Wave mechanical model understanding

The results considered in this section are very important. We have seen that the wave mechanical model can be used to explain the arrangement of elements in the periodic table. This model allows us to understand that the similar chemistry exhibited by the members of a given group arises from the fact that they all have the same valence electron configuration. Only the principal quantum number of the occupied orbitals changes in going down a particular group. 

To understand how the electron s position Is represented In the wave mechanical model... 

As we explore this topic, and as we use theories to explain other types of chemical behavior later in the text, it is important that we distinguish the observation (steel msts) from the attempts to explain why the observed event occurs (theories). The observations remain the same over the decades, but the theories (our explanations) change as we gain a clearer understanding of how nature operates. A good example of this is the replacement of the Bohr model for atoms by the wave mechanical model. 

It is important to note that wave-particle duality is an important part of our understanding of the modem atomic stmcture based on the wave mechanical model. Historical reconstmction presented in this study shows how scientists themselves had considerable difficulty in understanding and accepting this novel idea. Even leading schools of physicists (Bohr, Planck and Summerheld) were reluctant to incorporate de Broglie s ideas in the corpus of science. This episode shows clearly how (as in so many other episodes in the history of science, cf. Niaz 2009) progress in science is inevitably based on alternative interpretations of experimental data that lead to controversies. Furthermore, it seems that textbooks... 

Example 10.1 Understanding the Wave Mechanical Model of the Atom... 

Quantum wave mechanics gave chemistry a new "understanding," but it was an understanding absolutely dependent on purely chemical facts already known. What enabled the theoretician to get the right answer the first time, in a set of calculations, was the experimental facts of chemistry, which, Coulson wrote, "imply certain properties of the solution of the wave equation, so that chemistry could be said to be solving the mathematicians problems and not the other way around."36 So complex are the possible interactions among valence electrons that one must either use an exact mathematical model of a... 

The use of effective mass to understand the state of the microstructure is chosen to conserve the application of the free electron model by letting the mass of the electron incorporate the electron interactions with the lattice, which are experiencing potential energy interactions. Considering the total energy, E, of an electron in a solid, based on wave mechanics, then ... 

It is then quite understandable why, without the necessary mathematical machinery, the relevant concepts cannot be properly grasped. On the other hand, the mathematical disguise that is characteristic of quantum-chemistry courses makes both teachers and students pay more attention to the complexities of the mathematics (the tools, the trees ) and lose the physics (the actual world, the forest ). Although mathematics is essential for a deep understanding of quantum chemistry, the underlying physical picture and its connection with mathematics are equally important. AOs, MOs and related concepts derive from SchrOdinger s wave mechanics, which is an approximation to nature. According to Simons (96), "orbital concepts are merely aspects of the best presently available model they are not real in the same sense that experimental observations are. ... 

In order to describe microscopic systems, then, a different mechanics was required. One promising candidate was wave mechanics, since standing waves are also a quantized phenomenon. Interestingly, as first proposed by de Broglie, matter can indeed be shown to have wavelike properties. However, it also has particle-Uke properties, and to properly account for this dichotomy a new mechanics, quanmm mechanics, was developed. This chapter provides an overview of the fundamental features of quantum mechanics, and describes in a formal way the fundamental equations that are used in the construction of computational models. In some sense, this chapter is historical. However, in order to appreciate the differences between modem computational models, and the range over which they may be expected to be applicable, it is important to understand the foundation on which all of them are built. Following this exposition. Chapter 5 overviews the approximations inherent... 

The wave model fails to account for phenomena associated W ilh the absorption and emission of radiant energy. I o understand those processes, it is necessary to invoke a particle model in which electromagnetic radiation is viewed as a stream of discrete panicles, or wave packets, of energy called photons. The energy of a photon is proportional to the frequency of the radia turn. ITiese dual views of radiation as particles and as waves are not mutually exclusive bul. rather, cvimple mcniary. Indeed, the wave-panicle duality is found to apply to the behavior of streams of electrons, protons, and other elementary particles and is completely ra-lionali/cd by wave mechanics. 

Schrodinger developed the ideas of quantum (wave) mechanics in 1925. It was then applied to determine atomic and molecular structure. The idea of covalent bonding between two atoms based on the sharing of electron pairs was proposed by Lewis in 1916. The Lewis model (of dots and crosses to represent electrons) is still relevant and useful, but the quantum mechanical model (Chapters 2 and 12), incorporating wave-particle duality, Pauli s exclusion principle and Heisenberg s uncertainty principle, gives a deeper understanding of chemical bonds. 

It may be unexpected to find that number theory and traditional wave mechanics yield comparable reconstructions of extranuclear electronic configurations. However, both models are based on classical waves in three-dimensional space, appropriate for the understanding of atomic structure in tangent Euclidean space. 

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