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The Quantization in the Bohr's Theory About the Hydrogen Atom

Sangwha Yi

Published Oct 1, 2012• 0 citations
OpenAlex

Abstract

The article treats that the quantization in the Bohr’s theory about the hydrogen atom. If calculates the electron motion in the hydrogen atom by the classical mechanic, can do the quantization in the Bohr’s theory about the hydrogen atom. In this time, the electron’s orbit velocity is non-relativity velocity.

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of Bits and Bonds: Hi-Tech Methods Predict the Newest Molecules: Part 2. Quantization

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The Bohr model is historically important in the understanding of quantum physics. It gives many important results for the hydrogen atom including atomic size and ionization energy. It is sometimes referred to as a semi-classical calculation, because it includes the physics of angular momentum quantization without the full quantum mechanical description of an electron wave. It is tremendously useful for gaining physical intuition of the quantum nature of the atom. In the Bohr model of the hydrogen atom, an electron has a circular orbit with speed v and radius r about the proton. The Bohr quantization condition is that an integer number of electron (de Broglie) wavelengths must fit to the atomic circumference.
This chapter illustrates Niels Bohr's ideas in some detail. In the formulation of his model, Bohr assumed that the electron in the hydrogen atom moves under the influence of the Coulomb attraction between it and the positively charged nucleus, as assumed in classical mechanics. The Bohr model was very successful in explaining the discrete atomic spectra of one-electron atoms. The Bohr model is, of course, a theoretical model of an atom. Using Bohr's quantization postulate, find the linear velocity of the electron's sphere. To find the radius of the orbit, Bohr postulated that the angular momentum of the electron is quantized, i.e., it can only take values that are integer multiples of ħ. The chapter begins with considering the classical equation of motion for the electron in a circular orbit, which is based on Newton's laws of motion and Coulomb's law of electric force.
A model is proposed for the hydrogen atom in which the electron is an objectively real particle orbiting at very near to light speed. The model is based on the postulate that certain velocity terms associated with orbiting bodies can be considered as being affected by relativity. This leads to a model for the atom in which the stable electron orbits are associated with orbital velocities where Gamma is n/α, leading to the idea that it is Gamma that is quantized and not angular momentum as in the Bohr and other models. The model provides a mechanism which leads to quantization of energy levels within the atom and also provides a simple mechanical explanation for the Fine Structure Constant. The mechanism is closely associated with the Sampling theorem and the related phenomenon of aliasing developed in the mid-20th century by engineers at Bell labs.