Abstract
This article is about generalization and extension of the Bohr atomic model as well as the Rydberg formula to make them applicable to all atomic/ionic excited states and their energy levels. Bohr and Rydberg’s original works were deemed only for hydrogen and the hydrogen-like ions but in time many mistakenly have come to the conclusion that those original forms of the theory are applicable to all species. This article clarifies the subject and helps with the misunderstandings. The article reviews first the original theory of atoms, the related excited states, and the related energy levels. It then shows the shortcoming of the original formulations and makes changes to generalize the theory and extend their applications to all atoms and their related ions. The theory of atomic excited states is re-formulated using a newly defined parameter called “characteristic exponent k” and the corresponding ionization energy. Numerical calculations and detailed works for several elements are presented to establish a better understanding of excited states. The article seeks also for a connection between the atomic energy levels and the internal structures and inner electrons of atoms. Furthermore, a small data bank is generated using the calculated “characteristic exponents k” for elements to be utilized for future simulations, studies, and research activities.
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References
Zadeh DH (2021) Molecular theory considering nuclear potential wells. J Mol Model 27:185. https://doi.org/10.1007/s00894-021-04804-2
Zadeh DH (2019) A new approach to estimate atomic energies. J Mol Model 25:366. https://doi.org/10.1007/s00894-019-4259-1
Zadeh DH (2019) Atomic shells according to ionization energies. J Mol Model 25(8):251 https://link.springer.com/article/10.1007/s00894-019-4112-6
Zadeh DH (2017) Electronic structures of elements according to ionization energies. J Mol Model 23(12):357 https://link.springer.com/article/10.1007/s00894-017-3534-2
Politzer P, Zadeh DH (1994) Bond-breaking energies for 2, 2′-dichlorodiethyl sulfide (sulfur mustard) in media of different dielectric constants. J Phys Chem 98:1576–1578. https://doi.org/10.1021/j100057a008
Zadeh DH, Grice ME, Concha MC, Murray JS, Politzer P (1995) Nonlocal density functional calculation of gas phase heats of formation. J Comput Chem 16(5):654–658. https://doi.org/10.1002/jcc.540160513
Bohr N (1913) The spectra of helium and hydrogen. Nature 92:231–232. https://doi.org/10.1038/092231d0
Bohr N (1913) On the Constitution of Atoms and Molecules, Part I. Philos Mag 26(151):1–24. https://doi.org/10.1080/14786441308634955
Hehre WJ, Radom L, Schleyer PVR, Pople JA (1986) Ab initio molecular orbital theory. Wiley, New York. https://doi.org/10.1002/jcc.540070314
Sharpe AG (1986) Inorganic chemistry. Longman, London and New York. https://doi.org/10.1002/bbpc.19860901144
Szabo A, Ostlund NS (1989) Modern quantum chemistry. McGraw-Hill, New York ISBN-10: 0486691861
Atkins PW (1986) Physical chemistry. W.H. Freeman and Company, New York ISBN-10: 0716731681
Drago RS (1977) Physical methods in chemistry. Saunders College Publishing, Philadelphia ISBN-10: 0721631843
Pauling L, Wilson EB (1985) Introduction to quantum mechanics with applications to chemistry. Dover Publications, INC., New York ISBN-10:0486648710
Herzberg G (1945) Atomic spectra and atomic structure. Dover Publications, New York ISBN-10:0486601153
Johnson CS, Pedersen LG (1986) Problems and solutions in quantum chemistry and physics. Dover Publications, Inc., New York ISBN-10:0486151530
Sutton M (2004) Getting the numbers right: the lonely struggle of the 19th century physicist/chemist. Johannes Rydberg Chem World 1(7):38–41 ISSN 1473-7604
Martinson I, Curtis LJ (2005) Janne Rydberg – his life and work. Nucl Inst Methods Phys Res B 235(1–4):17–22. https://doi.org/10.1016/j.nimb.2005.03.137
Kramida A, Yu R, Reader J, NIST ASD Team (2014) NIST Ionization Energy Database NIST Atomic Spectra Database (ver. 5.2). National Institute of Standards and Technology, Gaithersburg. https://physics.nist.gov/asd; https://physics.nist.gov/PhysRefData/ASD/levels_form.html, https://physics.nist.gov/PhysRefData/ASD/ionEnergy.html
Morton DC, Wu Q, Drake GWF (2006) Energy levels for the stable isotopes of atomic helium can. J Phys 84:83–105. https://doi.org/10.1139/p06-009
Moore CE (1949) Atomic energy levels as derived from the analysis of optical spectra –hydrogen through vanadium, in Nat. Stand. Ref. Data Ser., NSRDS-NBS 35 Vol. I (Reprint of NBS Circ. 467, Vol. I, 1949), 359 pp. (Nat. Bur. Stand., U.S., 1971). https://doi.org/10.6028/NBS.NSRDS.35v1
Kramida A, Martin WC (1997) A compilation of energy levels and wavelengths for the spectrum of neutral beryllium (Be I). J Phys Chem Ref Data 26:1185–1194. https://doi.org/10.1063/1.555999
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Zadeh, D.H. Atomic excited states and the related energy levels. J Mol Model 28, 282 (2022). https://doi.org/10.1007/s00894-022-05257-x
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DOI: https://doi.org/10.1007/s00894-022-05257-x