Electron Bohr theory

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. 

Draw a picture of the electron jump corresponding to the first line in the visible emission spectrum of hydrogen according to the Bohr theory. 

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-... 

There is no question that, indirectly or directly, Kirrmann and Prevost were influenced by Lowry s theories for explanation of reaction mechanisms. Another important influence was Dupont, with whom they talked at length in the laboratory and who published a paper in 1927 in which he attempted to combine the electron octet theory of valence and Bohr s hydrogen electron model with classical concepts of stereochemistry. Dupont also adopted without reservation Lowry s application of ionic radicals in hydrocarbon chemistry. 66... 

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. 

The Bohr theory can be summarized as follows. An electron of charge —e and mass m in a circular orbit of radius r about an infinitely heavy positive charge of Ze obeys Newton s law for uniform circular motion5... 

A further refinement of the Bohr theory would require the exact and simultaneous measurement of electronic positions and velocities so that corrections to the theory could possibly be inferred from the deviation between theory and experiment. As we shall see, such exact measurements can not be made in principle in the universe as we know it. 

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. 

The first ionization energy of Li is found experimentally to be 5.363 eV. If the electron in the second shell (n = 2) is assumed to move in a central field of an effective nuclear charge, Zejy, consisting of the nucleus and the other electrons, by how many units of charge is the nucleus shielded by the other electrons Assume that the ionization energy can be calculated from Bohr theory. 

While h is quite small in the macroscopic world, it is not at all insignificant when the particle under consideration is of subatomic scale. Let us use an actual example to illustrate this point. Suppose the Ax of an electron is 10-14 m, or 0.01 pm. Then, with eq. (1.2.1), we get Apx = 5.27 x 10-21 kg m s-1. This uncertainty in momentum would be quite small in the macroscopic world. However, for subatomic particles such as an electron, with mass of 9.11 x 10-31 kg, such an uncertainty would not be negligible at all. Hence, on the basis of the Uncertainty Principle, we can no longer say that an electron is precisely located at this point with an exactly known velocity. It should be stressed that the uncertainties we are discussing here have nothing to do with the imperfection of the measuring instruments. Rather, they are inherent indeterminacies. If we recall the Bohr theory of the hydrogen atom, we find that both the radius of the orbit and the velocity of the electron can be precisely calculated. Hence the Bohr results violate the Uncertainty Principle. 

Take the Is electron as an example. In the Bohr theory, the electron moves in a fixed orbit of radius l o- On the other hand, in the wave mechanical treatment, the electron can in principle be found at any distance from the nucleus, and the most probable nucleus-electron separation is lao- Here we can see... 

Figure 7-9. Oxacarbenium ion transition state, Immucillin-H and DADMe-Immucillin-H are shown. The nomenclature - DADMe is (4 -Deaza-l -Aza-2/-Deoxy-l/,N-9-Methylene)-Immucillin-H. On die right, the molecular electrostatic potential surfaces (MEP) for the oxacarbenium/hypoxanthine pair at die transition state, Immucillin-H and DADMe-Immucillin-H are shown. MEP were calculated at HF/STO-3G theory level for optimized geometry at BlLYP/6-31G(d) theory level and visualized by Molekel 4.0 at electron density of 0.008 electron/bohr...

In the classical theory of electrodynamics, electromagnetic radiation is emitted when an electron moves in its orbit but, ac cording to the Bohr theory of the atom,... 

In most applications, the reduced mass is sufficiently close in value to the electronic mass me that it is customary to replace pt in the expressions for the energy levels and wave functions by me. The parameter aM = h2/fie 2 is thereby replaced by ao = h2/mee 2. The quantity ao is, according to the earlier 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 ft by me and atl by ao in the remainder of this book. 

Although valency strokes have been customary in chemical formulae for a century, one could not until recently attach to them any real notion about their true nature. On the patient paper one operated with them as with hooks which were undone, rotated etc. at will. Even the Rutherford-Bohr theory of the atom furnished no explanation, not even for the bonding of two hydrogen atoms to form a hydrogen molecule. The successful octet theory and the Lewis and Langmuir theory of the electron-pair bond associated with it was also still purely formal, but later was seen to be essentially correct. 

At a symposium on Ultra-Violet Light and X-Rays, held at the meeting of the American Association for the Advancement of Science at St. Louis in December 1919,1 I presented a set of computations of the K critical absorption frequencies based on the Rutherford-Bohr theory of atomic structure and the mechanism of radiation. The computed values equalled the observed values to within one or two per cent. In these computations the electrons were supposed to revolve in orbits which lay in planes passing through the nucleus of the atom. 

---