Quantum theory Bohr atom

On the basis of his quantum theory of atomic structure, Niels Bohr believed that, since Urbain s celtium had been obtained from the rare earths, it could not be element 72, for the latter must be quadrivalent rather than trivalent and must belong to the zirconium family. He showed that the chemical properties of an atom are determined by the number and arrangement of the electrons within it and especially by the number... 

A rational deduction of elemental abundance from solar and stellar spectra had to be based on quantum theory, and the necessary foundation was laid with the Indian physicist Meghnad Saha s theory of 1920. Saha, who as part of his postdoctoral work had stayed with Nernst in Berlin, combined Bohr s quantum theory of atoms with statistical thermodynamics and chemical equilibrium theory. Making an analogy between the thermal dissociation of molecules and the ionization of atoms, he carried the van t Hoff-Nernst theory of reaction-isochores over from the laboratory to the stars. Although his work clearly belonged to astrophysics, and not chemistry, it relied heavily on theoretical methods introduced by and associated with physical chemistry. This influence from physical chemistry, and probably from his stay with Nernst, is clear from his 1920 paper where he described ionization as a sort of chemical reaction, in which we have to substitute ionization for chemical decomposition. [81] The influence was even more evident in a second paper of 1922 where he extended his analysis. [82]... 

However, the electrostatic attraction between two charged particles is many trillions of times stronger than the gravitational force. Recall that it was the strong electrostatic attraction between a proton and an electron in the hydrogen atom that made Bohr s original picture of the atom impossible and led to the quantum theory of atoms. 

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. ... 

The experimental foundation of the quantum theory of atomic structure as put forward by Bohr, lies in the stability of the atom and in the existence of discrete energy levels and the ability of the atom to absorb and emit energy only in quanta, as demonstrated by the discontinuous nature of atomic spectra and by the critical potential measurements of Franck and Hertz. Bohr postulated that the atom could only exist in a limited number of orbits or stationary states, which were defined by the quantum condition that the angular momentum can assume only certain limited values which are given by the expressioiT ... 

In 1913 Bohr (while still in England) published three papers on the quantum theory of atoms. He explained that atoms exist in stationary states, and that when an atom changes from one state to another, there has... 

In 1913, Neils Bohr applied quantum theory to atomic structure, using his analysis of the spectral lines in the light emitted hy hydrogen atoms. Bohr explained the frequencies of these spectral lines hy expressing them in terms of the charge and mass of the electron and Planck s constant He postulated that an atom would not emit radiation while in one of its stable states, hut would do so when it made a transition between states. The frequency of the emitted radiation would be equal to the difference in energy between states divided by Planck s constant An atom could not absorb nor emit radiation continuously but could do so only in finite steps called quantum jumps. 

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. 

The purpose of this first computer laboratory is to review some of the fundamental concepts from classical physics, to understand what constitutes a solution to a problem in classical physics, and to introduce students to numerical solutions for the Newtonian equations of motion. QuickBASIC programs have been written which use PC graphics to display the trajeaory of an electron in the Thomson plum pudding model of the atom, the Bohr atom, and a classical model for the hydrogen-molecule ion. This early review of classical physics helps students appreciate more fully how fundamentally different quantum theory is. The material in this exercise is frequently used as a leaure demonstration to support a classroom lecture on the precursors to the quantum theory of atomic and molecular structure. 

Some important successes of classical quantum theory Bohr s theory of the atomic spectrum of hydrogen... 

Hund s interest shifted to spectroscopy in the aftermath of Bohr s visit to Born s institute in June 1922 for "Bohr s festival," during which Bohr delivered a major series of lectures on quantum theory and atomic physics that were said to have "revolutionized" physics at Gottingen. He avidly discussed spectroscopy with James Franck, Hertha Sponer, Jordan, and Heisenberg (figure 1.2) and started to work on the interpretation of complex atomic spectra in terms of the Russell-Saunders vector model. The first to show how the notion of spin and the Pauli exclusion principle could be used to explain the periodic system of the elements, Hund s book Linienspektren und Periodisches System der Elemente contributed greatly to familiarize scientists with these two rules (Hund 1927). 

The miderstanding of the quantum mechanics of atoms was pioneered by Bohr, in his theory of the hydrogen atom. This combined the classical ideas on planetary motion—applicable to the atom because of the fomial similarity of tlie gravitational potential to tlie Coulomb potential between an electron and nucleus—with the quantum ideas that had recently been introduced by Planck and Einstein. This led eventually to the fomial theory of quaiitum mechanics, first discovered by Heisenberg, and most conveniently expressed by Schrodinger in the wave equation that bears his name. 

Classical and Quantum Mechanics. At the beginning of the twentieth century, a revolution was brewing in the world of physics. For hundreds of years, the Newtonian laws of mechanics had satisfactorily provided explanations and supported experimental observations in the physical sciences. However, the experimentaUsts of the nineteenth century had begun delving into the world of matter at an atomic level. This led to unsatisfactory explanations of the observed patterns of behavior of electricity, light, and matter, and it was these inconsistencies which led Bohr, Compton, deBroghe, Einstein, Planck, and Schrn dinger to seek a new order, another level of theory, ie, quantum theory. 

Figure 5. Niels Bohr came up with the idea that the energy of orbiting electrons would be in discrete amounts, or quanta. This enabled him to successfully describe the hydrogen atom, with its single electron, In developing the remainder of his first table of electron configurations, however, Bohr clearly relied on chemical properties, rather than quantum theory, to assign electrons to shells. In this segment of his configuration table, one can see that Bohr adjusted the number of electrons in nitrogen s inner shell in order to make the outer shell, or the reactive shell, reflect the element s known trivalency.

The origin of electronic configuration Is frequently and inaccurately attributed to Niels Bohr, who introduced quantum theory to tire study of the atom. But Bohr essentially tidied up Thomson s pre-quantum configurations and took advantage of a more accurate knowledge erf the number of electrons each of the elements actually possessed. Furtlrer developments in quantum theory, including Pauli s occlusion principle and Schrodjtiger s equation. 

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. 

Particularly spectra and quantum theory seemed to indicate an order. A planetary model almost suggested itself, but according to classical physics, the moving electrons should emit energy and consequently collapse into the nucleus. The 28-year-old Niels Bohr ignored this principle and postulated that the electrons in these orbits were "out of law". This clearly meant that classical physics could not describe or explain the properties of the atoms. The framework of physical theory came crashing down. Fundamentally new models had to be developed.1... 

The first application of quantum theory to a problem in chemistry was to account for the emission spectrum of hydrogen and at the same time explain the stability of the nuclear atom, which seemed to require accelerated electrons in orbital motion. This planetary model is rendered unstable by continuous radiation of energy. The Bohr postulate that electronic angular momentum should be quantized in order to stabilize unique orbits solved both problems in principle. The Bohr condition requires that... 

Born s essays making up The Constitution of Matter were intended to be an aid to those who did not have "time to study the larger work of Sommerfeld," namely, Atomic Structure and Spectral Lines (1915), which laid out Bohr s first quantum theory and Sommerfeld s emendations.6 Bom and Sommerfeld were to have enormous influence on the development of quantum mechanics and its application to atoms and molecules. Not only did many European, British, and American scientists come to study at their physics institutes but they each gave influential series of lectures at foreign institutions, nowhere with more influence than in the United States. 

It has already been noted that the new quantum theory and the Schrodinger equation were introduced in 1926. This theory led to a solution for the hydrogen atom energy levels which agrees with Bohr theory. It also led to harmonic oscillator energy levels which differ from those of the older quantum mechanics by including a zero-point energy term. The developments of M. Born and J. R. Oppenheimer followed soon thereafter referred to as the Born-Oppenheimer approximation, these developments are the cornerstone of most modern considerations of isotope effects. 

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