Hydrogen-like atom Bohr model

This assumption is the basis of the Bohr model for the hydrogen-like atom. When solved for m, this balancing equation is... 

The simple Bohr model of the hydrogen-like atom (one electron only) predicts that the X-ray energy or the transition energy, AE, is given as... 

Orbital hybridization, like the Bohr model of the hydrogen atom in its ground state, is an effort to dress up a defective classical model by the assumption ad hoc of quantum features. The effort fails in both cases because the quantum-mechanics of angular momentum is applied incorrectly. The Bohr model assumes a unit of quantized angular momentum for the electron which is presumed to orbit the nucleus in a classical sense. Quantum-mechanically however, it has no orbital angular momentum. The hybridization model, in turn, spurns the commutation rules of quantized... 

At first Bohr s model appeared very promising. It fit the hydrogen atom very well. However, when this model was applied to atoms other than hydrogen, it did not work. In fact, further experiments showed that the Bohr model is fundamentally incorrect. Although the Bohr model paved the way for later theories, it is important to realize that the current theory of atomic structure is not the same as the Bohr model. Electrons do not move around the nucleus in circular orbits like planets orbiting the sun. Surprisingly, as we shall see later in this chapter, we do not know exactly how the electrons move in an atom. 

Bohr s model can be used for hydrogen-like ions—ions that have only one electron, such as He and Li. (a) Why is the Bohr model applicable to He ions but not to neutral He atoms (b) The ground-state energies of H, He, and Li are tabulated as follows ... 

At this point a Danish physicist, Niels Bohr, decided to take a fresh start. In effect, he faced the fact that an explanation is a search for likenesses between a system under study and a well-understood model system. An explanation is not good unless the likenesses are strong. Niels Bohr suggested that the mechanical and electrical behavior of macroscopic bodies is not a completely suitable model for the hydrogen atom. He pro-... 

Bohr s hydrogen atom model of 1913 had provided inspiration to a few physicists, like Kossel, who were interested in chemical problems but to very few chemists concerned with the explanation of valence. First of all, the Bohr atom had a dynamic character that was not consistent with the static and stable characteristics of ordinary molecules. Second, Bohr s approach, as amended by Kossel, could not even account for the fundamental tetrahedral structure of organic molecules because it was based on a planar atomic model. Nor could it account for "homopolar" or covalent bonds, because the radii of the Bohr orbits were calculated on the basis of a Coulombic force model. Although Bohr discussed H2, HC1, H20, and CH4, physicists and physical chemists mainly took up the problem of H2, which seemed most amenable to further treatment. 11... 

Like Bohr s model of the hydrogen atom, Sommerfeld s theory flowered only briefly. The creation of quantum mechanics and the discovery of electron spin, both in 1925, followed by Paul Dirac s theory in 1928, provided a solid theory-based underpinning for... 

The Schrodinger wave equation In 1926, Austrian physicist Erwin Schrbdinger (1887-1961) furthered the wave-particle theory proposed by de Broglie. Schrbdinger derived an equation that treated the hydrogen atom s electron as a wave. Remarkably, Schrbdinger s new model for the hydrogen atom seemed to apply equally well to atoms of other elements—an area in which Bohr s model failed. The atomic model in which electrons are treated as waves is called the wave mechanical model of the atom or, more commonly, the quantum mechanical model of the atom. Like Bohr s model,... 

Planck s revolutionary idea about energy provided the basis for Einstein s explanation of the photoelectric effect in 1906 and for the Danish physicist Niels Bohr s atomic model of the hydrogen atom in 1913. Their success, in turn, lent support to Planck s theories, for which he received the Nobel Prize in physics in 1918. In the mid-1920s the combination of Planck s ideas about the particle-like nature of electromagnetic radiation and Erench physicist Louis de Broglie s hypothesis of the wavelike nature of electrons led to the formulation of quantum mechanics, which is still the accepted theory for the behavior of matter at atomic and subatomic levels. 

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