Bohr model, physical chemistry

An overview of a scientific subject must include at least two parts retrospect (history) and the present status. The present status (in a condensed form) is presented in Chapters 2 to 21. In this section of the overview we outline (sketch) from our subjective point of view the history of electrochemical deposition science. In Section 1.2 we show the relationship of electrochemical deposition to other sciences. In this section we show how the development of electrodeposition science was dependent on the development of physical sciences, especially physics and chemistry in general. It is interesting to note that the electron was discovered in 1897 by J. J. Thomson, and the Rutherford-Bohr model of the atom was formulated in 1911. 

The quantum-mechanical model of the atom replaced the Bohr model in the early twentieth century. In the quantum-mechanical model Bohr orbits are replaced with quantum-mechanical orbitals. Orbitals are different from orbits in that they represent, not specific paths that electrons follow, but probability maps that show a statistical distribution of where the electron is likely to be found. The idea of an orbital is not easy to visualize. Quantum mechanics revolutionized physics and chemistry because in the quantums-mechanical model, electrons do not behave like particles flying through space. We cannot, in general, describe their exact paths. An orbital is a probability map that shows where the electron is likely to be found when the atom is probed it does not represent the exact path that an electron takes as it travels through space. 

To describe the three-dimensional nature of the electron s wavelike properties, we now liberate the electron from a circular orbit and allow it to have density anywhere along a circular path, out of the plane of that circle, and even at different distances from the nucleus — all while it s in a single quantum state. Let the circular orbit in the Bohr model correspond to motion along an angle (f>, measured from the x axis in the xy plane. Now we need to introduce two new coordinates to accommodate the new motions permitted to the electron. We will call the new coordinates 0 (the angle measured in any direction from the z axis) and r (the distance from the center of mass, which is roughly at the nucleus). Fig. 3.1 provides definitions for these spherical coordinates. (These are the conventional definitions for 0 and (f> in physics and chemistry, but unfortunately they are the reverse of the definitions often used in mathematics courses.)... 

In this chapter, we will attempt to provide an overview of several forms of spectroscopy to set the scene for more detailed descriptions in Chapter 10. Thus, we will have to compress the historical development to focus on the important case of the hydrogen spectrum and the Bohr model of the quantized levels within the H atom. We will revisit the details of the early twentieth century discoveries in chemistry and physics in Chapter 10. Since this may be the end of a one-semester course, we will stretch the Bohr model to treat x-rays but then show the need for more modern methods. We do this to introduce several spectroscopic techniques within a simple mathematical model and to create interest for a second semester of physical chemistry with the question If energy is quantized, what does this mean ... 

But Bom did not doubt the power of the physicist to explain the facts and laws of the chemist. In the lectures published as The Constitution of Matter, Bom developed a model of the distribution of valence electrons about a nucleus in the manner of Bohr (1913) and of Sommerfeld s protege, Kossel (1916). Born wrote, "When we contemplate the path by which we have come we realize that we have not penetrated far into the vast territory of chemistry yet we have travelled far enough to see before us in the distance the passes which must be traversed before physics can impose her laws upon her sister science."5... 

Bohr s atomic model was accepted in physics, with some reservation and received even less enthusiastically in chemistry, as there was no visible prospect of extending the treatment to other atoms, more complex than hydrogen. Chemical models of the era were all conditioned by the need to account for chemical interactions that bind atoms together into molecules. One of the more successful, due to Lewis, Langmuir and others, proposed a static... 

The models of Bohr, Sommerfeld and de Broglie provide a firm basis for the further development of a quantum theory of chemistry by re-assessment of the more advanced theories of quantum physics. However, there is little support for such a pursuit, not if we find statements like the following [14], put out by one of the world s leading publishers of academic science ... 

The Lewis model has become so famous and has for years been used so mechanically that some of the considerations underlying it are here presented. They demonstrate how deeply Lewis was concerned with the underlying physical cause of valence rather than with a simple rule of thumb. He further points up an operational difficulty in Bohr s atomic model if it gives no information as to the electron s movement within an orbit, we have no business postulating its movement. Furthermore, electrons orbiting around a nucleus could not possibly explain directed valences. Lewis, therefore, proposed a static model, confident that theoretical chemistry would somehow, some day, confirm it ... 

Bohr realised that, by purely theoretical considerations and the construction of models, the desired object of explaining the regularities in the structures of atoms (periodic system of the elements) would be very difficult to attain he therefore adopted a procedure by means of which, half theoretically and half empirically, making use of all the evidence provided by physics and chemistry, and, especially, by a thorough application of the data derived from the series spectra, there was evolved a picture of the building up of atoms. 

If Noddack s physics was avant garde, her chemistry was sound. By 1938 her article was gathering dust on back shelves, but Bohr had promulgated the liquid-drop model of the nucleus and the confused chemistry of uranium increasingly preoccupied Lise Meitner and Otto Hahn. 

Believing that a scientist well informed in physics and chemistry had a crucial role to play in the study of molecular structure, Lewis s study of Bohr s atomic model assured him that "while the orbit of one electron may as a whole affect the orbit of another electron, we should look for no effects which depend upon the momentary position of any electron in its orbit" (Lewis 1966/1923, 31-32). In that case, it was possible to translate the positions of the electrons in the static model into the average positions of more or less mobile electrons in the atomic model of the old quantum theory, and this equivalence would be fundamental in bringing together the chemical and physical evidence into a unified theory of atomic structure. 

Schrodinger s equation launched an entirely new field, called quantum mechanics (or wave mechanics), and began a new era in physics and chemistry. We now refer to the developments in quantum theory from 1913— when Bohr presented his model of the hydrogen atom—to 1926 as old quantum theory. ... 

In fact one can go even further back historically to examine whether, or the extent to which, the notion of electronic configurations originated with quantum theory. As the popular account has it, electronic configurations entered physics and chemistry when Bohr first introduced quantum theory into the study of atomic physics. This is perhaps a natural assumption given that there is a sense in which quantization of electron energy is synonymous with the notion of electrons in energy levels or shells. But, surprisingly perhaps, the idea of electrons in shells pre-dates Bohr s model of the atom and has no connection with quantum ideas of any form whatsoever. 

In fact the concept of electronic configuration as a causally explanatory feature has become very much the domain of chemistry or to be more precise it is the dominant paradigm in modem chemistry. Conversely, physicists are only too aware of the limitations of the electronic configuration model and they only draw upon it as a zero order approximation. Hettema and Kuipers further state that Bohr s theory of the atom, despite its level of approximation, is to be regarded as a physical theory because the explanation of the periodic table was only a spin-off from its development. But given Heilbron and Kuhn s detailed version of the historical development, it was precisely the explanation of the periodic table which provided the initial impetus for Bohr s famous theory of the atom, whereas the explanation of the hydrogen spectmm only arose later. (Heilbron and Kuhn, 1969). 

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