Atomic structure wave mechanical model

The wave-mechanical model of the atom shows a more complex structure of the atom and the way electrons configure themselves in the principal energy levels. Principal energy levels are divided into sublevels, each with its own distinct set of orbitals. This more complex structure is outlined with the help of this diagram. The principal energy levels in the atom are numbered 1 through 7. 

The modern view of the periodic table explains its structure in terms of an Aufbau procedure based on the wave-mechanical model of the hydrogen atom. Although seductive at first glance, the model is totally inadequate to account for details of the observed electronic configurations of atoms, and makes no distinction between isotopes of the same element. The attractive part of the wave-mechanical model is that it predicts a periodic sequence of electronic configurations readily specified as a function of atomic number. The periodicity follows from the progressive increase of four quantum numbers n, l, mi and s, such that... 

Each of the three theories accounts for some, but not all aspects of elemental periodicity. The common ground among the three may well reveal the suspected link with space-time structure. What is required is to combine aspects of the wave-mechanical model of hydrogen, the structure of atomic nuclei and number theory. 

In the next chapter we will see how our ideas about atomic structure help us understand how and why atoms combine to form compounds. As we explore this, and as we use theories to explain other t3q3es of chemical behavior later in the text, it is important that we distinguish the observation (steel rusts) 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. 

In this chapter, you learned about the electronic structure of the atom in terms of the older Bohr model and the newer quantum mechanical model. You learned about the wave properties of matter, and how to describe each individual electron in terms of its four quantum numbers. You then learned how to write the electron configuration of an atom and some exceptions to the general rules. 

In this section, you saw how the ideas of quantum mechanics led to a new, revolutionary atomic model—the quantum mechanical model of the atom. According to this model, electrons have both matter-like and wave-like properties. Their position and momentum cannot both be determined with certainty, so they must be described in terms of probabilities. An orbital represents a mathematical description of the volume of space in which an electron has a high probability of being found. You learned the first three quantum numbers that describe the size, energy, shape, and orientation of an orbital. In the next section, you will use quantum numbers to describe the total number of electrons in an atom and the energy levels in which they are most likely to be found in their ground state. You will also discover how the ideas of quantum mechanics explain the structure and organization of the periodic table. 

Schrodinger s quantum mechanical model of atomic structure is framed in the form of a wave equation, a mathematical equation similar in form to that used to describe the motion of ordinary waves in fluids. The solutions (there are many) to the wave equation are called wave functions, or orbitals, and are represented by... 

In the first years of 1900, however, physicists started studying the structure of atoms and soon realised that it was impossible to describe them with models of either particles or waves. Those models were inevitable in classical physics, and their failure could only mean that that physics is not valid at the atomic scale. The laws which apply to one level of reality are not necessarily valid at other levels, but this did not stop the unification process. In the end, quantum mechanics did manage to account for the atomic world, and it turned out that it could also explain the results of classical physics, which means that a bridge can actually be built between different levels of reality. A new synthesis, in other words, became possible because the quantum description of nature was able to contain, as a particular case, the description of classical physics. 

Before discussing in detail the numerical results of our computational work, we describe the theoretical and computational context of the present calculations apart from deficiencies of models employed in the analysis of experimental data, we must be aware of the limitations of both theoretical models and the computational aspects. Regarding theory, even a single helium atom is unpredictable [14] purely mathematically from an initial point of two electrons, two neutrons and two protons. Accepting a narrower point of view neglecting internal nuclear structure, we have applied for our purpose well established software, specifically Dalton in a recent release 2.0 [9], that implements numerical calculations to solve approximately Schrodinger s temporally independent equation, thus involving wave mechanics rather than quantum... 

Quantum chemistry is the appfication of quantum mechanical principles and equations to the study of molecules. In order to nnderstand matter at its most fundamental level, we must use quantum mechanical models and methods. There are two aspects of quantum mechanics that make it different from previous models of matter. The first is the concept of wave-particle duality that is, the notion that we need to think of very small objects (such as electrons) as having characteristics of both particles and waves. Second, quantum mechanical models correctly predict that the energy of atoms and molecules is always quantized, meaning that they may have only specific amounts of energy. Quantum chemical theories allow us to explain the structure of the periodic table, and quantum chemical calculations allow us to accurately predict the structures of molecules and the spectroscopic behavior of atoms and molecules. 

The quantum mechanical model of atomic structure is based on a set of postulates that can only be justified on the basis of their ability to rationalize experimental behavior. However, the foundations of quantum theory have their origins in the field of classical wave mechanics. The fundamental postulates are as follows ... 

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. 

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