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arXiv:0806.0652 · Old and New Concepts of Physics

Bohr's Atomic Model Revisited

Francisco Caruso, Vitor Oguri

Published Apr 1, 2009• 1 citation
arXivHTMLPDF

Abstract

Bohr's atomic model, its relationship to the radiation spectrum of the hydrogen atom and the inherent hypotheses are revisited. It is argued that Bohr could have adopted a different approach, focusing his analyzes on the stationary orbit of the electron and its decomposition on two harmonic oscillators and then imposing, as actually he did, Planck's quantization for the oscillators' energies. Some consequences of this procedure are examined.

DOI
10.2478/v10005-009-0004-3

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Bohr's atomic model, its relationship to the radiation spectrum of the hydrogen atom and the inherent hypotheses are revisited. It is argued that Bohr could have adopted a different approach, focusing his analyzes on the stationary orbit of the electron and its decomposition on two harmonic oscillators and then imposing, as actually he did, Planck's quantization for the oscillators' energies. Some consequences of this procedure are examined.
One of the most important developments of modern science was the emergence of the concept of energy quantization which forced its way into our previous classical understanding of matter in nature. Modern day view of matter constituents and present understanding of atomic structure basic to quantum chemistry arose in those first decades of last century. In this line, a key feature for the understanding of microscopic atomic structures and their stability was the concept of angular momentum quantization. To capture the beauty and the power of these concepts is therefore extremely relevant for apprehending the contemporary view of matter, energy and interactions in nature. In this work we present a possible alternative approach of quantizing the atomic orbit for the hydrogen's atom model proposed by Bohr without using his hypothesis of angular momentum quantization from the start. In our approach here we show that when we identify the number of photons and the quantum number for the orbit, we are led to Bohr's hypothesis as a consequence of the Planck's energy quantization.
Turning back to Niels Bohr's model of the hydrogen atom, the paper is trying to resolve one of the issues associated with the model.While N. Bohr in the framework of his model did not find any relation between electron's motion in the atom and radiation emitted, there is a reason to believe that the relation is bound to exist.Furthermore, it is already given by Rydberg's formula that expresses the frequency of radiation as a difference of two other frequencies associated in some manner with electron's rotation.Based on this approach a new value for the radius of the ground stationary orbit is calculated.It appears to be more than Bohr's radius by a factor of 1.588.The question why both values for the radius of the ground stationary orbit (Bohr's radius and a new one) are compatible with Rydberg's formula is considered.Finally, what exactly Niels Bohr overlooked in his model of the hydrogen atom, is discussed.It is established that Rydberg's formula can be derived from the more general parameterized postulates, when Niels Bohr used, regardless of the value of the parameter.
This chapter has provided an alternate method of solving simple problems in atomic physics under Bohr’s model to aid good mental picture of hydrogen atom to scientists. Two values of fundamental physical properties of an electron in the hydrogen atom has been identified. By limiting the orbiting electrons to a series of circular orbits having discrete radii, Bohr could account for the series of discrete wavelengths in the emission spectrum of hydrogen. Light, he proposed, radiated from hydrogen atoms only when an electron made a transition from an outer orbit to one closer to the nucleus. These physical properties (Ve = 174090.938ms-1& Pe = 1.585860888 × 10-25kgms-1) are constant in nature. The aim for the review was to contribute to the solution of disagreement between the Bohr’s wavelength (λ\lambdaλ0 = 91.12nm) and the Balmer’s experimental observation (λ\lambdaλ0 = 91.18nm) for the emission spectrum of hydrogen atom. There are two other constants δ\deltaδ = 7.199822 × 10-10 eVm and ζ\zetaζ = 1503796277m-1 that were identified in the Bohr’s equation of the hydrogen atom. The four fundamental physical constants can be applied to multi-electron systems because they are inherent characteristics of an electron. They can also be derived from the steady state hydrogen atom Schrodinger's equation. For a deeper understanding, these constants may be scrutinised for their determination. The study recommends that current quantum atomic models and equations governing quantum physics should be revisited for better applications and understanding of the physical world.