Revisiting Bohr’s Theory via a Relationship between Magnetic Constant and Bohr Radius of Any Element

Objectives: The purposes of this research are 1st, to show that there is a relationship between magnetic constant and Bohr radius for any atom and 2nd, to verify this relationship with illustrative calculations.

Place and Duration of Study: Department of Chemistry and Biochemistry, Research Division, Ude International Concepts LTD (862217), B. B. Agbor, Delta State, Nigeria; Owa Alizomor Secondary School, Owa Alizomor, Ika North East, Delta State, Nigeria.

Methods: Theoretical and calculational.

Results: The result of derived equations for Bohr radius for any atom as they relate to magnetic constant (μ0) and effective nuclear charge (Zeff) are as shown below where h, n, and c, are Planck’s constant, principal quantum number, and velocity of light in a vacuum respectively; E, EH, e, and me are average ionization energy (IE) for atom other than hydrogen, IE for hydrogen, charge of an electron, and mass of an electron respectively. Using the Bohr’s radius for hydrogen as an example the radius, a, obtainable from all equations are similar being ≈ 5.3 exp (-11) m. (From literature [12]) (From this research). The derived equation for effective nuclear charge (Zeff) is and using hydrogen as example, Zeff ≅1.

Conclusion: The results showed that magnetic constant like fine structure constant can be separately related to the radius of elements. Several pieces of evidence of this issue expressed via different equations may justify or validate Bohr’s classical model. If the mathematical equations can reproduce the parameters, ‘a’ and Zeff for hydrogen, multi-electron atoms could not be the exception. Reproducing ‘a’ and Zeff for hydrogen and by extension every hydrogenic atom (but not limited to hydrogenic atom as reported in the literature) seem to validate the equations in this research and Bohr’s original equation in particular.