Wave mechanical model of the atom

From a chemical point of view the most important result is that number theory predicts two alternative periodic classifications of the elements. One of these agrees with experimental observation and the other with a wave-mechanical model of the atom. The subtle differences must be ascribed to a constructionist error that neglects the role of the environment in the wave-mechanical analysis. It is inferred that the wave-mechanical model applies in empty space Z/N = 0.58), compared to the result, observed in curved non-empty space, (Z/N = t). The fundamental difference between the two situations reduces to a difference in space-time curvature. 

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 Schrodinger wave equation In 1926, Austrian physicist Erwin Schrbdinger (1887-1961) furthered the wave-particle theory proposed by de Broglie. Schrbdinger derived an equation that treated the hydrogen atom s electron as a wave. Remarkably, Schrbdinger s new model for the hydrogen atom seemed to apply equally well to atoms of other elements—an area in which Bohr s model failed. The atomic model in which electrons are treated as waves is called the wave mechanical model of the atom or, more commonly, the quantum mechanical model of the atom. Like Bohr s model,... 

O How does the wave mechanical model of the atom differ from Bohr s model ... 

The Bohr model was discarded because it could be applied only to hydrogen. The wave mechanical model can be applied to all atoms in basically the same form as we have just used it for hydrogen. In fact, the major triumph of this model is its ability to explain the periodic table of the elements. Recall that the elements on the periodic table are arranged in vertical groups, which contain elements that typically show similar chemical properties. For example, the halogens shown to the left are chemically similar. The wave mechanical model of the atom allows us to explain, based on electron arrangements, why these similarities occur. We will see later how this is done. 

Principal Components of the Wave Mechanical Model of the Atom... 

We have learned many properties of the elements and their compounds, but we have not discussed extensively the relationship between the chemical properties of a specific element and its position on the periodic table. In this chapter we will explore the chemical similarities and differences among the elements in the several groups of the periodic table and will try to interpret these data using the wave mechanical model of the atom. In the process we will illustrate a great variety of chemical properties and further demonstrate the practical importance of chemistry. 

Erwin Schrodinger proposes wave mechanical model of the atom. 

The firefly analogy is intended to demonstrate the concept of a probability map for electron density. In the wave mechanical model of the atom, we cannot say specifically where the electron is in the atom we can say only where there is a high probability of finding the electron. The analogy is to imagine a time-exposure photograph of a firefly in a closed room. Most of the time, the firefly will be found near the center of the room. 

Erwin Schrodinger proposes a wave-mechanical model of the atom (with electrons represented as wave trains). 

The selection rules given earlier for n and k were experimentally determined. The Bohr-Sommerfeld model for the atom did not account for them. Calculations based on the wave mechanical model indicate that n can change by any integer amount, as An = 0,1, 2, 3, etc., and that / must change by 1. This corresponds to the change in k that was determined experimentally. Since the wave mechanical model of the atom gives solutions in terms of statistical probability, a more accurate statement of the selection rule for / would be that the probability of a transition other than A/ = 1 is very small. 

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