Atomic structure quantum model

Temperature units/conversions Periodic table Basic atomic structure Quantum mechanical model Atomic number and isotopes Atoms, molecules, and moles Unit conversions Chemical equations Stoichiometric calculations Week 3 Atmospheric chemistry... 

This chapter builds an understanding of atomic structure in four steps. First, we review the experiments that led to our current nuclear model of the atom and see how spectroscopy reveals information about the arrangement of electrons around the nucleus. Then we describe the experiments that led to the replacement of classical mechanics by quantum mechanics, introduce some of its central features, and illustrate them by considering a very simple system. Next, we apply those ideas to the simplest atom of all, the hydrogen atom. Finally, we extend these concepts to the atoms of all the elements of the periodic table and see the origin of the periodicity of the elements. 

In recent years the old quantum theory, associated principally with the names of Bohr and Sommerfeld, encountered a large number of difficulties, all of which vanished before the new quantum mechanics of Heisenberg. Because of its abstruse and difficultly interpretable mathematical foundation, Heisenberg s quantum mechanics cannot be easily applied to the relatively complicated problems of the structures and properties of many-electron atoms and of molecules in particular is this true for chemical problems, which usually do not permit simple dynamical formulation in terms of nuclei and electrons, but instead require to be treated with the aid of atomic and molecular models. Accordingly, it is especially gratifying that Schrodinger s interpretation of his wave mechanics3 provides a simple and satisfactory atomic model, more closely related to the chemist s atom than to that of the old quantum theory. 

Figure 3.3 (a) The potential energy function assumed in the particle-in-a-one-dimensional-box model, (b) A wave function satisfying the boundary conditions, (c) An unacceptable wave function. (Reproduced with permission from P. A. Cox, Introduction to Quantum Theory and Atomic Structure, 1996, Oxford University Press, Oxford, Figure 2.6.)... 

The initial purpose of pioneer quantum mechanics was to provide the theoretical framework to account for the structure of hydrogen and the nuclear model of atoms in general. The final result, a quantum theory of atomic structure can be discussed in terms of the time-independent Schrodinger equation, in its most general form... 

Quotation from Sommerfeld, Atomic Structures, 79. On p. vi, Sommerfeld notes that in the chapter on the natural system of the elements, "the former discussions of molecular models and atomic volumes have been thoroughly pared down." At Harvard in 1925, Edwin Kemble s course in quantum mechanics included the second edition of Sommerfeld s Aufbau, according to Schweber (1990 348). Similarly, Joseph Hirschfelder was reading it as an undergraduate at Yale according to Hirschfelder, "My Adventures in Theoretical Chemistry," Ann.Rev.P.Chem. 33 (1983) 129, on 4. 

What is the quantum mechanical model of the atom, and how does a understanding of atomic structure enable chemists to explain the properties of substances and their chemical bonding ... 

The first sections of this reference book set the stage for the presentation of the elements. First is the section How to Use This Book followed by a short introduction. Next is A Short History of Chemistry, the narrative of which progresses from prehistoric times to the Age of Alchemy and then to the Age of Modern Chemistry. Next is the section titled Atomic Structure, which traces the history of our knowledge of the structure of the atom some theoretical models, including quantum mechanics the discovery of subatomic (nuclear) particles... 

During this period, accurate solutions for the electronic structure of helium (1) and the hydrogen molecule (2) were obtained in order to verify that the Schrodinger equation was useful. Most of the effort, however, was devoted to developing a simple quantum model of electronic structure. Hartree (3) and others developed the self-consistent-field model for the structure of light atoms. For heavier atoms, the Thomas-Fermi model (4) based on total charge density rather than individual orbitals was used. 

The breakthrough in understanding atomic structure came in 1926, when the Austrian physicist Erwin Schrodinger (1887-1961) proposed what has come to be called the quantum mechanical model of the atom. The fundamental idea behind the model is that it s best to abandon the notion of an electron as a small particle moving around the nucleus in a defined path and to concentrate instead on the electron s wavelike properties. In fact, it was shown in 1927 by Werner Heisenberg (1901-1976) that it is impossible to know precisely where an electron is and what path it follows—a statement called the Heisenberg uncertainty principle. 

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... 

Now that we ve seen how atomic structure is described according to the quantum mechanical model, let s return briefly to the subject of atomic line spectra first mentioned in Section 5.3. How does the quantum mechanical model account for the discrete wavelengths of light found in a line spectrum ... 

Problems involving rotation occur frequently in the quantum theory. This section discusses two models which look rather artificial, but which serve to introduce some important ideas. They have a direct application to the rotations of molecules, but are especially useful in the context of atomic structure, discussed in Chapters 4 and 5. 

The quantum mechanical model of atomic structure is far too difficult to be explained in detail in an AP Chemistry course. However, some aspects of the theory are appropriate, and you should know them. These include the predicted number and shapes of orbitals in each energy level the number of electrons found in each orbital, sublevel, and energy level and the meaning of the four quantum numbers. 

Bohr s importance can be attributed first and foremost to his model of the hydrogen atom. In a series of three papers, now called the Trilogy, Bohr laid the foundation for a quantum theory of atomic structure. The Trilogy was published in Phiksophical Magazine in 1913 and these three papers established Bohr s reputation. ... 

There arc fundamental dil fcrcnees between the quantum and molecular mechanics approaches. They illustrate the dilemma that cun confront the medicinal chemist. Quantum mechanics is derived from basic theoretical principles at the atomic level. The model itself is exact, but the equations used in the technique are only approximate. The molecular properties are derived from the electronic structure of the molecule. The assumption is made that the distribution of electrons within a molecule can be described by a linear. sum of functions that represent an atomic orbital. (For carbon, this would be s./>,./>,. etc.) Quantum mechanics i.s computation intensive, with the calculation time for obtaining an approximate solution increasing by approximately N time.s. where N i.s the number of such functions. Until the advent of the high-.speed supercomputers, quantum mechanics in its pure form was re.stricted to small molecules. In other words, it was not practical to conduct a quantum mechanical analysis of a drug molecule. 

The Hartree orbitals are the foundation of the quantum explanation of atomic structure. They justify the shell model of the atom, they explain the structure of the periodic table, and they provide the starting point for the quantum explanation of chemical bond formation in the following chapter. 

The traditional model of atomic structure has been the quantum-mechanical analogue of a solar system, with electrons perturbing each other only a little from their individual states of definite energy and angular momentum. On the other hand, the traditional model for molecular structure has been the quantum-mechanical counterpart of balls held together by springs in a fairly rigid, well-defined structure. These two pictures are so different and lend themselves to such different computational methods that they have remained as separated, almost unrelated fields within chemical physics. 

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