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An Approach to the Understanding of Structure and Stability of Atom

Seikh Hannan Mandal

Published May 15, 2012• 0 citations
OpenAlex

Abstract

The objective of this article is to show how experimental discoveries in atomic physics are logically connected, and we land up with the consistent theoretical explanation to the structure and stability of the atom. It is also shown that Bohr’s correspondence principle and Erhenfest’s adiabatic invariant hypothesis act as a guiding rules to this route. As a generalization to Bohr’s quantum condition, the Wilson-Sommerfeld quantization condition for multi-periodic system is presented with a derivation.

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The objective of this article is to show how experimental discoveries in atomic physics are logically connected, and we land up with the consistent theoretical explanation to the structure and stability of the atom. It is also shown that Bohr’s correspondence principle and Erhenfest’s adiabatic invariant hypothesis act as a guiding rules to this route. As a generalization to Bohr’s quantum condition, the Wilson-Sommerfeld quantization condition for multi-periodic system is presented with a derivation.
Abstract The development of the complex of assumptions and methods now referred to as the “old quantum theory” mainly took place in the first five years following the introduction of the Bohr atomic model in 1913. Three guiding principles emerged that were used, sometimes in overlapping ways, to explain the flood of spectroscopic data that needed to be explained. First, quantization rules (or conditions) were proposed to single out the allowed orbital motions of electrons in atoms. These rules were derived in various forms by Planck, Sommerfeld, and Wilson, but were put into their most general form by Schwarzschild, who recognized the underlying principle as the quantization of the action variables of a multiply periodic classical system. Second, the special role of the action variables in quantization was given convincing support by the transfer of the adiabatic principle of mechanics to quantum theory (work primarily due to Paul Ehrenfest). Third, the correspondence principle, or statement of asymptotic coincidence of quantum and classical theory in the limit of large quantum numbers, originally introduced by Bohr in 1913 as a supporting argument for his quantization of angular momentum in his theory of the hydrogen atom, was extended by Bohr and Kramers to provide selection rules and approximate intensity predictions evening the regime low quantum numbers.
Abstract We review the Bohr atomic model, where certain conditions (quantum conditions) were used to select certain “allowed” circular orbits for the electrons in an atom. Sommerfeld realized that a more generalized condition, applied to the action variables, would be consistent with the Bohr condition and also allow elliptical orbits. This condition amounted to the quantization of the phase space occupied by an orbit. This had independently been suggested by Planck. We also discuss the similarities between classical mechanics and the geometric optics limit of a wave theory.
Abstract The attempt to explain atomic structure was one of the main motives for the genesis of quantum mechanics (Bohr’s atomic model, spectral lines, etc.); at the same time it represented the first true testing ground for the new theory. The explanation of the existence of discrete atomic levels, their quantitative prediction, understanding of the periodic structure of the elements, the correct interpretation of chemical bonds, etc., can be regarded without exaggeration as one of the greatest achievements of the scientific thought of our time. A door to an entirely new world— that of the atomic and subatomic phenomena—opened, triggering an impressive advance in basic scientific knowledge and modern technology, unprecedented in human history. The very concepts and many of the mathematical tools of quantum mechanics have, in many cases, sprung from the efforts to solve these problems. In this chapter, we study atomic structure, and try to illustrate some of these features.
In a major work of 1918 (‘On the quantum theory of line-spectra’) Bohr reconsidered the general principles of quantum and atomic theory. Apart from reinterpreting his original theory, he introduced the correspondence principle as a crucial connection between quantum and classical physics. What was the nature of this principle and what role did it play in the understanding of atomic structure? In applying the new principle, Bohr and his assistant H. A. Kramers relied on Einstein’s radiation theory. Bohr used the correspondence principle as a selection principle, and Kramers showed how it could account quantitatively for the Stark effect. However, not all physicists appreciated the Copenhagen ‘magic wand’ and Bohr’s use of it. Sommerfeld was the most prominent of the sceptics, but not the only one. The chapter also briefly considers the role of the correspondence principle in the early phase of the new quantum mechanics.