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.pdfQuantum mechanics 4.2 (т.зн.)
The Danish physicist Niels Bohr pioneered the use of the quantum hypothesis in developing a successful theory of atomic structure. Adopting Rutherford's nuclear model, he proposed in 1913 that the atom is like a miniature solar system, with the electrons moving in orbits around the nucleus just as the planets move around the Sun. Although the electrical attraction between the electrons and nucleus is mathematically similar to the gravitational attraction between the planets and the Sun, the quantum hypothesis is needed to restrict the electrons to certain orbits and to forbid them from radiating energy except when jumping from one orbit to another.
Bohr's model provided a good description of the spectra and other properties of atoms containing only one electron–neutral hydrogen and singly ionized helium–but could not be satisfactorily extended to multielectron atoms or molecules. It relied on an inconsistent mixture of old and new physical principles, hinting but not clearly specifying how a more adequate general theory might be constructed.
The nature of light was still puzzling to those who demanded that it should behave either like waves or like particles. Two experiments performed by American physicists seemed to favour the particle theory: Robert A. Millikan's confirmation of the quantum theory of the photoelectric effect proposed by Einstein; and Arthur H. Compton's experimental demonstration that X rays behave like particles when they collide with electrons. The findings of these experiments had to be considered along with the unquestioned fact that electromagnetic radiation also exhibits wave properties such as interference and diffraction.
Louis de Broglie, a French physicist, proposed a way out of the dilemma: accept the wave–particle dualism as a description not only of light but also of electrons and other entities previously assumed to be particles. In 1926 the Austrian physicist Erwin Schrödinger constructed a mathematical «wave mechanics» based on this proposal. His theory tells how to write down an equation for the wave function of any physical system in terms of the masses and charges of its components. From the wave function, one may compute the energy levels and other observable properties of the system.
Schrödinger's equation, the most convenient form of a more general theory called quantum mechanics to which the German physicists Wer-
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ner Heisenberg and Max Born also contributed, was brilliantly successful. Not only did it yield the properties of the hydrogen atom but it also allowed the use of simple approximating methods for more complicated systems even though the equation could not be solved exactly. The application of quantum mechanics to the properties of atoms, molecules, and metals occupied physicists for the next several decades.
The founders of quantum mechanics did not agree on the philosophical significance of the new theory. Born proposed that the wave function determines only the probability distribution of the electron's position or path; it does not have a well-defined instantaneous position and velocity. Heisenberg made this view explicit in his indeterminacy principle: the more accurately one determines the position, the less accurately the velocity is fixed; the converse is also true. Heisenberg's principle is often called the uncertainty principle, but this is somewhat misleading. It tends to suggest incorrectly that the electron really has a definite position and velocity and that they simply have not been determined.
Einstein objected to the randomness implied by quantum mechanics in his famous statement that God “does not play dice.” He also was disturbed by the apparent denial of the objective reality of the atomic world: Somehow the electron's position or velocity comes into existence only when it is measured. Niels Bohr expressed this aspect of the quantum worldview in his complementarity principle, building on de Broglie's resolution of the wave–particle dichotomy: A system can have such properties as wave or particle behaviour that would be considered incompatible in Newtonian physics but that are actually complementary; light exhibits either wave behaviour or particle behaviour, depending on whether one chooses to measure the one property or the other. To say that it is really one or the other, or to say that the electron really has both a definite position and momentum at the same time, is to go beyond the limits of science.
Bohr's viewpoint, which became known as the Copenhagen Interpretation of quantum mechanics, was that reality can be ascribed only to a measurement. Einstein argued that the physical world must have real properties whether or not one measures them; he and Schrödinger published a number of thought experiments designed to show that things can exist beyond what is described by quantum mechanics. During the 1970s and 1980s, advanced technology made it possible to actually perform some of these experiments, and quantum mechanics was vindicated in every case.
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Chemistry 6.3 (т.зн.)
The long-standing problem of the nature of the force that holds atoms together in molecules was finally solved by the application of quantum mechanics. Although it is often stated that chemistry has been «reduced to physics» in this way, it should be pointed out that one of the most important postulates of quantum mechanics was introduced primarily for the purpose of explaining chemical facts and did not originally have any other physical justification. This was the so-called exclusion principle put forth by the Austrian physicist Wolfgang Pauli, which forbids more than one electron occupying a given quantum state in an atom. The state of an electron includes its spin, a property introduced by the Dutch-born American physicists George E. Uhlenbeck and Samuel A. Goudsmit. Using that principle and the assumption that the quantum states in a multi-electron atom are essentially the same as those in the hydrogen atom, one can postulate a series of «shells» of electrons and explain the chemical valence of an element in terms of the loss, gain, or sharing of electrons in the outer shell.
Some of the outstanding problems to be solved by quantum chemistry were: (1) The «saturation» of chemical forces. If attractive forces hold atoms together to form molecules, why is there a limit on how many atoms can stick together (generally only two of the same kind)?
(2) Stereochemistry–the three-dimensional structure of molecules, in particular the spatial directionality of bonds as in the tetrahedral carbon atom. (3) Bond length–i.e., there seems to be a well-defined equilibrium distance between atoms in a molecule that can be determined accurately by experiment. (4) Why some atoms (e.g., helium) normally form no bonds with other atoms, while others form one or more. (These are the empirical rules of valence.)
Soon after J.J. Thomson's discovery of the electron in 1897, there were several attempts to develop theories of chemical bonds based on electrons. The most successful was that proposed in the United States by G.N. Lewis in 1916 and Irving Langmuir in 1919. They emphasized shared pairs of electrons and treated the atom as a static arrangement of charges. While the Lewis–Langmuir model as a whole was inconsistent with quantum theory, several of its specific features continued to be useful.
The key to the nature of the chemical bond was found to be the quan- tum-mechanical exchange effect, first described by Heisenberg in 1926–
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27. Resonance is related to the requirement that the wave function for two or more identical particles must have definite symmetry properties with respect to the coordinates of those particles–it must have plus or minus the same value (symmetric or antisymmetric, respectively) when those particles are interchanged. Particles such as electrons and protons, according to a hypothesis proposed by Enrico Fermi and P.A.M. Dirac, must have antisymmetric wave functions. Exchange may be imagined as a continual jumping back and forth or interchange of the electrons between two possible states. In 1927 the German physicists Walter Heitler and Fritz London used this idea to obtain an approximate wave function for two interacting hydrogen atoms. They found that with an antisymmetric wave function (including spin) there is an attractive force, while with a symmetric one there is a repulsive force. Thus two hydrogen atoms can form a molecule if their electron spins are opposite, but not if they are the same.
The Heitler–London approach to the theory of chemical bonds was rapidly developed John C. Slater and Linus C. Pauling in the United States. Slater proposed a simple general method for constructing multipleelectron wave functions that would automatically satisfy the Pauli exclusion principle. Pauling introduced a valence-bond method, picking out one electron in each of the two combining atoms and constructing a wave function representing a paired-electron bond between them. Pauling and Slater were able to explain the tetrahedral carbon structure in terms of a particular mixture of wave functions that has a lower energy than the original wave functions, so that the molecule tends to go into that state.
About the same time another American scientist, Robert S. Mulliken, was developing an alternative theory of molecular structure based on what he called molecular orbitals. (The idea had been used under a different name by John E. Lennard-Jones of England in 1929 and by Erich Hückel of Germany in 1931.) Here, the electron is not considered to be localized in a particular atom or two-atom bond, but rather it is treated as occupying a quantum state (an «orbital») that is spread over the entire molecule.
In treating the benzene molecule by the valence-bond method in 1933, Pauling and George W. Wheland constructed a wave function that was a linear combination of five possible structures–i.e., five possible arrangements of double and single bonds. Two of them are the structures that had been proposed by the German chemist August Kekulé (later Kekule von Stradonitz) in 1865, with alternating single and double
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bonds between adjacent carbon atoms in the six-carbon ring. The other three (now called Dewar structures for the British chemist and physicist James Dewar, though they were first suggested by H. Wichelhaus in 1869) have one longer bond going across the ring. Pauling and Dewar described their model as involving resonance between the five structures. According to quantum mechanics, this does not mean that the molecule is sometimes «really» in one state and at other times in another, but rather that it is always in a composite state.
The valence-bond method, with its emphasis on resonance between different structures as a means of analyzing aromatic molecules, dominated quantum chemistry during the 1930s. The method was comprehensively presented and applied in Pauling's classic treatise The Nature of the Chemical Bond (1939), the most important work on theoretical chemistry in the 20th century. One reason for its popularity was that ideas similar to resonance had been developed by organic chemists, notably F.G. Arndt in Germany and Christopher K. Ingold in England, independently of quantum theory during the late 1920s.
After World War II there was a strong movement away from the va- lence-bond method toward the molecular-orbital method, led by Mulliken in the United States and by Charles Coulson, Lennard-Jones, H.C. Longuet-Higgins, and Michael J.S. Dewar in England. The advocates of the molecular-orbital method argued that their approach was simpler and easier to apply to complicated molecules, since it allowed one to visualize a definite charge distribution for each electron.
Rutherford, Ernest, Baron Rutherford of Nelson, of Cambridge 0.9 (т.зн.)
British physicist who laid the groundwork for the development of nuclear physics. He was awarded the Nobel Prize for Chemistry in 1908.
Rutherford is to be ranked in fame with Sir Isaac Newton and Michael Faraday. Indeed, just as Faraday is called the «father of electricity», so a similar description might be applied to Rutherford in relation to nuclear energy. He contributed substantially to the understanding of the disintegration and transmutation of the radioactive elements, discovered and named the particles expelled from radium, identified the alpha particle as a helium atom and with its aid evolved the nuclear theory of atomic structure, and used that particle to produce the first artificial dis-
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integration of elements. Rutherford was the principal founder of the field of atomic physics. In the universities of McGill, Manchester, and Cambridge he led and inspired two generations of physicists who–to use his own words–«turned out the facts of Nature», and in the Cavendish Laboratory his «boys» discovered the neutron and artificial disintegration by accelerated particles.
Early life 3.1 (т.зн.)
Rutherford was the fourth of the 12 children of James, a wheelwright at Brightwater near Nelson on South Island, New Zealand, and Martha Rutherford. His parents, who had emigrated from Great Britain, denied themselves many comforts so that their children might be well educated. In 1887 Ernest won a scholarship to Nelson College, a secondary school, where he was a popular boy, clever with his hands, and a keen footballer. He won prizes in history and languages as well as mathematics. Another scholarship allowed him to enroll in Canterbury College, Christchurch, from where he graduated with a B.A. in 1892 and an M.A. in 1893 with first-class honours in mathematics and physics. Financing himself by part-time teaching, he stayed for a fifth year to do research in physics, studying the properties of iron in high-frequency alternating magnetic fields. He found that he could detect the electromagnetic waves–wireless waves–newly discovered by the German physicist Heinrich Hertz, even after they had passed through brick walls. Two substantial scientific papers on this work won for him an «1851 Exhibition» scholarship, which provided for further education in England.
Before leaving New Zealand he became unofficially engaged to Mary Newton, a daughter of his landlady in Christchurch. Mary preserved his letters from England, as did his mother, who lived to age 92. Thus, a wealth of material is available that sheds much light on the nonscientific aspects of his fascinating personality.
On his arrival in Cambridge in 1895, Rutherford began to work under J.J. Thomson, professor of experimental physics at the university's Cavendish Laboratory. Continuing his work on the detection of Hertzian waves over a distance of two miles, he gave an experimental lecture on his results before the Cambridge Physical Society and was delighted when his paper was published in the Philosophical Transactions of the Royal Society of London, a signal honour for so young an investigator.
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Rutherford made a great impression on colleagues in the Cavendish Laboratory, and Thomson held him in high esteem. He also aroused jealousies in the more conservative members of the Cavendish fraternity, as is clear from his letters to Mary. In December 1895, when Röntgen discovered X rays, Thomson asked Rutherford to join him in a study of the effects of passing a beam of X rays through a gas. They discovered that the X rays produced large quantities of electrically charged particles, or carriers of positive and negative electricity, and that these carriers, or ionized atoms, recombined to form neutral molecules. Working on his own, Rutherford then devised a technique for measuring the velocity and rate of recombination of these positive and negative ions. The published papers on this subject remain classics to the present day.
In 1896 the French physicist Henri Becquerel discovered that uranium emitted rays that could fog a photographic plate as did X rays. Rutherford soon showed that they also ionized air but that they were different from X rays, consisting of two distinct types of radiation. He named them alpha rays, highly powerful in producing ionization but easily absorbed, and beta rays, which produced less radiation but had more penetrating ability. He thought they must be extremely minute particles of matter.
In 1898 Rutherford was appointed to the chair of physics at McGill University in Montreal. To Mary he wrote, «the salary is only 500 pounds but enough for you and me to start on». In the summer of 1900 he traveled to New Zealand to visit his parents and get married. When his daughter Eileen, their only child, was born the next year, he wrote his mother «it is suggested that I call her ‘Ione' after my respect for ions in gases».
Contributions in physics 5.3 (т.зн.)
Toward the end of the 19th century many scientists thought that no new advances in physics remained to be made. Yet within three years Rutherford succeeded in marking out an entirely new branch of physics called radioactivity. He soon discovered that thorium or its compounds disintegrated into a gas that in turn disintegrated into an unknown «active deposit», likewise radioactive. Rutherford and a young chemist, Frederick Soddy, then investigated three groups of radioactive ele- ments–radium, thorium, and actinium. They concluded in 1902 that radioactivity was a process in which atoms of one element spontaneously
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disintegrated into atoms of an entirely different element, which also remained radioactive. This interpretation was opposed by many chemists who held firmly to the concept of the indestructibility of matter; the suggestion that some atoms could tear themselves apart to form entirely different kinds of matter was to them a remnant of medieval alchemy.
Nevertheless, Rutherford's outstanding work won him recognition by the Royal Society, which elected him a fellow in 1903 and awarded him the Rumford medal in 1904. In his book Radio-activity (1904) he summarized the results of research in that subject. The evidence he marshaled for radioactivity was that it is unaffected by external conditions, such as temperature and chemical change; that more heat is produced than in an ordinary chemical reaction; that new types of matter are produced at a rate in equilibrium with the rate of decay; and that the new products possess distinct chemical properties.
Rutherford, a prodigious worker with tremendous powers of concentration, continued to make a succession of brilliant discoveries–and with remarkably simple apparatus. For example, he showed (1903) that alpha rays can be deflected by electric and magnetic fields, the direction of the deflection proving that the rays are particles of positive charge; he determined their velocity and the ratio of their charge (E) to their mass (M). These results were obtained by passing such particles between thin, matchbox-sized metal plates stacked closely together, each plate charged oppositely to its neighbour in one experiment and in another experiment putting the assembly in a strong magnetic field; in each experiment he measured the strengths of the fields which just sufficed to prevent the particles from emerging from the stack.
Rutherford wrote 80 scientific papers during his seven years at McGill, made many public appearances, among them the Silliman Memorial Lectures at Yale University in 1905, and received offers of chairs at other universities. In 1907 he returned to England to accept a chair at the University of Manchester, where he continued his research on the alpha particle. With the ingenious apparatus that he and his research assistant, Hans Geiger, had invented, they counted the particles as they were emitted one by one from a known amount of radium; and they also measured the total charge collected, from which the charge on each particle could be detected. Combining this result with the rate of production of helium from radium, determined by Rutherford and the American chemist Bertram Borden Boltwood, Rutherford was able to deduce Avogadro's number (the con-
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stant number of molecules in the molecular weight in grams of any substance) in the most direct manner conceivable. With his student Thomas D. Royds he proved in 1908 that the alpha particle really is a helium atom, by allowing alpha particles to escape through the thin glass wall of a containing vessel into an evacuated outer glass tube and showing that the spectrum of the collected gas was that of helium. Almost immediately, in 1908, came the Nobel Prize–but for chemistry, for his investigations concerning the disintegration of elements.
In 1911 Rutherford made his greatest contribution to science with his nuclear theory of the atom. He had observed in Montreal that fastmoving alpha particles on passing through thin plates of mica produced diffuse images on photographic plates, whereas a sharp image was produced when there was no obstruction to the passage of the rays. He considered that the particles must be deflected through small angles as they passed close to atoms of the mica, but calculation showed that an electric field of 100,000,000 volts per centimetre was necessary to deflect such particles traveling at 20,000 kilometres per second, a most astonishing conclusion. This phenomenon of scattering was found in the counting experiments with Geiger; Rutherford suggested to Geiger and a student, Ernest Marsden, that it would be of interest to examine whether any particles were scattered backward–i.e., deflected through an angle of more than 90 degrees. To their astonishment, a few particles in every 10,000 were indeed so scattered, emerging from the same side of a gold foil as that on which they had entered. After a number of calculations, Rutherford came to the conclusion that the intense electric field required to cause such a large deflection could occur only if all the positive charge in the atom, and therefore almost all the mass, were concentrated on a very small central nucleus some 10,000 times smaller in diameter than that of the entire atom. The positive charge on the nucleus would therefore be balanced by an equal charge on all the electrons distributed somehow around the nucleus. This theory of atomic structure is known as the Rutherford atomic model.
Although in 1904 Hantaro Nagaoka, a Japanese physicist, had proposed an atomic model with electrons rotating in rings about a central nucleus, it was not taken seriously, because, according to classical electrodynamics, electrons in orbit would have a centripetal acceleration toward the centre of rotation and would thus radiate away their energy, falling into the central nucleus almost immediately. This idea is in
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marked contrast with the view developed by J.J. Thomson in 1910; he envisaged all the electrons distributed inside a uniformly charged positive sphere of atomic diameter, in which the negative «corpuscles» (electrons) are imbedded. It was not until 1913 that Niels Bohr, a Danish physicist, postulated that electrons, contrary to classical electrodynamics, do not radiate energy during rotation and do indeed move in orbits about a central nucleus, thus upholding the convictions of Nagaoka and Rutherford. A knighthood conferred in 1914 further marked the public recognition of Rutherford's services to science.
Later years 1.5 (т.зн.)
During World War I he worked on the practical problem of submarine detection by underwater acoustics. He produced the first artificial disintegration of an element in 1919, when he found that on collision with an alpha particle an atom of nitrogen was converted into an atom of oxygen and an atom of hydrogen. The same year he succeeded Thomson as Cavendish professor. Although his experimental contributions henceforth were not as numerous as in earlier years, his influence on research students was enormous. In the second Bakerian lecture he gave to the Royal Society in 1920, he speculated upon the existence of the neutron and of isotopes of hydrogen and helium; three of them were eventually discovered by workers in the Cavendish Laboratory.
His service as president of the Royal Society (1925–30) and as chairman of the Academic Assistance Council, which helped almost 1,000 university refugees from Germany, increased the claims upon his time. But whenever possible he worked in the Cavendish Laboratory, where he encouraged students, probed for the facts, and always sought an explanation in simple terms. When in 1934 Enrico Fermi in Rome successfully disintegrated many different elements with neutrons, Rutherford wrote to congratulate him «for escaping from theoretical physics».
Rutherford read widely and enjoyed good health, the game of golf, his home life, and hard work. He could listen to the views of others, his judgments were fair, and from his many students he earned affection and esteem. In 1931 he was made a peer, but any gratification this honour may have brought was marred by the death of his daughter. He died in Cambridge following a short illness and was buried in Westminster Abbey.
Thomas Edward Allibone
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