediate interval. This version includes the introduction of integration limits in an arbitrary energy interval.
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IONESCU, Lavinel G., and Luis Alcides Brandini De Boni. "THEODORO AUGUSTO RAMOS - A BRAZILIAN CONTRIBUTION TO THE MODEL OF THE ATOM." SOUTHERN BRAZILIAN JOURNAL OF CHEMISTRY 13, no. 13 (2005): 1–12. http://dx.doi.org/10.48141/sbjchem.v13.n13.2005.4_2005.pdf.

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The present article discusses the contribution of Theodoro Augusto Ramos, A Brazilian mathematician, to the model of the atom. In a paper entitled "The Theory of Relativity and the Spectral Lines of Hydrogen", presented to the Brazilian Academy of Sciences in November 1923, Theodoro Ramos analyzed the fine spectra of the hydrogen atom using the principles of the general theory of relativity. His results represent an improvement of the Bohr-Sommerfeld model.
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47

Chabab, M., A. Lahbas, and M. Oulne. "Closed analytical solutions of Bohr Hamiltonian with Manning-Rosen potential model." International Journal of Modern Physics E 24, no. 11 (2015): 1550089. http://dx.doi.org/10.1142/s0218301315500895.

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In the present paper, we have obtained closed analytical expressions for eigenvalues and eigenfunctions of the Bohr Hamiltonian with the Manning–Rosen potential for [Formula: see text]unstable nuclei as well as exactly separable rotational ones with [Formula: see text]. Some heavy nuclei with known [Formula: see text] and [Formula: see text] bandheads have been fitted by using two parameters in the [Formula: see text]unstable case and three parameters in the axially symmetric prolate deformed one. A good agreement with experimental data has been achieved.
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48

Li, Rujiang, Xiao Lin, Shisheng Lin, Xu Liu, and Hongsheng Chen. "Atomically thin spherical shell-shaped superscatterers based on a Bohr model." Nanotechnology 26, no. 50 (2015): 505201. http://dx.doi.org/10.1088/0957-4484/26/50/505201.

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49

Gulshani, P. "Derivation of microscopic uni-axial unified adiabatic Bohr–Mottelson rotational model." Nuclear Physics A 832, no. 1-2 (2010): 18–48. http://dx.doi.org/10.1016/j.nuclphysa.2009.11.007.

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50

Trippe, Sascha. "The “graviton picture”: a Bohr model for gravitation on galactic scales?" Canadian Journal of Physics 93, no. 2 (2015): 213–16. http://dx.doi.org/10.1139/cjp-2014-0158.

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Modified Newtonian dynamics (MOND) provides a successful description of stellar and galactic dynamics on almost all astronomical scales. A key feature of MOND is the transition function from Newtonian to modified dynamics, which corresponds to the empirical mass discrepancy–acceleration (MDA) relation. However, the functional form of the MDA relation does not follow from theory in a straightforward manner; in general, empirical MDA relations are inserted ad hoc into analyses of stellar dynamics. I revisit the possibility of gravity being mediated by massive virtual particles, gravitons. Under certain reasonable assumptions, the resulting “graviton picture” implies a MDA relation that is equivalent to the — empirical — “simple μ” function of MOND, which is in very good agreement with observations. I conclude that the “graviton picture” offers a simple description of gravitation on galactic scales, potentially playing a role for gravitation analogous to the role played by Bohr’s model for atomic physics.
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