Wave mechanics periodic table

The characteristic values of Z/N = x and of 0.58 for observed and wave-mechanical periodicities are the limits of converging Fibonacci fractions around 3/5. The segmentation of the table into groups of 2 and 8 and of periods 2,8,18,32 summarizes the observed periodicity as a subset of nuclide periodicity. The sublevel structure, despite formal resemblance to the wave-mechanical H solution, emerges from number theory without reference to atomic structure. 

Only with Bohr s 1913-1923 introduction of the "old quantum theory" (itself strongly inspired by chemical periodicity patterns vide infra) and the final discovery of Schrodinger s wave mechanics in 1925 would the periodic table be supplanted as the deepest expression of current chemical understanding ([21], p 2). 

Methods can be based on some preconceived concept of bonding, with ionic and covalent extremes, or on pattern recognition based on the periodic table. Miscellaneous methods of limited applicability link bond strength with other physical properties. The a priori calculation of heats of formation by wave mechanics is possible in theory. In practice, the most widely applied method incorporates experimental data to derive atom or bond parameters which can then be used for calculations on closely related compounds. 

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. 

Now we are ready to apply the method of wave mechanics to study the electronic structure of the atoms. At the beginning of this chapter, we concentrate on the hydrogen atom, which consists of one proton and one electron. After treating the hydrogen atom, we will proceed to the other atoms in the Periodic Table. 

Theoretical chemistry reached its pinnacle during the Sommerfeld era, before the advent of wave mechanics. The theoretically superior new theory, although it eliminated the paradoxes of zero angular momentum of the hydrogen ground-state, the orbital motion in helium and the nature of stationary states, it defined the periodic table less well and confused the simple picture of chemical bonding. Theoretical chemistry still suffers from that body blow. 

On a plot of Z/N vs Z for all stable nuclides the field of stability is outlined very well by a profile, defined by the special points of the periodic table derived from 4. Furthermore, hem lines that divide the 264 nuclides into 11 groups of 24 intersect the convergence line, Z/N = r, at most of the points that define the periodic function. If the hem lines are extended to intersect the line Z/N = 0.58, a different set of points are projected out and found to match the periodicity, derived from the wave-mechanical model. 

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... 

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. 

There is more good news. Anyone who has stared at the periodic table and has taken basic chemistry knows that the orbital structure postulated for atoms is the same for all kinds of atoms. And all atoms exhibit a line spectrum that is independent of the viewer s position. So there is no reason, in principle, why you couldn t solve this problem for other sorts of atoms too. The basic ideas are indeed the same. Of course, problems arise in interpretation. For example, if we are interpreting our little electron as a wave, then what are we supposed to do with two electrons After all, a wave plus a wave is still just a wave. As near as I can tell, quantum mechanics still has a way to go before it replaces the old fashioned pictures of helium, lithium and other, more complex, atoms. And any physicist can tell you that molecules, stripped of their pretty spherical symmetry, are trouble indeed. 

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 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. 

By populating the orbitals from the wave mechanical model (the aufbau principle), the form of the periodic table can be explained... 

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. 

We have shown that there are two possible cases for the wave function of a system of identical particles, the symmetric and the antisymmetric cases. Experimental evidence (such as the periodic table of the elements to be discussed later) shows that for electrons only the antisymmetric case occurs. Thus we have an additional postulate of quantum mechanics, which states that the wave function of a system of electrons must be antisymmetric with respect to interchange of any two electrons. Was important postulate is called the Pauli principle, after the physicist Wolfgang Pauli. 

Transition metals owe their location in the periodic table to the filling of the d subshells, as you Saw in Figure 6.31. Many of the chemical and physical properties of transition metals result from the unique characteristics of the d orbitals. For a given transition-metal atom, the valence (n — l)d orbitals are smaller than the corresponding valence ns and np orbitals. In quantum mechanical terms, the (n — l)d orbital wave functions drop off more rapidly as we move away from the nucleus than do the ns and np orbital wave functions. This characteristic feature of the d orbitals limits their interaction with orbitals on neighboring atoms, but not so much that they are insensitive to... 

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