Wave mechanical atom

QM grew out of studies of blackbody radiation and of the photoelectric effect. Besides QM, radioactivity and relativity contributed to the transition from classical to modem physics. The classical Rutherford nuclear atom, the Bohr atom, and the Schrodinger wave-mechanical atom are discussed. Hybridization, wavefunctions, Slater determinants and other basic concepts are explained. For obtaining eigenvectors and eigenvalues from the secular equations the elegant and simple matrix diagonalization method is explained and used. All the necessary mathematics is explained. 

Table 8.2 Allowed quantum numbers and electron counts for the first four wave-mechanical atomic energy levels...

Figore 2.3 Comparison of the (a) Bohr and (b) wave-mechanical atom models in terms of electron distribution. (Adapted from Z. D. Jastrzeb-ski, I7ie Nature and Properties of Engineering Materials, 3rd edition, p. 4. Copyright 1987 by John Wiley Sons, New York. Reprinted by permission of John Wiley Sons, Inc.)... 

Describe some of the differences between the orbits of the Bohr atom and the orbitals of the wave mechanical atom. Are there any similarities ... 

The theory of chemical reactions has many facets iiicliidiiig elaborate qnaritiim mechanical scattering approaches that treat the kinetic energy of atoms by proper wave mechanical methods. These approaches to chemical reaction theory go far beyond the capabilities of a product like HyperChem as many of the ideas arc yet to have wide-spread practical im plemeiitation s. 

Schutte, C. J. H. (1968) The Wave Mechanics of Atoms, Molecules and Ions, Arnold, London. 

In 1913 Niels Bohr proposed a system of rules that defined a specific set of discrete orbits for the electrons of an atom with a given atomic number. These rules required the electrons to exist only in these orbits, so that they did not radiate energy continuously as in classical electromagnetism. This model was extended first by Sommerfeld and then by Goudsmit and Uhlenbeck. In 1925 Heisenberg, and in 1926 Schrn dinger, proposed a matrix or wave mechanics theory that has developed into quantum mechanics, in which all of these properties are included. In this theory the state of the electron is described by a wave function from which the electron s properties can be deduced. 

MaxweU-Boltzmaim particles are distinguishable, and a partition function, or distribution, of these particles can be derived from classical considerations. Real systems exist in which individual particles ate indistinguishable. Eor example, individual electrons in a soHd metal do not maintain positional proximity to specific atoms. These electrons obey Eermi-Ditac statistics (133). In contrast, the quantum effects observed for most normal gases can be correlated with Bose-Einstein statistics (117). The approach to statistical thermodynamics described thus far is referred to as wave mechanics. An equivalent quantum theory is referred to as matrix mechanics (134—136). 

The year 1926 was an exciting one. Schrddinger, Heisenberg and Dirac, all working independently, solved the hydrogen atom problem. Schrddinger s treatment, which we refer to as wave mechanics, is the version that you will be fanuliar with. The only cloud on the horizon was summarized by Dirac, in his famous statement ... 

Scientists in the 1920s, speculating on this problem, became convinced that an entirely new approach was required to treat electrons in atoms and molecules. In 1924 a young French scientist, Louis de Broglie (1892-1987), in his doctoral thesis at the Sorbonne made a revolutionary suggestion. He reasoned that if light could show the behavior of particles (photons) as well as waves, then perhaps an electron, which Bohr had treated as a particle, could behave like a wave. In a few years, de Broglie s postulate was confirmed experimentally. This led to the development of a whole new discipline, first called wave mechanics, more commonly known today as quantum mechanics. 

It was a characteristic feature of Bohr s classical quantum mechanics that it could never be generalized to give good quantitative results for systems containing more than one electron. The extension from N = 1 to N = 2, 3,. . . came first with modern wave mechanics and Heisenberg s discovery in 1926 of the exchange phenomenon in the He-atom, which, with the identity... 

This assumption is no longer valid in its place the wave mechanics provides the simple explanation that the repulsive forces arise from the interpenetration of the atoms. As a simple example, we may consider the hydrogen ion and the chloride ion according to the wave mechanics the potential energy of these two ions at a distance R apart, assuming that no deformation occurs, is6... 

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