Atom, Bohr theory

The classical description of the atom (Bohr theory) assumed that electrons move on trajectories around the nucleus. The energy of each electron was thought to relate to the electron s distance from the nucleus. This view is intuitively appealing because it coincides with our physical understanding of classical mechanics. Yet it is incorrect for several reasons. 

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). 

Moseley photographed characteristic spectra for some 38 elements that could serve as x-ray tube targets. In two papers,37 he not only uncovered structure in the K and L spectra—he alscr established the atomic number as more fundamental than the atomic weight, and he provided brilliant support for- the Bohr theory of atomic structure. 

Bohr theory, the radius of the circular orbit of the electron in the ground state of the hydrogen atom (Z = 1) with a stationary nucleus. Except in Section 6.5, where this substitution is not appropriate, we replace fx by and by ao in the remainder of this book. 

Bohr theory the first theory of atomic structure which involved definite internal energy levels for electrons. 

The carbon atom has, outside its nucleus, six electrons which, on the Bohr theory of atomic structure, were believed to be arranged in orbits at increasing distance from the nucleus. These orbits corres-... 

The Bohr theory also permits a calculation of the total energy, E, of the atom from Hamilton s equation ... 

This section started with the discovery of Soddy and Fajans on radioactive decay around 1910 and the relationship of radioactive decay to the periodic table. At this point in the history, we understand the periodic table and we understand the role of isotopes in the periodic table. We have not yet understood the structure of the modern Table, i.e. first row two elements, second row eight elements, etc. That understanding can be based on Bohr theory of the hydrogen atom originally developed in 1911 and is summarized in Bohr s famous article in Zeitschrift fur Physik (Bohr 1922). 

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. 

The Bohr theory of atomic structure allotted to each extra-nuclear electron within the atom a definite geometrical orbit and, more important, associated with each orbit a fixed total energy value. 

Figure 8. A Bohr-Sommerfeld model of the xenon atom. (From H. A. Kramers and H. Horst, The Atom and the Bohr Theory of its Structure, 1924).

It was the apparent violation of this requirement that led to the postulate of quantization in the Bohr theory of the hydrogen atom. However, we are concerned here with the classical result in which the charge does radiate. Our objective is to describe the emitted radiation some distance r from the emitter. 

A more detailed account of the Bohr theory of the hydrogen atom is given in Chap. 2 and Apps. II and III. 

The quantity a0 is interpreted in the Bohr theory as the radius of the smallest orbit in the hydrogen atom its value is 0.530 A. 

The hydrogen-atom solutions are called atomic orbitals, by analogy with the orbits of the Bohr theory. Orbitals with / = 1 are called s orbitals, and those with l = 2, 3, and 4, arc called p, d, and / orbitals, respectively. (This notation comes from the names used to describe different series of spectroscopic lines.) The value of n is also specified, so that, for example, 2p is used to denote orbitals with n = 2 and l = 1 in this case, there are three possible m values, and 2p refers to the whole set of these. Table 4.1 lists the orbitals with n up to three, showing their names and the number of possible m values in each case. 

The sizes of atomic orbitals also increase with the energy indeed as in the Bohr theory (see eqn 4.13), the average radius of an orbital is given approximately by... 

A note of caution The Bohr theory, even when improved and amplified, applies only to hydrogen and hydrogen-like species, such as He+ and Li+. The theory explains neither the spectra of atoms containing even as few as two electrons, nor the existence and stability of chemical compounds. The next advance in the understanding of atoms requires an understanding of the wave nature of matter. 

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