Bohr’s planetary model

Bohr s planetary model of the atom, in which electrons orbit the nucleus much like planets orbit the sun, is a graphical representation that helps us understand how electrons can possess only certain quantities of energy. 

Was this youT answeT An orbit is a distinct path followed by an object in its revolution around another object. In Bohr s planetary model of the atom, he proposed an analogy between electrons orbiting the atomic nucleus and planets orbiting the sun. 

The angular momentum or an electron moving in an orbit of the type described by Bohr is ail axial vector L = r x p, formed from the radial distance r between electron and nucleus and the linear momentum p of the electron relative lo a fixed nucleus. Figure 2 shows the customary method used to illustrate the axial vector L in terms of the orbital morion of any object, of which the electron of the Bohr atom is only one example. Although Bohr s planetary model needed only circular orbits lo explain the spectral lines observed in the spectrum of a hydrogen atom, subsequent... 

The nuclear concentration of mass anticipated Rutherford s model of the atom, and Bohr s planetary model by a decade. The spectral integers, linked to a standing-wave pattern, predates de Broglie s proposal by two decades. 

Niels Bohr s planetary model of the hydrogen atom—in which a nucleus is surrounded by orbits of electrons—resembles the solar system. Electrons could be excited by quanta of energy and move to an outer orbit (excited level). They could also emit radiation when falling to their original orbit (ground state). Basic components of the Bohr model include the following ... 

The emerging picture is one in which the quantum-mechanical equivalents of the constants of motion for the two valence electrons in these atoms are like those associated with the near-rigid rotations, bending vibrations, and stretching vibrations we normally associate with linear triatomic molecules. These new results bring into question the range of validity of the nearly-independent-particle model, the quantum-mechanical counterpart of Bohr s planetary model, for atoms with more than one valence electron. 

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... 

Besides the huge difference in size between the solar system and an atom, there was another crucial difference between Bohr s planetary model of an atom and the planetary model of the solar system. 

Bohr s planetary model of the atom states that electrons in a hydrogen atom move in a circular orbit of radius r around a proton. The proton is so heavy in comparison with the electron that the center of mass of this system coincides with the position of the nucleus. Following Bohr, calculate the total electron energy. 

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. 

Bohr s planetary atomic model proved to be a tremendous success. By utilizing Planck s quantum hypothesis, Bohr s model solved the mystery of atomic spectra. Despite its successes, though, Bohr s model was limited because it did not explain why energy levels in an atom are quantized. Bohr himself was quick to point out that his model was to be interpreted only as a crude beginning, and the picture of electrons whirling about the nucleus like planets about the sun was not to be taken literally (a warning to which popularizers of science paid no heed). 

Bohr supplemented Rutherford s planetary model of the atom with the assumption that an electron of mass moves in a circular orbit of radius r about a... 

The incompatibility of Rutherford s planetary model, based soundly on experimental data, with the principles of classical physics was the most fundamental of the conceptual challenges facing physicists in the early 1900s. The Bohr model was a temporary fix, sufficient for the interpretation of hydrogen (H) atomic spectra as arising from transitions between stationary states of the atom. The stability of atoms and molecules finally could be explained only after quantum mechanics had been developed. 

Realizing that Rutherford s planetary model of the atom is incompatible with the classical Maxwell theory of radiation—which stipulates that a charged electron in circular motion will continually emit radiation and thereby lose energy, its orbit will shrink, and it will quickly spiral into the nucleus—Niels Bohr in 1913 (see Fig. 3.25) asserted that an electron in an atomic orbit simply does not radiate in other words Maxwell s theory does not apply at this level. Bohr s main contribution was to make two nonclassical assumptions. ... 

What Bohr understood about the nucleus he embodied in a landmark lecture to the Danish Academy on January 27, 1936, subsequently published in Nature, Neutron capture and nuclear constitution exploited the phenomenon of neutron capture to propose a new model of the nucleus once again, as he had with Rutherford s planetary model of the atom, Bohr stood on the solid ground of experiment to argue for radical theoretical change. 

How does the modern electron cloud model of the atom differ from Bohr s original planetary model of the atom ... 

Part (b) is correct in the view of contemporary quantum theory. Bohr s explanation of emission and absorption hne spectra appears to have universal validity. Parts (a) and (c) are artifacts of Bohr s early planetary model of the hydrogen atom and are not considered to be valid today. 

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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