A Mathematical Relationship between Hydrogenic Periodic Property and Nuclear Properties in Furtherance of Bohr’s Theory

Ikechukwu I. Udema *

Department of Chemistry and Biochemistry, Research Division, Ude International Concepts LTD (RC: 862217), B. B. Agbor, Delta State, Nigeria.

*Author to whom correspondence should be addressed.


Abstract

Background: Atomic physics and nuclear matter physics are often exclusively studied. However, atomic properties are a direct function of nuclear properties. Establishing a mathematical relationship between nuclear and atomic properties could serve the interest of nuclear and atomic engineers. Nuclear - and atomic-based instrumentation engineering and nuclear medicine (and perhaps atomic medicine) applications could be the benefits.

Objectives: The research is undertaken to 1) link nuclear property, the mass-radius of the nucleon, and ionization energy of hydrogen via the derivation of appropriate equation and 2) determine the mass-radii of the nucleons and some leptons.

Methods: Theoretical and computational methods.

Results and Discussion: As applicable to the previous results in the literature, the larger the mass of the elementary particles, the longer the radii. For the particles investigated, the order of the radius is muon (m-)<proton (p+)< neutron (n)< tauon (t-) corresponding to increasing mass, m-<p+< n<t-. The values of the mass radii were respectively » 0.1240, 1.1012, 1.1027, and 2.0855 fm.

Conclusion: Nuclear properties such as the radius of any nucleon (ΓN) can be mathematically linked to atomic properties such as the ionization energy of hydrogen via equation which shows that ΓN is inversely proportional to the ionization energy of hydrogen and directly proportional to the rest-mass of the particle.

Keywords: Hydrogenic ions, nuclear and hydrogenic properties, nucleon and Bohr’s radii, hydrogenic ionization energy


How to Cite

Udema, I. I. (2022). A Mathematical Relationship between Hydrogenic Periodic Property and Nuclear Properties in Furtherance of Bohr’s Theory. Asian Journal of Research and Reviews in Physics, 6(3), 1–6. https://doi.org/10.9734/ajr2p/2022/v6i3117

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References

Seif WM, Mansour H, Systematics of nucleon density distributions and neutron skin of nuclei. Int. J. Mod. Phys. E. 2015;24(11): 1-14.

Udema II. Renaissance of Bohr's model via derived alternative equation. Am. J. Mod. Phys. 2017;6(2):23-31.

Mills RL. The fallacy of Feynman’s and related arguments on the stability of the hydrogen atom according to quantum mechanics. Annales de la Fondation Louis de Broglie. 2005;30(2):129-149.

Bochkarev OV, Chulkov LV. Egelhof P, Geissel H, Golovkov MS, Irnich H, et al. Evidence for a neutron skin in 20N. Eur. Phys. J.1998;1:15-17.

Kneen WR, Rogers MJ Wand Simpson P. Chemistry. Facts, patterns, and principles. 1st ed. London: The English Language Book Society and Addison-Wesley Publishers Limited; 1972.

Udema II. Revisiting Bohr’s theory via a relationship between magnetic constant and Bohr radius of any element. Asian J. Phys. Chem. Sci. 2018;6(1):1-11.

Strutinsky VM, Magner AG, Denisov VYu. Density distribution in nuclei. Z. Phys. A-Atoms & Nuclei. 1985;322: 49-156.

Gharaei R, Hadikhani A, Zanganeh V. An explanation for the anomaly problem of diffuseness parameter of the nucleus-nucleus potential in heavy-ion fusion reactions: A possible thermal relation. Nucl. Physics A. 2019;990:47-63.

Udema II. Theoretical determination of the mass radii of the nucleons and heavier subatomic particles. Asian J. Res. Rev. Phys. 2020;3(4):1-10.

Lyuboritskij VE, Gutsche Th, Faessler A. Electromagnetic structure of the nucleon in the perturbative chiral quark model. Phys. Rev. C - Nuclear Phys. 2001; 64 (6): 652031-652316.

Gentile TR, Crawford CB. Neutron charge radius and the neutron form factor. Phys. Rev. C. 2011;83:1-6.

Carson CE. The proton radius puzzle. Prog. Part. Nucl. Phys. 2015;82:59-77.

Pohl R, Antognini A, Nez F, Amaro FD, Biraben F, Cardoso JMR, et al. The size of the proton. Nature. 2010;466:213- 216.

Pohl R, Nez F, Fernandes LMP, Amaro FD, Biraben F, Cardoso JMR, Covita DS, Dax A. Dhawan S, Diepold M, et al. Laser spectroscopy of muonic deuterium. Science. 2016;353:669-673.

Peset C, Pineda A. The Lamb shift in muonic hydrogen and the proton radius from effective field theories. Eur. Phys. J. A. 2015;51(156):arXiv.

Kelkar NG, Mart T, Nowakowski M. Extraction of the proton charge radius from experiments. Makara J. Sci. 2016;20(3):1-10.

Xiong W, Gasparian A, Gao H, Dutta D, Khandaker M, Liyanage N, et al. A small proton charge radius from electron – proton scattering experiment. Nature. 2019;575(7781):147-170.

Hare HG, Papini G. Mass radius of the nucleon. Canadian J. Phys. 1972;50:1163-1168.

Byrne J. The mean square charge radius of the neutron. Neutron News. 1994; 5(4): 15-17.

Pohl R, Gilman R, Miller GA. Pachnucki K. Muonic hydrogen and the proton radius puzzle. Annu. Rev. Nucl. Part. Sci. 2013;63:175-205.

Mohr PJ, Taylor BN, Newel DB. CODATA recommended values of the fundamental physical constants-2010. J. Phys. Chem. Ref. Data. 2012;41(4):1–84.