The Rutherford-Bohr atom

The planetary model of the atom was proposed by Rutherford in 1912 following the a particle scattering experiments of Geiger and Marsden, which showed most the mass of an atom to be concentrated in a tiny positive nucleus. The orbiting of light electrons resembles the problem of planetary motion first solved by Newton. 

Consider again the particle moving uniformly in a circle (Section 3.4)  

Differentiating twice with respect to time, remembering that r and or are constant, gives the acceleration 

By Newton s Second Law, a force must act on the particle to keep it in its circular motion, with x and y components obtained from eqns 4.1 and 4.2 as 

In a planetary system, the centripetal force is provided by the gravitational pull of the Sun. In atoms, this force comes from electrostatic interaction 

The atom of hydrogen, of atomic number Z = i, in its ground state has a single electron in the K shell of principal quantum number n — i the atom of helium (Z = z) has two electrons in this orbit. This, however, is the maximum number of electrons that can be accommodated in the first shell, for it is an essential feature of the Bohr theory that an orbit of principal quantum number n can accept not more than 2tz2 electrons. Thus the maximum permissible number of electrons in each shell is as follows  

In lithium (Z = 3) two electrons can be placed in the K shell, but the third must enter the L shell of higher energy. The difference in energy between these shells is immediately reflected in the ionization energies of the lithium atom, 5-36 eV to remove the L electron, a further 75 3 eV to remove the second electron, and a further 121-8 eV to remove the last electron. Thus the ion Li+ may be expected to be of common occurrence, whereas the ions Li2+ and Li3+ will be highly unstable and will readily acquire electrons to revert to a state of lower ionization. 

The L shell can accommodate a total of 8 electrons, and as further electrons are added to form the sequence of elements beryllium, boron, carbon, etc., these electrons take their place in the second shell until finally, at the end of the second period, neon (Z = 10) is reached, with both the first and second shells fully occupied and with an electronic structure which can be symbolized as (2, 8). The addition of further electrons to form the sequence of elements sodium, magnesium, etc., of the third period requires the formation of a new shell, and in sodium (Z = 11) a single electron occupies the M shell of principal quantum number 3 again the ionization energies reflect the difference in energy between this electron and those more tightly bound in the L and K shells. 

The third period terminates at argon (Z — 18) with the configuration (2, 8, 8), but here a new phenomenon occurs although the M shell is not yet fully occupied, the further electrons in potassium (Z = 19) and calcium (Z = 20) enter the N shell. Only after two electrons have taken their place in this shell is the development of the M shell resumed to give the transition elements scandium, titanium, etc. it is finally com- 

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The mathematical treatment of the Rutherford-Bohr atom was especially productive in Denmark and Germany. It led directly to quantum mechanics, which treated electrons as particles. Electrons, however, like light, were part of electromagnetic radiation, and radiation was generally understood to be a wave phenomenon. In 1924, the French physicist Prince Louis de Broglie (1892-1987), influenced by Einstein s work on the photoelectric effect, showed that electrons had both wave and particle aspects. Wave mechanics, an alternative approach to quantum physics, was soon developed, based on the wave equation formulated in 1926 by the Austrian-born Erwin Schrodinger (1887-1961). Quantum mechanics and wave mechanics turned out to be complementary and both were fruitful for an understanding of valence. 

This book aims at giving a general account of the principles of valency and molecular constitution founded on the Rutherford-Bohr atom. 

Compare the Rutherford, Bohr, and quantum mechanical models of the atom. 

An overview of a scientific subject must include at least two parts retrospect (history) and the present status. The present status (in a condensed form) is presented in Chapters 2 to 21. In this section of the overview we outline (sketch) from our subjective point of view the history of electrochemical deposition science. In Section 1.2 we show the relationship of electrochemical deposition to other sciences. In this section we show how the development of electrodeposition science was dependent on the development of physical sciences, especially physics and chemistry in general. It is interesting to note that the electron was discovered in 1897 by J. J. Thomson, and the Rutherford-Bohr model of the atom was formulated in 1911. 

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. 

For nearly half a century, Mendeleev s periodic table remained an empirical compilation of the relationship of the elements. Only after the first atomic model was developed by the physicists of the early twentieth century, which took form in Bohr s model, was it possible to reconcile the involved general concepts with the specificity of the chemical elements. Bohr indeed expanded Rutherford s model of the atom, which tried to connect the chemical specificity of the elements grouped in Mendeleev s table with the behavior of electrons spinning around the nucleus. Bohr hit upon the idea that Mendeleev s periodicity could... 

The last big problem facing early twentieth century physics was Ernest Rutherford s atomic structure. Physicists knew that Rutherford s atom could not exist, but no one could come up with anything better. The man who would resolve this conundrum showed up at Manchester, England, in 1912 to work for Rutherford. Rutherford himself had worked for J.J. Thomson and had disproved Thomson s plum pudding structure of the atom. Now, the new man in Manchester, Niels Bohr, was about to do the same thing to Rutherford. By the end of his career, Bohr would have contributed as much as anyone to understanding Feynman s little particles. Science is a meritocracy. Poor kids can excel and get ahead in the world of science just as easily as the well-heeled. For example. 

Like Rutherford, he pictured the atom as a tiny nucleus with an electron moving around it like a planet orbiting the sun. Bohr,... 

By the 1930s, the structure of the atom worked out by Rutherford, Bohr, and others had answered the pressing questions fac-... 

Equation (2.2) is just the Rutherford cross section for scattering of, strictly speaking, free charges. To apply this to atomic electrons that are not free but can be excited4 with energy En, Bohr surmised the sum rule... 

In the early part of the twentieth century, then, a simple model of atomic structure became accepted, now known as the Rutherford nuclear model of the atom, or, subsequently, the Bohr-Rutherford model. This supposed that most of the mass of the atom is concentrated in the nucleus, which consists of protons (positively charged particles) and neutrons (electrically neutral particles, of approximately the same mass). The number of protons in the nucleus is called the atomic number, which essentially defines the nature of... 

Scientists of the nineteenth century lacked the concepts necessary to explain line spectra. Even in the first decade of the twentieth century, a suitable explanation proved elusive. This changed in 1913 when Niels Bohr, a Danish physicist and student of Rutherford, proposed a new model for the hydrogen atom. This model retained some of the features of Rutherford s model. More importantly, it was able to explain the line spectrum for hydrogen because it incorporated several new ideas about energy. As you can see in Figure 3.8, Bohr s atomic model pictures electrons in orbit around a central nucleus. Unlike Rutherford s model, however, in which electrons may move anywhere within the volume of space around the nucleus, Bohr s model imposes certain restrictions. 

Explain how the Bohr atomic model differs from the Rutherford atomic model, and explain the observations and inferences that led Bohr to propose his model. 

Both the Rutherford and Bohr atomic models have been described as planetary models. In what ways is this comparison appropriate In what ways is this comparison misleading ... 

Shortly after coming to Rutherford s laboratory, Bohr set to work on the problem of understanding the structure of atoms. Rutherford s discovery of the atomic nucleus had introduced formidable problems. It seemed necessary to assume that the electrons in an atom orbited the nucleus. Otherwise, the electrical attraction between the electrons and the nucleus would cause the electrons and the nucleus to collide with one another. But, as we have seen, the assumption that the electrons orbited the nucleus didn t seem to work either. Orbiting electrons should lose energy and fall into the nucleus anyway. 

The 3rd Solvay Conference in Physics took place in 1921, after a long interruption due to the First World War. Its theme was Atoms and Electrons. 20 It was centered on the Rutherford model of the atom and Niels Bohr s atomic theory. Bohr, however, was not able to attend the conference because of illness. 

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