Bohr hydrogen atom

An atomic unit of length used in quantum mechanical calculations of electronic wavefunctions. It is symbolized by o and is equivalent to the Bohr radius, the radius of the smallest orbit of the least energetic electron in a Bohr hydrogen atom. The bohr is equal to where a is the fine-structure constant, n is the ratio of the circumference of a circle to its diameter, and is the Rydberg constant. The parameter a includes h, as well as the electron s rest mass and elementary charge, and the permittivity of a vacuum. One bohr equals 5.29177249 x 10 meter (or, about 0.529 angstroms). 

Figure 3.2 A diagram of the Bohr hydrogen atom (not drawn to scale the orbits are actually much larger than the nucleus). The electron is elevated to a higher-energy orbit when energy is absorbed.

The following is an energy-level diagram for electronic transitions in the Bohr hydrogen atom. 

The center of mass of the Bohr hydrogen atom lies between the nucleus and the electron, a distance... 

Use equation 9.34 to determine the radii, in meters and angstroms, of the fourth, fifth, and sixth energy levels of the Bohr hydrogen atom. 

Assume that the motion of the earth around the sun is described by the Bohr hydrogen atom theory. The electrostatic attraction is replaced by the gravitational attraction, given by the formula... 

Rgure 2.2 (a) The first three electron energy states for the Bohr hydrogen atom. 

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. 

To make an informed guess for your first value of ot, you may wish to reread the section on the Bohr theory of the hydrogen atom and the Schroedinger wave functions for the hydrogen atom in a good physical or general chemistry book (see Bibliography). 

Zg is the effective charge number in the interaction of two unlike atoms, and is the Bohr radius for the hydrogen atom, 0.5292 x 10 cm. There exist a number of approximations for Z but a simple description based on a mean value is as follows. 

The concept of chemical periodicity is central to the study of inorganic chemistry. No other generalization rivals the periodic table of the elements in its ability to systematize and rationalize known chemical facts or to predict new ones and suggest fruitful areas for further study. Chemical periodicity and the periodic table now find their natural interpretation in the detailed electronic structure of the atom indeed, they played a major role at the turn of the century in elucidating the mysterious phenomena of radioactivity and the quantum effects which led ultimately to Bohr s theory of the hydrogen atom. Because of this central position it is perhaps not surprising that innumerable articles and books have been written on the subject since the seminal papers by Mendeleev in 1869, and some 700 forms of the periodic table (classified into 146 different types or subtypes) have been proposed. A brief historical survey of these developments is summarized in the Panel opposite. 

Figure Al.l Radial functions for a hydrogen atom. (Note that the horizontal scale is the same in each graph but the vertical scale varies by as much as a factor of 100. The Bohr radius Oq = 52.9 pm.)...

Bohr s treatment gave spectacularly good agreement with the observed fact that a hydrogen atom is stable, and also with the values of the spectral lines. This theory gave a single quantum number, n. Bohr s treatment failed miserably when it came to predictions of the intensities of the observed spectral lines, and more to the point, the stability (or otherwise) of a many-electron system such as He. 

The hydrogen atom, containing a single electron, has played a major role in the development of models of electronic structure. In 1913 Niels Bohr (1885-1962), a Danish physicist, offered a theoretical explanation of the atomic spectrum of hydrogen. His model was based largely on classical mechanics. In 1922 this model earned him the Nobel Prize in physics. By that time, Bohr had become director of the Institute of Theoretical Physics at Copenhagen. There he helped develop the new discipline of quantum mechanics, used by other scientists to construct a more sophisticated model for the hydrogen atom. 

The last equation written is the one Bohr derived in applying his model to the hydrogen atom. Given... 

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-... 

These ideas were so revolutionary that they would not have been accepted except for the fact that Bohr was able to propose a way to calculate exactly the energy levels for the hydrogen atom. Within ten years Bohr s calculational methods were completely replaced by better techniques, but his postulate that only certain atomic energy states are possible has been repeatedly shown to be correct. 

Soon after Bohr developed his initial configuration Arnold Sommerfeld in Munich realized the need to characterize the stationary states of the electron in the hydrogen atom by. means of a second quantum number—the so-called angular-momentum quantum number, Bohr immediately applied this discovery to many-electron atoms and in 1922 produced a set of more detailed electronic configurations. In turn, Sommerfeld went on to discover the third or inner, quantum number, thus enabling the British physicist Edmund Stoner to come up with an even more refined set of electronic configurations in 1924. 

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 energy rule for the neutral atoms was obviously in contradiction to Bohr s calculation on the hydrogen atom, which indicated that the energies should be increasing with increasing n. It is typical of the nature of "frontier-research" that Bohr abandoned this rule for the higher atoms, since it led to the wrong... 

In an early model of the hydrogen atom proposed by Niels Bohr, the electron traveled in a circular orbit of radius uncertainty principle rules out this model. 

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