Bohr’s theory

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. 

I should also mention Sommerfeld, who extended Bohr s theory to try and account for the extra quantum numbers observed experimentally. Sommerfeld allowed the electrons to have an elliptic orbit rather than a circular one. 

Scerri, E, (1994) Prediction of the Nature of Hafnium from Chemistry, Bohr s Theory and Quantum Theory , Annals of Science 51, 131-150. 

The units we use in daily life, such as kilogram (or pound) and meter (or inch) are tailored to the human scale. In the world of quantum mechanics, however, these units would lead to inconvenient numbers. For example, the mass of the electron is 9.1095 X J0 31 kg and the radius of the first circular orbit of the hydrogen atom in Bohr s theory, the Bohr radius, is 5.2918 X 10 11 m. Atomic units, usually abbreviated as au, are introduced to eliminate the need to work with these awkward numbers, which result from the arbitrary units of our macroscopic world. The atomic unit of length is equal to the length of the Bohr radius, that is, 5.2918 X 10 n m, and is called the bohr. Thus 1 bohr = 5.2918 X 10"11 m. The atomic unit of mass is the rest mass of the electron, and the atomic unit of charge is the charge of an electron. Atomic units for these and some other quantities and their values in SI units are summarized in the accompanying table. 

In Bohr s theory, only estimates of maximum and minimum impact parameters are necessary. Better computations are required for determining the transverse distribution of lost energy or the effect of secondary electrons. The minimum impact parameter according to classical mechanics is ze2/mv2 from angular momentum consideration in quantum mechanics, it is h /mv. In practice, the larger of these two is taken. Also, the impulse approximation used by Bohr for the maximum impact parameter is not an absolute rule energy transfer beyond bmax falls off exponentially (Orear et al., 1956 Mozumder, 1974). 

According to Bohr s theory, the frequencies that correspond to the lines in the emission... 

Bohr s theory of the periodic system of the elements.. . . The physicist who did not live through that period can hardly imagine the excitement felt by a new graduate student, picking up Number 1 of Volume 9 of the Zeitschrift and there reading for the first time the complete explanation of the periodic system of the elements. 16... 

Bohr s theory rightly explains the fundamental origin of line spectrum according to which ... 

The discovery of the rare earth elements provide a long history of almost two hundred years of trial and error in the claims of element discovery starting before the time of Dalton s theory of the atom and determination of atomic weight values, Mendeleev s periodic table, the advent of optical spectroscopy, Bohr s theory of the electronic structure of atoms and Moseley s x-ray detection method for atomic number determination. The fact that the similarity in the chemical properties of the rare earth elements make them especially difficult to chemically isolate led to a situation where many mixtures of elements were being mistaken for elemental species. As a result, atomic weight values were not nearly as useful because the lack of separation meant that additional elements would still be present within an oxide and lead to inaccurate atomic weight values. Very pure rare earth samples did not become a reality until the mid twentieth century. 

Bohr next applied his theory to helium ions—helium atoms in which one of the two electrons is removed—and again the predictions of the theory exactly matched results obtained in experiments. The scientific world was convinced. For example, when Einstein heard of the results, he reversed himself and said, This is a tremendous achievement—Bohr s theory must be right. ... 

Bohr s theory not only solved the puzzle of the rare earths, it also explained why Mendeleev s periodic law works so well in most cases. Elements with the same number of electrons in the outermost shell have similar properties. For example, both sodium and potassium have a single electron in the outer shell. Magnesium and calcium, which are also chemically and physically similar, each have two. Carbon and silicon have four. And so on. 

Bohr s theory received a striking confirmation when the element hafnium was discovered at his institute in 1923. During the early 1920s most chemists believed that element 72 would turn out to be a rare earth. But Bohr s theory implied that this element should have four electrons in its outermost shell, not three as the rare earths did. It should therefore have properties similar to those of the element zirconium. 

STOPPING POWER, LET, AND FLUCTUATIONS 2.1. Bohr s Theory and the Bragg Rule... 

Spectroscopy was to prove indispensable in unlocking the structure of atoms, particulary their electronic stmcture— but those developments would depend on other, later researchers. Max Planck s analysis of blackbody radiation and Bohr s theory of the hydrogen spectrum are just two examples. 

In the modern model of the atom, based on wave mechanics, the conception of electronic orbits in the old model is replaced by the idea of the probability of the occurrence of an electron at a given point. The conclusions, however, which can be drawn from the older model remain the same in the newer conception, and it is important to remember that in this new model the essential points of Bohr s theory have not been discarded, but merely interpreted differently and very greatly refined. 

Millikan s experiment did not prove, of course, that (he charge on the cathode ray. beta ray, photoelectric, or Zeeman particle was e. But if we call all such particles electrons, and assume that they have e/m = 1.76 x Hi" coulombs/kg. and e = 1.60 x 10" coulomb (and hence m =9.1 x 10 " kg), we find that they fit very well into Bohr s theory of the hydrogen atom and successive, more comprehensive atomic theories, into Richardson s equations for thermionic emission, into Fermi s theory of beta decay, and so on. In other words, a whole web of modem theory and experiment defines the electron. The best current value of e = (1.60206 0.00003) x 10 g coulomb. 

By 1903. llie wave theory of light based oil Maxwell s equations was well established, but certain phenomena would not fit in. It seemed that emission and absorption of hght occur discontinuously. This led Einstein to (lie view that the energy is concentrated in discrete particles. It was a revolutionary idea, very hard to understand, as the successes of the wave theory were undeniable. It seemed that light had to be understood sometimes as waves, sometimes as particles, and physicists had to get used to it, The idea was incorporated into Bohr s theory of the hydrogen atom and forms an essential part of it. 

N. Bohr 3 discussed the fitness of configurations of the electrons in various atoms for the formation of ions. N. V. Sidgwiek has extended Bohr s theory to the electronic structure of atoms in co-ordination compounds. The subject was also discussed by J. D. M. Smith, and others at the Faraday Society s discussion on The Electronic Theory of Valency. A. Job discussed the catalyzed reaction NH3+HC1—NH4CI on the assumption that an unstable electronic system is formed as an intermediate product. 

Bohr s theory was extended in various ways, especially by Somerfeld, who showed how to deal with elliptical orbits. There was a certain amount of qualitative success in applying the theory to atoms with several electrons. These developments in what is now called the old quantum theory were important as they laid much of the groundwork necessary for a correct theory. Ultimately, they were unsuccessful. Bohr s theory did not really explain what is going on why should only some orbits be allowed Where does the quantization condition (eqn 4.12) come from Following the developments of... 

Let us consider two nondegenerate stationary states m and n of a system, with energy values Em and E where Em > E . According to Bohr s theory, the frequency of the absorbed radiation is given by... 

The principal quantum number, n, corresponds to the energy levels in Bohr s theory. The bigger the value of n, the further the electron cloud from the nucleus, hence the higher the potential energy of the electron. 

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