The atom and the Bohr theory of its structure

Introduction.

As early as 400 b.c. the Greek philosopher, Democritus, taught that the world consisted of empty space and an infinite number of small invisible particles. These particles, differing in form and magnitude, by their arrangements and movements, by their unions and disunions, caused the existence of physical bodies with different characteristics, and also produced the observed variations in these bodies. This theory, which no doubt antedated Democritus, later became known as the Atomic Theory, since the particles were called atoms, i.e. the “indivisible.”

But the atomic conception was not the generally accepted one in antiquity. Aristotle (384-322 b.c.) 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 had thus a sound physical basis, and proved particularly attractive to those philosophers who tried to explain the mysterious activity of matter in terms of exact measurements. The atomic hypothesis was never completely overthrown, being supported after the time of Aristotle by Epicurus (c. 300 b.c.), who introduced the term “atom,” and by the Latin poet, Lucretius (c. 75 b.c.) in his De Rerum Natura. Even in the Middle Ages it was supported by men of independent thought, such as Nicholas of Autrucia, who assumed that all natural activities were due to unions or disunions of atoms. It is interesting to note that in 1348 he was forced to retract this heresy. With the impetus given to the new physics by Galileo (1600) the atomic view gradually spread, sometimes explicitly stated as atomic theory, sometimes as a background for the ideas of individual philosophers. Various investigators developed comprehensive atomic theories in which they attempted to explain nearly everything from purely arbitrary hypotheses; they occasionally arrived at very curious and amusing conceptions. For example, about 1650 the Frenchman, Pierre Gassendi, following some of the ancient atomists, explained the solidity of bodies by assuming a hook-like form of atom so that the various atoms in a solid body could be hooked together. He thought of frost as an element with tetrahedral atoms, that is, atoms with four plane faces and with four vertices each; the vertices produced the characteristic pricking sensation in the skin. A much more thorough treatment of the atomic theory was given by Boscovich (1770). He saw that it was unnecessary to conceive of the atoms as spheres, cubes, or other sharply defined physical bodies; he considered them simply as points in space, mathematical points with the additional property of being centres of force. He assumed that any two atoms influenced each other with a force which varied, according to a complicated formula, with the distance between the centres. But the time was hardly ripe for such a theory, inspired as it evidently was by Newton’s teachings about the gravitational forces between the bodies of the universe. Indeed there were no physical experiments whose results could, with certainty, be assumed to express the properties of the individual atoms.

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 (1627-1691) 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 rôle 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 (1660-1734), 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 (not a compound) 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.

Weighing had indeed been used previously in chemical experiments, but the experimenters had been satisfied with very crude precision, and the results had little influence on chemical theory. For example, the phlogiston theory was maintained in spite of the fact that it was well known that metallic oxide weighed more than the metal from which it was obtained. Lavoisier now showed, by very careful weighings, that chemical combinations or decompositions can never change the total weight of the substances involved; a given quantity of metallic oxide weighs just as much as the metal and the oxygen taken individually, or vice versa. From the point of view of the atomic theory, this obviously means that the weight of individual atoms is not changed in the combinations of atoms which occur in the chemical processes. In other words, the weight of an atom is an invariable quantity. Here, then, we have the first property of the atom itself to be established by experiment—a property, indeed, which most atomists had already tacitly assumed.

Moreover, by the practice of weighing it was determined that to every chemical combination there corresponds a definite weight ratio among the constituent parts. This also had been previously accepted by most chemists as highly probable; but it must be admitted that the law at one time was assailed from several sides.

In comparing the weight ratios in different chemical compounds certain rules were, in the meantime, obtained. In many ways the most important of these, the so-called law of multiple proportions, was enunciated in the beginning of the last century by the Englishman, John Dalton. As an example of this law we may take two compounds of carbon and hydrogen called methane or marsh gas and ethylene, in which the quantities of hydrogen compounded with the same quantity of carbon are as two is to one. Another example may be seen in the compounds of carbon and oxygen. In the two compounds of carbon and oxygen, carbon monoxide and carbon dioxide, the weight ratios between the carbon and oxygen are respectively as three to four and three to eight. A definite quantity of carbon has thus in carbon dioxide combined with just twice as much oxygen as in carbon monoxide. No less than five oxygen compounds with nitrogen are known, where with a given quantity of nitrogen the oxygen is combined in ratios of one, two, three, four and five.

These simple number relations can be explained very easily by the atomic theory, by assuming, first, that all atoms of the same element have the same weight; and second, that in a chemical combination between two elements the atoms combine to form an atomic group characteristic of the compound in question—a compound atom, as Dalton called it, or a molecule, as the atomic group is now called. These molecules consist of comparatively few atoms, as, for example, one of each kind, or one of one kind and two, three or four of another, or two of one kind and three or four of another, etc. When three elements are involved in a chemical compound the molecule must contain at least three atoms, but there may be four, five, six or more. The law of multiple proportions thus takes on a more complicated character, but it remains apparent even in this case.

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.

While Dalton’s theory could not give information about the absolute weights in grams of the atoms of various elements, it could say something about the relative atomic weights, i.e., the ratios of the weights of the different kinds of atoms, although it is true that these ratios could not always be determined with certainty. If, for example, the ratio between the oxygen and hydrogen in water is found to be as eight to one, then the weight ratio between the oxygen atom and the hydrogen atom will be as eight to one, if the water molecule is composed of one oxygen atom and one hydrogen atom (as Dalton supposed, see Fig. 2). But it will be as sixteen to one, if the water molecule is composed of one oxygen and two hydrogen atoms (as we now know to be the case). On the other hand, a ratio of seven to one will be compatible with the experimental ratio of eight to one only if we assume that the water molecule consists of fifteen atoms, eight of oxygen and seven of hydrogen, a very improbable hypothesis. In another case let us compare the quantities of oxygen and of hydrogen which are compounded with the same quantities of carbon in the two substances, carbon monoxide and methane respectively. On the assumption that the molecules in question have a simple structure, we can draw conclusions about the ratio of the atomic weights of hydrogen and oxygen. Now, if a ratio such as seven to one or fourteen to one is obtained while the analysis of water gives eight to one or sixteen to one, then either the structure of the molecule is more complicated than was assumed, or the analyses must be improved by more careful experiments. We can thus understand that the atomic theory can serve as a controlling influence on the analysis of chemical compounds.

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.

A much firmer foundation for the choice made appears later in the Avogadro Law; starting with the fact that different gases show great similarity in their physical conduct—for instance, all expand by an increase of ¹/₂₇₃ of their volume with an increase in temperature from 0° C. to 1° C.—the Italian, Avogadro, in 1811, put forward the hypothesis that equal volumes of all gases at the same temperature and pressure contain equal numbers of molecules. A few examples suffice to show the usefulness of this rule.

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 (sometimes with one other letter from the Latin name) is made to indicate the element itself, an atom of the element, and its atomic weight with respect to hydrogen as unity, while a small subscript to the initial designates the number of atoms to be used. For example, in the chemical formula for sulphuric acid, H₂SO₄, the symbolic formula means that this substance is a chemical compound of hydrogen, sulphur and oxygen, that the acid molecule consists of two atoms of hydrogen, one atom of sulphur and four atoms of oxygen, and that the weight ratios between the three constituent parts is as 2×1 = 2 to 32 to 4×16 = 64, or as 1:16:32. To say that the chemical formula of zinc chloride is ZnCl₂ means that the zinc chloride molecule consists of one atom of zinc and two atoms of chlorine. Furthermore the changes which take place in a chemical process may be indicated in a very simple way. Thus the decomposition of water into hydrogen and oxygen may be represented by the so-called chemical “equation” 2H₂O ⇾ 2H₂+O₂, where H₂ and O₂ signify the molecules of hydrogen and oxygen respectively. Conversely, the combination of hydrogen and oxygen to form water will be given by the equation 2H₂+O₂ ⇾ 2H₂O.

As a consequence of the development of the atomic theory the atoms of the elements became, so to speak, the building stones of which the elements and the chemical compounds are built. It can also be said that the atoms are the smallest particles 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 (see p. 97).

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 (corresponding to simple atomic combinations) could actually be produced. Clearly it was one of the greatest problems of chemistry to find the laws governing these cases.

It had early been known that the elements seemed to fall into two groups, characterized by certain fundamental differences, the metals and the metalloids. In addition, there were recognized two very important groups of chemical compounds, i.e. acids and bases, possessing the property of neutralizing each other to form a third group of compounds, the so-called salts. The phenomenon called electrolysis, in which an electric current separates a dissolved salt or an acid into two parts which are carried respectively with and against the direction of the current, indicates strongly that the forces holding the atoms together in the molecule are of an electrical nature, i.e. of the same nature as those forces which bring together bodies of opposite electrical charges. One is led to denote all metals as electropositive and all metalloids as electronegative, which means that in a compound consisting of a metal and a metalloid the metal appears with a positive charge and the metalloid with a negative charge. The chemist Berzelius did a great deal to develop electrical theories for chemical processes. Great difficulties, however, were encountered, some proving for the time being insurmountable. Such a difficulty, for example, is the circumstance that two atoms of the same kind (like two hydrogen atoms) can unite into a diatomic molecule, although one might expect them to be similarly electrified and to repel rather than attract each other.

Another circumstance playing a very important part in determining the chemical compounds which are possible, is the consideration of what is called valence.

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+H₂SO₄ ⇾ H₂+ZnSO₄

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, NH₃; others, again, are tetravalent, such as carbon, which unites with hydrogen to form marsh gas CH₄, and with oxygen to form carbon dioxide CO₂. 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 (see Fig. 3, A, B, C).

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 CH₄, 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 CH₂ but C₂H₄. 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

where the dashes correspond to hooks (cf. Fig. 3, D). Such a formula is called a structural formula.

Even if we are not allowed to think of the atoms in the molecules as held together by hooks, it is well to have some sort of concrete picture of molecular structure. It is possible to represent the tetravalent carbon atom in the form of a tetrahedron, and to consider the united atoms or atomic groups as placed at the four vertices. With such a spatial representation we can get an idea about many chemical questions which otherwise would be difficult to explain. We know, for example, that two compound molecules having the same kind and number of atoms and the same bonds (and hence the same structural formulæ), may yet be different in that they are images of each other like a pair of gloves. Substances whose molecules are symmetrical in this way can be distinguished from each other by their different action on the passage of light. This molecular chemistry of space, or stereo-chemistry as it is called, has proved of great importance in explaining difficult problems in organic chemistry, i.e. the chemistry of carbon. Although there have never been many chemists who really have believed the carbon atom to be a rigid tetrahedron, we must admit that in this way it has been possible to get on the track of the secrets of atomic structure.

In comparing the properties of the elements with their atomic weights, there has been discovered a peculiar relation which remained for a long time without explanation, but which later suggested a certain connection between the inner structure of an atom and its chemical properties. We refer to the natural or periodic system of the elements which was enunciated in 1869 by the Russian chemist, Mendelejeff, and about the same time and independently by the German, Lothar Meyer. This system will be understood most clearly by examining the table on p. 23, where the elements with their respective atomic weights and chemical symbols are arranged in numbered columns so that the atomic weights increase upon reading the table from left to right or from top to bottom. It will be seen that in each of the nine columns there are collected elements with related properties, forming what may be called chemical families. The table as here given is of a recent date and differs from the old table of Mendelejeff, both in the greater number of elements and in the particulars of the arrangement. With each element there is associated a number which indicates its position in the series with respect to increasing atomic weight. Thus hydrogen has the number 1, helium 2, etc., up to uranium, the atom of which is the heaviest of any known element, and to which the number 92 is given. In each of the columns the elements fall naturally into two sub-groups, and this division is indicated in the table by placing the chemical symbols to the right or left in the column.

On close examination it becomes evident that the regularity in the system is not entirely simple. First of all some cases will be found where the atomic weight of one element is greater than that of the following element. (The cases of argon and potassium on the one hand and cobalt and nickel on the other are examples.) Such an interchange is absolutely necessary if the elements which belong to the same chemical family are to be placed in the same column. As a second instance of irregularity, attention must be called to Column VIII. in the table. While in the first score or so of elements it is always found that two successive elements have different properties and clearly belong to distinct chemical families, in the so-called iron group (iron, cobalt and nickel) we meet with a case where successive elements resemble each other in many respects (for instance, in their magnetic properties). Since there are two more such “triads” in the periodic system, however, we cannot properly call this an irregularity. But in addition to these difficulties there is what we may even call a kind of inelegance presented by the so-called “rare earths” group. In this group there follow after lanthanum thirteen elements whose properties are rather similar, so that it is very difficult to separate them from each other in the mixtures in which they occur in the minerals of nature. (In the table these elements are enclosed in a frame.)

On the other hand, the apparent absence of an element in certain places in the table (indicated by a dash) 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.

To lift a stone of 5 pounds through a distance of 10 feet demands an expenditure of work amounting to 5 × 10 = 50 foot-pounds; but the stone is now enabled to perform an equally large amount of work in falling back these 10 feet. The stone, by its height above the earth and by the attraction of the earth, now has in its elevated position what is called “potential” energy to the amount of 50 foot-pounds. If the stone as it falls lifts another weight by some such device as a block and tackle, the potential energy lost by the falling stone will be transferred to the lifted one. If the apparatus is frictionless, the falling stone can lift 5 pounds 10 feet or 10 pounds 5 feet, etc., so that all the 50 foot-pounds of potential energy will be stored in the second stone. If instead of being used to lift the second stone, the original stone is allowed to fall freely or to roll down an inclined plane without friction, the velocity will increase as the stone falls, and, as the potential energy is lost, another form of energy, known as energy of motion or kinetic energy, is gained. Conversely, a body when it loses its velocity can do work, such as stretching a spring or setting another body in motion. Let us suppose that the stone is fastened to a cord and is swinging like a pendulum in a vacuum where there is no resistance to its motion. The pendulum will alternately sink and rise again to the same height. As the pendulum sinks, the potential energy will be changed into kinetic energy, but as it rises again the kinetic will be exchanged for potential. Thus there is no loss of energy, but merely a continuous exchange between the two forms.

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.

With the assistance of the molecular theory it becomes possible to interpret as purely mechanical the transformation of mechanical work into heat energy. Let us suppose that a falling body strikes a piston at the top of a gas-filled cylinder, closed at the bottom. If the piston is driven down, the gas will be compressed and therefore heated, for the speed of the molecules will be increased by collisions with the piston in its downward motion. In this example the kinetic energy given to the piston by the exterior falling body is used to increase the kinetic energy of the molecules of the gas. When the molecules contain more than one atom, attention must also be given to the rotations of the atoms in a molecule about each other. A part of any added kinetic energy in the gas will be used to increase the energy of the atomic rotations.

The next step is to assume that, in solids and liquids, heat is purely a molecular motion. Here, too, the development of heat after collision with a moving body should be treated as a transformation of the kinetic energy of an individual, visible body into an inner kinetic energy, divided among the innumerable invisible molecules of the heated solid or liquid. In considering the internal conduct of gases it is unnecessary (at least in the main) to consider any inner forces except the repulsions in the collisions of the molecules. In solids and liquids, however, the attractions of the tightly packed molecules for each other must not be neglected. Indeed the situation is too complicated to be explained by any simple molecular theory. Not all energy transformations can be considered as purely mechanical. For instance, heat can be produced in a body by rays from the sun or from a hot fire, and, conversely, a hot body can lose its heat by radiation. Here, also, we are concerned with transformations of energy; therefore the law for the conservation of energy still holds, i.e. the total amount of energy can neither be increased nor decreased by transformations from one form to another. For the production of 1 B.T.U. of heat a definite amount of radiation energy is required; conversely, the same amount of radiation energy is produced when 1 B.T.U. of heat is transformed into radiation. This change cannot, however, be explained as the result of mechanical interplay between bodies in motion.

The mechanical theory of heat is very useful when we restrict ourselves to the transfer of heat from one body to another, which is in contact with it. When applied to gases the theory leads directly to Avogadro’s Law. If two masses of gas have the same temperature, i.e., if no exchange of heat between them takes place even if they are in contact with each other, then the average value of the kinetic energy of the molecules must be the same in both gases. If one gas is hydrogen and the other oxygen, the lighter hydrogen molecules must have a greater velocity than the heavier oxygen molecules; otherwise they cannot have the same kinetic energy (the kinetic energy of a body is one-half the product of the mass and the square of the velocity). Since the pressure of a gas depends upon the kinetic energy of the molecules and upon their number per cubic centimetre, at the same temperature and pressure equal volumes must contain equal numbers of oxygen and of hydrogen molecules. As Joule showed in 1851, from the mass of a gas per cubic centimetre and from its pressure per square centimetre, the average velocity of the molecules can be calculated. For hydrogen at 0° C. and atmospheric pressure the average velocity is about 5500 feet per second; for oxygen under the same conditions it is something over 1300 feet per second.

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.

Let us assume that the temperature of a mass of gas is 100° C. at a certain altitude, and 0° C. one metre lower, i.e., the molecules have different average velocities in the two places. The difference between the velocities will gradually decrease and disappear on account of molecular collisions. We might expect this “levelling out” process or equilibration to proceed very rapidly because of the great velocity of the molecules, but we must consider the fact that the molecules are not entirely free in their movements. In reality they will travel but very short distances before meeting other molecules, and consequently their directions of motion will change. It is easy to understand that the difference between the velocities of the molecules of the gas will not disappear so quickly when the molecules move in zigzag lines with very short straight stretches. The greater velocity in one part of the gas will then influence the velocity in the other part only through many intermediate steps. Gases are therefore poor conductors of heat. When the molecular velocity of a gas and its conductivity of heat are known, the average length of the small straight pieces of the zigzag lines can be calculated—in other words, the length of the mean free path. This length is very short; for oxygen at standard temperature and pressure it is about one ten-thousandth of a millimetre, or 0·1 μ, where μ is 0·001 millimetre or one micron.

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 (in other words, upon the number of molecules per cubic centimetre) 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 (at 0° C. and atmospheric pressure). 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 μμ, where μμ means 10⁻⁶ 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 × 10¹⁸. 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 × 10⁻²⁴ grams, and one gram of hydrogen contains about 6 × 10²³ atoms and 3 × 10²³ 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 (to about one ten-millionth of an atmosphere) there will still be 3 × 10¹² 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.