Abstract
The aims of this research were: 1) To derive alternative equation into which can be substituted known experimental data and known physical constants for the calculation of Bohr’s radii of atoms for some elements, 2) respond to some of the objections raised against (or the short coming of Bohr’s theory,) and 3) make a case for the justification of Bohr’s theory. Apart from other elements, Bohr’s radius( a 0 ) for hydrogen was 0.5291 A; the radii for Na([Ne]3s 1 ) and Na + ([Ne]3s 0 ) were 2.5844 A and 0.5675A respectively which correspond to effective nuclear charges ( Z eff ) equal to 1.8424 and 3.7291 respectively at the 1 st and 2 nd principal quantum numbers ( n ) respectively. The results were obtained based on two definitions: a 0 αn 2 / Z eff (from initial Bohr’s equation) and a 0 αn/( ξ n ) ½ (from the derived equation, where ξ n is the average ionization energy). In conclusion, an alternative equation to Bohr’s equation was successfully derived. No single model should always be a solution to all scientific questions. Both original Bohr’s equation and derived equation can give, after calculation, similar value of any atomic radius. Therefore, Bohr’s theory stands scientifically justified.
Highlights
The year, 2016, is about a 100 years after Bohr published his famous model for hydrogen atom in particular
As shown in Eq (2), a0 is directly proportional to the square of principal quantum number and inversely proportional to the effective nuclear charge
It is clear that a0 is inversely proportional to the square root of the average ionization energy and directly proportional to the principal quantum number
Summary
The year, 2016, is about a 100 years after Bohr published his famous model for hydrogen atom in particular. Literature [1, 2] is loaded with very reprehensible comments on Bohr’s model. Characteristically scientific in content with the intention of further comprehension of the basis or justification for the claim made by Bohr, with regard to his theory of atomic structure using hydrogen atom as a case study. Modern approach in the description of hydrogen atom and its electron in particular is mainly based on Schrödinger-Dirac formalism. It is too obvious that classical mechanics upon which Bohr’s model is based is very different from quantum mechanics, which is predominantly mathematical in nature and used to predict the position and momentum of an electron. The focus of this paper ab initio, is on Bohr’s model
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