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Fine Structure Constant Is Related to Effective Nuclear Charge and Bohr’S Radius for Any Atom

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Fine Structure Constant Is Related to Effective Nuclear Charge and Bohr’S Radius for Any Atom Asian Journal of Physical and Chemical Sciences 3(4): 1-8, 2017; Article no.AJOPACS.36931 ISSN: 2456-7779 Fine Structure Constant is Related to Effective Nuclear Charge and Bohr’s Radius for Any Atom Ikechukwu Iloh Udema1* 1Owa Alizomor Mixed Sec. Sch. Owa Alizomor, Ika North East/Ude International Concepts LTD (862217), B. B. Agbor, Delta State, Nigeria. Author’s contribution The sole author designed, analyzed and interpreted and prepared the manuscript. Article Information DOI: 10.9734/AJOPACS/2017/36931 Editor(s): (1) Macid Nurbas, Chemical Engineering Department, Eskisehir Osmangazi University, Turkey. (2) Shi-Hai Dong, Centro de Innovacion Desarrollo y Tecnologico en Computo, Instituto Politecnico Nacional Unidad Profesional Adolfo Lopez Mateos, Mexico. Reviewers: (1) Stanislaw Olszewski, Polish Academy of Science, Poland. (2) Jagdish Prakash, University of Botswana, Botswana. (3) Adel H. Phillips, Ain-Shams University, Egypt. Complete Peer review History: http://www.sciencedomain.org/review-history/21766 Received 23rd September 2017 Accepted 1st November 2017 Original Research Article Published 6th November 2017 ABSTRACT Objectives: The objectives of this research were to show that fine structure constant (a) is an intrinsic property of any matter (element) and 2) to relate it to other physical property of elements such as Bohr’s radius of any element and effective nuclear charge. Methods: The method is essentially theoretical which entailed the substitution of experimental data, ionization energy into derived equations in order to verify the universality of a as an intrinsic property of elemental matter. Results: The results for hydrogen showed that the effective nuclear charge, Zeff (@ 1) and Bohr’s radius obtained by calculation after substituting appropriate average ionization energy into different equations were very similar. The results for other elements that are non-hydrogenic showed similar similarity of values regardless of the equation used. = : Where the principal quantum a number, n1, EI is the average ionization energy of any element, and me is the mass of an electron. Conclusion: The fine structure constant is an intrinsic property of matter. There is a relationship between the fine structure constant and well known periodic properties of elemental matter, effective nuclear charge, average ionization energy, and Bohr’s radius for any atom, other than hydrogenic atoms. _____________________________________________________________________________________________________ *Corresponding author: E-mail: [email protected]; Udema; AJOPACS, 3(4): 1-8, 2017; Article no.AJOPACS.36931 Keywords: Fine structure constant; periodic properties of elements; hydrogen atom; non-hydrogenic atom; Bohr’s radii. 1. INTRODUCTION parameters are respectively, charge of an electron, Planck’s constant and speed of light in The term fine structure constant (a) has been free space and ħ = h/2p. [2,5,6]. But that is an subjected to a lot of misgivings and equation yielding upon calculation 4.061407 exp 2 interpretation, which are subjective, mystical and (-13)/C /Jm which is very different from the true strangely scientific in nature. It does not seem to value. have any useful value or significance. Treating a as mere figure is subjective and amount to As observed by Sherbon [3], Sommerfeld [4] trivialization in nature. If complete science or idea defined a as the ratio of the speed of the electron is one that is not just testable but subject to in the ground state of the Bohr’s hydrogen atom mathematical formalism, then the strong to the speed of light. This is highly instructive or mathematical formulations which give an informative. The notion of negative kinetic energy impression that a is a difficult concept is has been questioned [7]. It is described as being unnecessarily strange. As a mystery it implies nonsensical [7]. This is understandable that it is not subject to human-level activity called considering the fact that the farther away the scientific process. The misgivings, electron from the nucleus, the higher the misinterpretations and mysticism associated with potential energy but the kinetic energy a can be attested to in part as follows. “…It has decreases. The minimum energy needed to been a mystery ever since it was discovered remove an electron in the outermost energy level more than fifty years ago, and all good of an atom in its ground state is the kinetic energy otherwise called average ionization theoretical physicists put this number up on their 2 wall and worry about it. Immediately you would energy: But mec is not kinetic energy (me is the like to know where this number for a coupling mass of an electron). Given that it may take comes from: is it related to p or perhaps to the some time, t to escape nuclear attraction base of natural logarithms? Nobody knows. It’s completely, “the power” to remove the electron one of the greatest damn mysteries of physics: a is: magic number that comes to us with no understanding by man. You might say the ‘hand = − (1) of God’ wrote that number, and ‘we don’t know how He pushed his pencil.’ We know what kind Thus in line with Sommerfeld definition, the of a dance to do experimentally to measure this expression for a may be: number very accurately, but we don’t know what kind of dance to do on the computer to make this number come out, without putting it in secretly!” a = ( ~ 7.297666718 exp (-3)) (2) [1]. Perhaps Indian or Italian dance style only may be the answer; but this must not be without Definition as advanced by Chakeres [8] is a little time consciousness! bit confusing. The average ionization energy, E , H of hydrogen is conceptually related to the change However, a is said to come from spectroscopy in the velocity of an electron from the annihilation where it is used in the development of J.J. velocity of c to velocity (v), ac. Again, this means Ballmer’s series of a spectral lines into multiple ½ very close components [2]. Other uses of a are: that c/v (º c/ac) = 1/a) where v = (2EI/me) . Thus various determinations such as interferometry the correct expression is: and Bloch oscillations, the neutron Compton = 137.0303048 (3) wavelength measurement, unfamiliar areas such √ as AC Josephson effect and quantum Hall effect in condense matter physics etc [3]. Also, it has where c = 2.9979 exp (+8) m/s; me = 9.103 exp (- application in the determination of the strength of 31) kg; EI for hydrogen is 1312000 J/mol. the electromagnetic interaction and it was according to Sherbon [3] initially introduced by It is against the backdrop of different opinions Sommerfeld [4]. Fine structure constant, a is held regarding what a stands for and for the fact defined as a ratio of the constant, e, h, and c, that it seems to be tied only to hydrogen, the having the expression: a = e2/ħc where the objectives of this research are 1) to show that a 2 Udema; AJOPACS, 3(4): 1-8, 2017; Article no.AJOPACS.36931 is an intrinsic property of any matter (element) abbreviations such as tan and cos so as to give and 2) to relate it to other physical property of even greater respectability to the journal. elements such as Bohr’s radius of any element and effective nuclear charge. There are equations in literature that deserve being numbered in this research. Example 2. FURTHER THEORETICAL DEVELOP- presented in different ways by Chakeres [8] and MENT Danescu [2] are respectively, m 2.1 Review of Literature on Mathematical 2a = (5) Models of Fine Structure Constant m a = . = a (6) The purpose of this section is the derivation or p ħ formulation of verifiable mathematical models However, review paper by Dattoli [1] presented that can relate a to other physical properties, theories and methods for the determination of a namely ionization energy of not just hydrogenic atoms but multi-electron atoms and radius of any (sometimes written as aQED): The mathematical atom. Meanwhile, according to Dattoli [1] formalism may not be too familiar though such arguments related to the Dirac monopoles may formalism represents an expression of superior allow the derivation of independent formulae for knowledge in higher mathematics, but there are some results shown in the paper that cannot the definition of fine structure constant, a. be obtained from some of the equations. One Anyone who has deep understanding of higher of such claim in literature is: mathematics may consult the paper by Preskill [9] who envisaged a magnetic monopole as a = exp − = 136.976(8) where semi-infinitely long, infinitesimally thin solenoid. a a How argument related to Dirac monopole can a = , where G is Newton’s gravitational ħ allow the derivation of formula for a is not constant. Given that the latest gravitational certain. But an example of what seems to be the constant cited elsewhere [11] is 6.67384 (80) exp 3 2 formula is what according to Dattoli [1] has been (-11) m /kg.s ; mp/me = 1836.1; me.mp = described as Wyler [10] “marvelous” formula: 2 1.52348025 exp (-57) kg ; aG = 3.21722883 exp(- ( ) p 42); = 5.420069 exp +20 ; exp − = a = a = = 7.289276981 exp(−3) (4) a p ! 2.469022 exp(−19). It is where QED is the not-too-familiar quantum obvious that this result is slightly different from electrodynamics. that observed in literature. In the same paper [1] is: a = . It is clear that a does not have p QED The value indicated in Eq. (4) is slightly different any other meaning other than how it was defined from what is presented in Eq. (2). A very in literature. If so, the latter equation may not be confusing formula which cannot be made part of valid considering what e stands for.
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