The Planetary Model

The other outstanding problem of classical physics was to understand the way in which atoms emit radiation only at discrete wavelengths, as formulated 

Between Rutherford and Bohr, Nagaoka s model was presented ten years later in the form of a miniature solar system, postulated to be stable when in a stationary state of mechanical and electrostatic equilibrium between electron and nucleus. This equilibrium is identihed by minimization of the total energy, 

The condition dEjdr = 0 identihes the stationary states with radii 

Allowed energies are obtained by substituting r back into (4.17)  

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Using these ideas, Bohr developed a conceptual model in which an electron moving around the nucleus is restricted to certain distances from the nucleus, with these distances determined by the amount of energy the electron has. Bohr saw this as similar to how the planets are held in orbit around the sun at given distances from the sun. The allowed energy levels for any atom, therefore, could be graphically represented as orbits around the nucleus, as shown in Figure 5.13. Bohr s quantized model of the atom thus became known as the planetary model. 

The planetary model of the atom was proposed by Rutherford in 1912 following the a particle scattering experiments of Geiger and Marsden, which showed most the mass of an atom to be concentrated in a tiny positive nucleus. The orbiting of light electrons resembles the problem of planetary motion first solved by Newton. 

For theoretical chemistry to succeed it must develop the power to elucidate the behaviour of chemical substances to the satisfaction of experimental chemists, known to operate at many different levels. Understanding is not promoted by the generation of numbers, however accurate or numerous, without a simple picture that tells the story. It is inevitable that the chain of reasoning must reduce the problem of understanding the behaviour of substances, to the understanding of molecules, atoms, electrons, and eventually the aether. Again, this ladder of understanding should not be obscured by complicated mathematical relationships that cannot be projected into a simple picture. Small wonder that the planetary model of the atom, inspired by Kepler, and discredited almost a hundred years ago, is still the preferred icon to represent nuclear installations and activity in the commercial world. Theoretical chemistry should also communicate with the predominantly nonscientist population of the world, but in order to tell a story it is first of all necessary to know the story. 

However, the planetary model which is also a densest packing model probably symbolizes Kepler s best attempt at attaining a unified... 

Quantum theory was developed primarily to find an explanation for the stability of atomic matter, specifically the planetary model of the hydrogen atom. In the Schrodinger formulation the correct equation was obtained by recognizing the wave-like properties of an electron. The first derivation by Schrodinger [30] was done by analogy with the relationship that was known to exist between wave optics and geometrical optics in the limit where the index of refraction, n does not change appreciably over distances of order A. This condition leads to the eikonal equation (T3.15)... 

Rutherford proposed a model of the atom in which the charge on the nucleus was +Ze, with Z electrons surrounding the nucleus out to a distance of about 10 ° m (0.1 nm). The Rutherford model for a gold atom has 79 electrons (each with a charge of —le) arranged about a nucleus of charge +79e. The electrons occupy nearly the entire volume of the atom, whereas nearly all its mass is concentrated in the nucleus this model is often called the planetary model. ... 

The physical structure of the atom, as determined by experiments, is summarized in the planetary model. In an atom with atomic number Z, there are Z electrons moving around a dense nucleus, which has positive charge +Ze. 

I he atom is the most fundamental concept in the science of chemistry. A chem- I ical reaction occurs by regrouping a set of atoms initially found in those molecules called reactants to form those molecules called products. Atoms are neither created nor destroyed in chemical reactions. Chemical bonds between atoms in the reactants are broken, and new bonds are formed between atoms in the products. We have traced the concept of the atom from the suppositions of the Greek philosophers to the physics experiments of Thomson and Rutherford and we have arrived at the planetary model of the atom. We have used the Coulomb force and potential energy laws describing the interactions among the nucleus and the electrons in the planetary atom to account for the gain and loss of electrons by atoms,... 

This all too human attempt by Mendeleev to cram the ether concept into his Periodic Table illustrates our very human limitations in trying to fit our own world views to facts. Figure 306 depicts mid-nineteenth-century illustrations of dinosaurs. The bones were crammed into the shapes of bear-like or ox-like creatures because these were the largest land carnivores and herbivores then known. Indeed, the planetary model of the atom, developed by Bohr in 1913 and later completely eclipsed, was probably based upon his desire for a unity in the universe and an analogy with the solar system. 

Arthur Koestler in The Sleepwalkers 2-62] called this planetary model "a false inspiration, a supreme hoax of the Socratic dairmm.. . However, the planetary model, which is also a densest packing model, probably represents Kepler s best attempt at attaining a uni fed view of his work both in astronomy and in what we call today crystallography. 

The development of quantum mechanics enabled chemists to describe electron energies and locations outside the nucleus more accurately than was possible with the planetary model for the atom. The meanings and implications of quantum numbers, photons, electromagnetic radiation, and radial probability distributions are central to describing the atom in terms of quantum mechanics. Other central ideas include the aufbau principle and the uncertainty principle. 

Danish physicist Niels Bohr postulated that the electron in hydrogen traveis around the nucleus in the manner in which a planet orbits the Sun. Hence his model was called the "planetary model."... 

Finally, an explanation was provided in 1913 by Niels Bohr (1885-1962), a Danish physicist who tackled the problem of trying to understand fundamental atomic structure. Bohr postulated that the electron in hydrogen travels around the nucleus in the manner in which a planet orbits the Sun. Hence his model was called the planetary model. The important distinction between the orbit of a planet around the Sun and the orbit of an electron around a nucleus is that the distance of a planet from the Sun is arbitrary, whereas in the Bohr model an electron cannot exist at just any distance from a nucleus. An electron can orbit the nucleus only at particular fixed, or discrete, distances from the nucleus. 

The planetary model of the hydrogen atom seemed at first to successfully explain the spectrum that is observed in the ultraviolet, visible, and infrared radiation regions. Qualitatively, Bohr s planetary model provides a reasonable explanation for the origin of spectral lines for all elements. Quantitatively, however, Bohr s model provides only approximate results for the hydrogen atom, but wildly incorrect results for all other atoms. These discrepancies were soon discovered. One, involving... 

Alpha particles bounced back, Rutherford reasoned, because the atom is not a pudding. The atom is mostly empty space with an incredibly small, incredibly dense, positively charged core. Rutherford proposed a new model—the planetary model—in which negatively charged electrons in huge orbits circled a tiny, dense, positively charged nucleus. 

Einstein was not the only one to find Planck s concept useful. In the laboratory of J. J. Thomson, Niels Bohr was in conflict with his mentor over the proper model for an atom. Thomson adhered to his plum pudding model, and Bohr preferred the planetary model of Rutherford. Finally Thomson suggested that Bohr work with Rutherford (who by this time had relocated in Manchester), and Bohr obliged. 

Bohr felt instinctively that Planck s quantized energies were related to the discrete lines of elemental spectra— and to the planetary model of the atom— but he could not find the connection. Thirty years earlier Johann Jakob Balmer, a teacher at a girls secondary school, part-time lecturer at the University of Basel (where, we may note, Paracelsus burned the works of Galen), and mathematics hobbyist had found a numerical relationship between frequencies of the lines in the hydrogen spectrum. The relationship was not obvious because it depended on the reciprocal squares of integers, and this was the very feature that caught Bohr s attention. He later said, As soon as I saw Balmer s formula, the whole thing was immediately clear to me. ... 

Lewis was unable to explain why two electrons favoured forming localised electron-pair bonds, although they would be expected to repel each other. Indeed to resolve this contradiction, he proposed (wrrMigly) that Coulomb s law may not be valid at the short interelectron distances found in bonds. He also recognised the disparity between his static view of the electrons in atoms and the planetary model which Bohr had developed in 1913. In 1923 Lewis proposed [2] that if the electron... 

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