Read Ebook: The atom and the Bohr theory of its structure by Holst Helge Kramers Hendrik Anthony Rutherford Ernest Author Of Introduction Etc Lindsay Rachel T Translator Lindsay Robert Bruce Translator

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PAGE PREFACE vii FOREWORD xi

INTERPRETATION OF SYMBOLS AND PHYSICAL CONSTANTS 209

THE ATOM AND THE BOHR THEORY OF ITS STRUCTURE

ATOMS AND MOLECULES

Introduction.

But the atomic conception was not the generally accepted one in antiquity. Aristotle was not an atomist, and denied the existence of discontinuous matter; his philosophy had a tremendous influence upon the ideas of the ancients, and even upon the beliefs of the Middle Ages. It must be confessed that his conception of the continuity of matter seemed to agree best with experiment, because of the apparent homogeneity of physical substances such as metal, glass, water and air. But even this apparent homogeneity could not be considered entirely inconsistent with the atomic theory, for, according to the latter, the atoms were so small as to be invisible. Moreover, the atomic theory left the way open for a more complete understanding of the properties of matter. Thus when air was compressed and thereafter allowed to expand, or when salt was dissolved in water producing an apparently new homogeneous liquid, salt water, or when silver was melted by heat, or light changed colour on passing through wine, it was clear that something had happened in the interior of the substances in question. But complete homogeneity is synonymous with inactivity. How is it possible to obtain a definite idea of the inner activity lying at the bottom of these changes of state, if we do not think of the phenomenon as an interplay between the different parts of the apparently homogeneous matter? Thus, in the examples above, the decrease in the volume of the air might be considered as due to the particles drawing nearer to each other; the dissolving of salt in water might be looked upon as the movement of the salt particles in between the water particles and the combination of the two kinds; the melting of silver might naturally appear to be due to the loosening of bonds between the individual silver particles.

The Atomic Theory and Chemistry.

In the meantime atomic investigations of a very different nature had been influencing the new science of chemistry, in which the atomic theory was later to prove itself extraordinarily fruitful. It was particularly unfortunate that in chemistry, concerned as it is with the inner activities of the elements, Aristotle's philosophy was long the prevailing one. He adopted and developed the famous theory of the four "elements," namely, the dry and cold earth, the cold and damp water, the damp and warm air, the warm and dry fire. These "elements" must not be confused with the chemical elements known at the present day; they were merely representatives of the different consistent combinations of the four fundamental qualities, dryness and wetness, heat and cold. From the symmetry in the system these were supposed to be the principles by means of which all the properties of matter could be explained. Neither the four "elements" nor the four fundamental qualities could be clearly defined; they were vague ideas to be discussed in long dialectic treatises, but were founded upon no physical quantities which could be measured.

A system of chemistry which had its theoretical foundations in the Greek elemental conceptions naturally had to work in the dark. Undoubtedly this uncertainty contributed to the relatively insignificant results of all the labour expended in the Middle Ages on chemical experiments, many of which had to do with the attempt to transmute the base metals into gold. Naturally there were many important contributions to chemistry, and the theories were changed and developed in many ways in the course of time. The alchemists of the Middle Ages thought that metal consisted only of sulphur and quicksilver; but the interpretation of this idea was influenced by the Greek elemental theory which was maintained at the same time; thus these new metal "elements" were considered by many merely as the expressions of certain aspects of the metallic characteristics, rather than as definite substances, identical with the elements bearing these names. It is, however, necessary to guard against attributing to a single conception too great influence on the historical development of the chemical and physical sciences. That the growth of the latter was hindered for so long a time was due more to the uncritical faith in authority and to the whole characteristic psychological point of view which governed Western thought in the centuries preceding the Renaissance.

Robert Boyle is one of the men to whom great honour is due for brushing aside the old ideas about the elements which had originated in obscure philosophical meditations. To him an element was simply a substance which by no method could be separated into other substances, but which could unite with other elements to form chemical compounds possessing very different characteristics, including that of being decomposable into their constituent elements. Undoubtedly Boyle's clear conception of this matter was connected with his representation of matter as of an atomic nature. According to the atomic conception, the chemical processes do not depend upon changes within the element itself, but rather in the union or disunion of the constituent atoms. Thus when iron sulphide is produced by heating iron and sulphur together, according to this conception, the iron atoms and the sulphur atoms combine in such a way that each iron atom links itself with a sulphur atom. There is then a definite meaning in the statement that iron sulphide consists of iron and sulphur, and that these two substances are both represented in the new substance. There is also a definite meaning, for instance, in the statement that iron is an element, namely, that by no known means can the iron be broken down into different kinds of atoms which can be reunited to produce a substance different from iron.

The clarity which the atomic interpretation gave to the conception of chemical elements and compounds was surely most useful to chemical research in the following years; but before the atomic theory could play a really great r?le in chemistry, it had to undergo considerable development. In the time of Boyle, and even later, there was still uncertainty as to which substances were the elements. Thus, water was generally considered as an element. According to the so-called phlogiston theory developed by the German Stahl , a theory which prevailed in chemistry for many years, the metals were chemical compounds consisting of a gaseous substance, phlogiston, which was driven off when the metals were heated in air, and the metallic oxide which was left behind. It was not until the latter half of the eighteenth century that the foundation was laid for the new chemical science by a series of discoveries and researches carried on by the Swedish scientist Scheele, the Englishmen Priestley and Cavendish, and particularly by the Frenchman Lavoisier. It was then discovered that water is a chemical compound of the gaseous elements oxygen and hydrogen, that air is principally a mixture of oxygen and nitrogen, that combustion is a chemical process in which some substance is united with oxygen, that metals are elements, while metallic oxides, on the other hand, are compounds of metal and oxygen, etc. Of special significance for the atomic theory was the fact that Lavoisier made weighing one of the most powerful tools of scientific chemistry.

When Dalton in the beginning of last century formulated the theory of the formation of chemical compounds from the atoms of the elements, he at once turned atomic theory into the path of more practical research, and it was soon evident that chemical research had then obtained a valuable tool. It may be said that Dalton's atomic theory is the firm foundation upon which modern chemistry is built.

In order to choose between the different possible ratios of atomic weights, for example, the eight to one or the sixteen to one in the case of oxygen and hydrogen, Dalton had to make certain arbitrary assumptions. The first of these is that two elements of which only one compound is known appear with but one atom each in a molecule. Partly on account of this assumption and partly on account of the incompleteness of his analyses, Dalton's values of the ratios of the atomic weights of the atoms and his pictures of the structure of molecules differ from those of the present day, as is obvious from Fig. 2.

When one volume of the gas chlorine unites with one volume of hydrogen there result two volumes of the gas, hydrogen chloride, at the same temperature and pressure. According to Avogadro's Law one molecule of chlorine and one molecule of hydrogen unite to become two molecules of hydrogen chloride, and since each of these two molecules must contain at least one atom of hydrogen and one atom of chlorine, it follows that one molecule of chlorine must contain two atoms of chlorine and that one molecule of hydrogen must contain two atoms of hydrogen. From this one can see that even in the elements the atoms are united into molecules. It is now well established that most elements have diatomic molecules, though some, including mercury and many other metals, are monatomic. When oxygen and hydrogen unite to form water, one litre of oxygen and two litres of hydrogen produce two litres of water vapour at same temperature and pressure. Accordingly, one molecule of oxygen and two molecules of hydrogen form two molecules of water. If the oxygen molecule is diatomic like the hydrogen, then one molecule of water contains one atom of oxygen and two atoms of hydrogen. Since the weight ratio between the oxygen and hydrogen in water is eight to one, the atomic weight of oxygen must be sixteen times that of hydrogen.

Through such considerations, supported by certain other rules, it has gradually proved possible to obtain reliable figures for the ratios between the atomic weights of all known elements and the atomic weight of hydrogen. For convenience it was customary to assign the number 1 to the latter and to call the ratio between the weight of the atom of a given element and the weight of the hydrogen atom the atomic weight of the element in question. Thus the atomic weight of oxygen is 16, that of carbon 12, because one carbon atom weighs as much as 12 hydrogen atoms. Nitrogen has the atomic weight 14, sulphur 32, copper 63.6, etc.

A summary of the chemical properties and chemical compounds was greatly facilitated by the symbolic system initiated by the Swedish chemist, Berzelius. In this system the initial of the Latin name of the element is made to indicate the el still hides in Helen's bosom? Does the conflict which it symbolizes beset her heart?

The enchanted mirror is still again, and a curious scene is reflected from it. A large and lofty room, windowless, lit by flaring lamps hung at intervals round the walls; the panels contain carvings in bas-relief of Egyptian emblems and devices; columns surround the central space, their capitals carved with the lotos-flower, their bases planted amidst papyrus leaves. A border of hieroglyphic inscription encircles the walls, just beneath the ceiling. In each corner of the room rests a red granite sarcophagus, and between each pair of pillars stands a mummy in its wooden case. At that end farthest from the low-browed doorway--which is guarded by two great figures of Isis and Osiris, sitting impassive, with hands on knees--is raised an altar of black marble, on which burns some incense. The perfumed smoke, wavering upwards, mingles with that of the lamps beneath the high ceiling. The prevailing color is ruddy Indian-red, relieved by deep blue and black, while brighter tints show here and there. Blocks of polished stone pave the floor, and dimly reflect the lights.

In front of the altar stands a ministerial figure,--none other than Manetho, who must have taken orders,--and joins together, in holy matrimony, the yellow-bearded Thor and the dark-haired Helen. Master Hiero, his round, snub-nosed face icles which the chemists reckon with in the chemical processes, but it does not follow from the theory that these building stones in themselves are indivisible. The theory leaves the way open to the idea that they are composed of smaller parts. A belief founded on such an idea was indeed enunciated by the Englishman, Prout, a short time after Dalton had developed his atomic theory. Prout assumed that the hydrogen atoms were the fundamental ones, and that the atoms of the other elements consisted of a smaller or larger number of the atoms of hydrogen. This might explain the fact that within the limits of experimental error, many atomic weights seemed to be integral multiples of that of hydrogen--16 for oxygen, 14 for nitrogen, and 12 for carbon, etc. This led to the possibility that the same might hold for all elements, and this hypothesis gave impetus to very careful determinations of atomic weights. These, however, showed that the assumption of the integral multiples could not be verified. It therefore seemed as if Prout's hypothesis would have to be given up. It has, however, recently come into its own again, although the situation is more complicated than Prout had imagined .

Dalton's atomic theory gave no information about the atoms except that the atoms of each element had a definite constant weight, and that they could combine to form molecules in certain simple ratios. What the forces are which unite them into such combinations, and why they prefer certain unions to others, were very perplexing problems, which could only be solved when chemical and physical research had collected a great mass of information as a surer source of speculation.

From the knowledge of atomic weights it was easy to calculate what weight ratios might be found to exist in chemical compounds, the molecules of which consisted of simple atomic combinations. Thus many compounds which were later produced in the laboratory were first predicted theoretically, but only a small part of the total number of possible compounds could actually be produced. Clearly it was one of the greatest problems of chemistry to find the laws governing these cases.

As mentioned above, one atom of oxygen combines with two atoms of hydrogen to form water, while one atom of chlorine combines with but one atom of hydrogen to form hydrogen chloride. The oxygen atom thus seems to be "equivalent" to two hydrogen atoms or two chlorine atoms, while one chlorine atom is "equivalent" to one hydrogen atom. The atoms of hydrogen and chlorine are for this reason called monovalent, while that of oxygen is called divalent. Again an acid is a chemical compound containing hydrogen, in which the hydrogen can be replaced by a metal to produce a metallic salt. Thus, when zinc is dissolved by sulphuric acid to form hydrogen and the salt zinc sulphate, the hydrogen of the acid is replaced by the zinc and the chemical change may be expressed by the formula

Zn+H?SO? ? H?+ZnSO?

In this, one atom of zinc changes place with two atoms of hydrogen. The zinc atom is therefore divalent. This is consistent with the fact that one zinc atom will combine with one oxygen atom to form zinc oxide. To take another example, if silver is dissolved in nitric acid, one atom of silver is exchanged for one atom of hydrogen. Silver, therefore, is monovalent, and we should expect that one atom of oxygen would unite with two atoms of silver. Some elements are trivalent, as, for example, nitrogen, which combines with hydrogen to form ammonia, NH?; others, again, are tetravalent, such as carbon, which unites with hydrogen to form marsh gas CH?, and with oxygen to form carbon dioxide CO?. A valence greater than seven or eight has not been found in any element.

If we consider the matter rather roughly and more or less as Gassendi did, we can explain the concept of valence by assuming that the atoms possess hooks; thus hydrogen and chlorine are each furnished with one hook, oxygen and zinc with two hooks, nitrogen with three hooks, etc. When a hydrogen atom and a chlorine atom are hooked together, there are no free hooks left, and consequently the compound is said to be saturated. When one hydrogen atom is hooked into each of the hooks of an oxygen or carbon atom the saturation is also complete .

The matter is not so simple as this, however, since the same element can often appear with different valences. Iron may be divalent, trivalent or hexavalent in different compounds. In many cases, however, where an examination of the weight ratios seems to show that an element has changed its valence, this is not really true. It was mentioned previously that carbon forms another compound with hydrogen in addition to CH?, namely, ethylene, containing half as much hydrogen in proportion to the same amount of carbon. With the aid of Avogadro's Law, it is found that the ethylene molecule is not CH? but C?H?. Thus we can say that the two carbon atoms in the molecule are held together by two pairs of hooks, and consequently the compound can be expressed by the formula

H-C-H ? H-C-H

On the other hand, the apparent absence of an element in certain places in the table cannot by any means be looked upon as irregular. In Mendelejeff's first system there were many vacant spaces. With the help of his table Mendelejeff was, to some extent, able to predict the properties of the missing elements. An example of this is the case of the element between gallium and arsenic. This is called germanium, and was discovered to have precisely the properties which had been predicted for it--a discovery which was one of the greatest triumphs in favour of the reality of the periodic system. On the whole, the elements discovered since the time of Mendelejeff have found their natural positions in the table. This is seen, for example, in the case of the so-called "inactive gases" of the atmosphere, helium, argon, neon, xenon, krypton and niton, which have the common property of being able to form no chemical combinations whatever. Their valence is therefore zero, and in the table they are placed by themselves in a separate column headed with zero.

To explain the mystery of the periodic system, it was necessary to make clear not only the regularity of it, but also the apparent irregularities which seemed to be arbitrary individual peculiarities of certain elements or groups. In the periodic system, chemistry laid down some rather searching tests for future theories of atomic structure.

THE PERIODIC OR NATURAL SYSTEM OF THE ELEMENTS

The Molecular Theory of Physics.

From a consideration of the chemical properties of the elements we shall now turn to an examination of the physical characteristics, although in a certain sense chemistry itself is but one special phase of physics.

If matter is really constructed of independently existing particles--atoms and molecules--the interplay of the individual parts must determine not only the chemical activities, but also the other properties of matter. Since most of these properties are different for different substances, or in other words are "molecular properties," it is reasonable to suppose that in many cases explanations can be more readily given by considering the molecules as the fundamental parts. It is natural that the first attempts to develop a molecular theory concerned gases, for their physical properties are much simpler than those of liquids or solids. This simplicity is indeed easily understood on the molecular theory. When a liquid by evaporation is transformed into a gas, the same weight of the element has a volume several hundred times greater than before. The molecules, packed together tightly in the liquid, in the gas are separated from each other and can move freely without influencing each other appreciably. When two of them come very close to each other, mutually repulsive forces will arise to prevent collision. Since it must be assumed that in such a "collision" the individual molecules do not change, they can then to a certain extent be considered as elastic bodies, spheres for instance.

From considerations of this nature the kinetic theory of gases developed. According to this a mass of gas consists of an immense number of very small molecules. Each molecule travels with great velocity in a straight line until it meets an obstruction, such as another molecule or the wall of the containing vessel; after such an encounter the molecule travels in a second direction until it collides again, and so on. The pressure of the gas on the wall of the container is the result of the very many collisions which each little piece of wall receives in a short interval of time. The magnitude of the pressure depends upon the number, mass and velocity of the molecules. The velocity will be different for the individual molecules in a gas, even if all the molecules are of the same kind, but at a given temperature an average velocity can be determined and used. If the temperature is increased, this average molecular velocity will be increased, and if at the same time the volume is kept constant, the pressure of the gas on the walls will be increased. If the temperature and the average velocity remain constant while the volume is halved, there will be twice as many molecules per cubic centimetre as before. Therefore, on each square centimetre of the containing wall there will be twice as many collisions, and consequently the pressure will be doubled. Boyle's Law, that the pressure of a gas at a given temperature is inversely proportional to its volume, is thus an immediate result of the molecular theory.

The molecular theory also throws new light upon the correspondence between heat and mechanical work and upon the law of the conservation of energy, which about the middle of the nineteenth century was enunciated by the Englishman, Joule, the Germans, Mayer and Helmholtz, and the Dane, Colding. A brief discussion of heat and energy will be given here, since some conception of these phenomena is necessary in understanding what follows.

If a moving body meets resistance, or if its free fall is halted by a fixed body, it might seem as if, at last, the energy were lost. This, however, is not the case, for another transformation occurs. Every one knows that heat is developed by friction, and that heat can produce work, as in a steam-engine. Careful investigations have shown that a given amount of mechanical work will always produce a certain definite amount of heat, that is, 400 foot-pounds of work, if converted into heat, will always produce 1 B.T.U. of heat, which is the amount necessary to raise the temperature of 1 pound of water 1? F. Conversely, when heat is converted into work, 1 B.T.U. of heat "vanishes" every time 400 foot-pounds of work are produced. Heat then is just a special form of energy, and the development of heat by friction or collision is merely a transformation of energy from one form to another.

All these results of the atomic and molecular theory, however, gave no information about the absolute weight of the individual atoms and molecules, nor about their magnitude nor the number of molecules in a cubic centimetre at a given temperature and pressure. As long as such questions were unsolved there was a suggestion of unreality in the theory. The suspicion was easily aroused that the theory was merely a convenient scheme for picturing a series of observations, and that atoms and molecules were merely creations of the imagination. The theory would seem more plausible if its supporters could say how large and how heavy the atoms and molecules were. The molecular theory of gases showed how to solve these problems which chemistry had been powerless to solve.

In addition to the velocity of the molecules, the length of the mean free path depends upon the average distance between the centres of two neighbouring molecules and upon their size. There is difficulty in defining the size of molecules because, as a rule, each contains at least two atoms; but it is helpful to consider the molecules, temporarily, as elastic spheres. Even with this assumption we cannot yet determine their dimensions from the mean free path, since there are two unknowns, the dimensions of the molecules and their number per cubic centimetre. Upon these two quantities depends, however, also the volume which will contain this number of molecules, if they are packed closely together. If we assume that we meet such a packing when the substance is condensed in liquid form, this volume can be calculated from a knowledge of the ratio between the volume in liquid form and the volume of the same mass in gaseous form . Then from this result and the length of the mean free path the two unknowns can be determined. Although the assumptions are imperfect, they serve to give an idea about the dimensions of the molecules; the results found in this way are of the same order of magnitude as those derived later by more perfect methods of an electrical nature.

The radius of a molecule, considered as a sphere, is of the order of magnitude 0?1 ??, where ?? means 10?? millimetre or 0?001 micron. Even if a molecule is by no means a rigid sphere, the value given shows that the molecule is almost unbelievably small, or, in other words, that it can produce appreciable attraction and repulsion in only a very small region in space.

The number of molecules in a cubic centimetre of gas at 0? C. and atmospheric pressure has been calculated with fair accuracy as approximately 27 x 10??. From this number and from the weight of a cubic centimetre of a given gas the weight of one molecule can be found. One hydrogen molecule weighs about 1?65 x 10??? grams, and one gram of hydrogen contains about 6 x 10?? atoms and 3 x 10?? molecules. The weight of the atoms of the other elements can be found by multiplying the weight of the hydrogen atom by the relative atomic weight of the element in question--16 for oxygen, 14 for nitrogen, etc. If the pressure on the gas is reduced as much as possible there will still be 3 x 10?? molecules in a cubic centimetre, and the average distance between molecules will be about one micron. The mean free path between two collisions will be considerable, about two metres, for instance, in the case of hydrogen.

The values found for the number, weight and dimensions of molecules are either so very large or so extremely small that many people, instead of having more faith in the atomic and molecular theory, perhaps may be more than ever inclined to suppose the atoms and molecules to be mere creations of the imagination. In fact, it is only two or three decades ago that some physicists and chemists--led by the celebrated German scientist, Wilhelm Ostwald--denied the existence of atoms and molecules, and even went so far as to try to remove the atomic theory from science. When these sceptics, in defence of their views, said that the atoms and molecules were, and for ever would be, completely inaccessible to observation, it had to be admitted at that time that they were seemingly sure of their argument, in this one objection at any rate.

A series of remarkable discoveries at the close of the nineteenth century so increased our knowledge of the atoms and improved the methods of studying them that all doubts about their existence had to be silenced. However incredible it may sound, we are now in a position to examine many of the activities of a single atom, and even to count atoms, one by one, and to photograph the path of an individual atom. All these discoveries depend upon the behaviour of atoms as electrically charged, moving under the influence of electrical forces. This subject will be developed in another section after a discussion of some phenomena of light, an understanding of which is necessary for the appreciation of the theory of atomic structure proposed by Niels Bohr.

In the molecular theory of gases, where we have to do with neutral molecules, much progress has in the last years been made by the Dane, Martin Knudsen, in his experiments at a very low pressure, when the molecules can travel relatively far without colliding with other molecules. While his researches give information on many interesting and important details, his work gives at the same time evidence of a very direct nature concerning the existence of atoms and molecules.

LIGHT WAVES AND THE SPECTRUM

The Wave Theory of Light.

On the surface of a body of water there may exist at the same time several wave systems; large waves created by winds which have themselves perhaps died down, small ripples produced by breezes and running over the larger waves, and waves from ships, etc. The form of the surface and the changes of form may thus be very complicated; but the problem is simplified by combining the motions of the individual wave systems at any given point. If one system at a given time gives a crest and another at the same instant also gives a crest at the same point, the two together produce a higher crest. Similarly, the resultant of two simultaneous troughs is a deeper trough; a crest from one system and a simultaneous trough from the other partially destroy or neutralize each other. A very interesting yet simple case of such "interference" of two wave systems is obtained when the systems have equal wave-lengths and equal amplitudes. Such an interference can be produced by throwing two stones, as much alike as possible, into the water at the same time, at a short distance from each other. When the two sets of wave rings meet there is created a network of crests and troughs. Figs. 4 and 5 show photographs of such an interference, produced by setting in oscillation two spheres which were suspended over a body of water.

The velocity of light in free space is a constant, the same for all wave-lengths. It was first determined by the Danish astronomer Ole R?mer by observations of the moons of Jupiter. According to the measurements of the present day the velocity of light is about 1,000,000 feet or 300,000 kilometres per second. In centimetres it is thus about 3 x 10??.

In the latter part of the nineteenth century the German physicist, H. Hertz, succeeded in producing electromagnetic waves with oscillations of the order of magnitude of 100,000,000 per second, corresponding to wave-lengths of the order of magnitude of several metres.

Moreover, he proved the existence of the oscillating electric forces by producing electric sparks in a circle of wire held in the path of the waves. He showed also that these electromagnetic waves were reflected and interfered with each other according to the same laws as in the case of light waves. After these discoveries there could be no reasonable doubt that light waves were actually electromagnetic waves, but so small that it would be totally impossible to examine the oscillations directly with the assistance of electric instruments.

But there was in this work of Hertz no solution of the problems about the nature of ether and the processes underlying the oscillations. More and more, scientists have been inclined to rest satisfied with the electromagnetic description of light waves and to give up speculation on the nature of the ether. Indeed, within the last few years, specially through the influence of Einstein's theory of relativity, many doubts have arisen as to the actual existence of the ether. The disagreement about its existence is, however, more a matter of definition than of reality. We can still talk about light as consisting of ether waves if we abandon the old conception of the ether as a rigid elastic body with definite material properties, such as specific gravity, hardness and elasticity.

The Dispersion of Light.

It has been said that the wave-length of light is much shorter than that of the Hertzian waves. This does not mean that all light waves have the same wave-length and frequency. The light which comes to us from the sun is composed of waves of many different wave-lengths and frequencies, to each of which corresponds a particular colour.

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