THE ATOM
AND THE BOHR THEORY
OF ITS STRUCTURE

Original Title:
“Bohr’s Atomteori, almenfatteligt fremstillet”

Translated from the Danish by R. B. Lindsay,
Fellow of the American-Scandinavian Foundation,
1923, and Rachel T. Lindsay

THE ATOM AND
THE BOHR THEORY
OF ITS STRUCTURE

An Elementary Presentation

BY

H. A. KRAMERS

LECTURER AT THE INSTITUTE OF THEORETICAL PHYSICS
IN THE UNIVERSITY OF COPENHAGEN

AND

HELGE HOLST

LIBRARIAN AT THE ROYAL TECHNICAL COLLEGE OF COPENHAGEN

WITH A FOREWORD BY

SIR ERNEST RUTHERFORD, F.R.S.

NEW YORK
ALFRED A. KNOPF
1923

PRINTED IN GREAT BRITAIN BY
MORRISON AND GIBB LTD., EDINBURGH

PREFACE

At the close of the nineteenth century and the beginning of the twentieth, our knowledge of the activities in the interior of matter experienced a development which surpassed the boldest hopes that could have been entertained by the chemists and physicists of the nineteenth century. The smallest particles of chemistry, the atoms of the elements, which hitherto had been approached merely by inductive thought, now became tangible realities, so to speak, which could be counted and whose tracks could be photographed. A series of remarkable experimental investigations, stimulated largely by the English physicist, J. J. Thomson, had disclosed the existence of negatively charged particles, the so-called electrons, ¹/₂₀₀₀ the mass of the smallest atom of the known elements. A theory of electrons, based on Maxwell’s classical electrodynamical theory and developed mainly through the labours of Lorentz in Holland and Larmor in England, had brought the problem of atomic structure into close connection with the theory of radiation. The experiments of Rutherford proved, beyond a doubt, that atoms were composed simply of light, negative electric particles, and small heavy, positive electric particles. The new “quantum theory” of Planck was proving itself very powerful in overcoming grave difficulties in the theory of radiation. The time thus seemed ripe for a comprehensive investigation of the fundamental problem of physics—the constitution of matter, and an explanation in terms of simple general laws of the physical and chemical properties of the atoms of the elements.

During the first ten years of the new century the problem was attacked with great zeal by many scientists, and many interesting atomic models were developed and studied. But most of these had more significance for chemistry than for physics, and it was not until 1913 that the work of the Danish physicist, Niels Bohr, paved the way for a really physical investigation of the problem in a remarkable series of papers on the spectrum and atomic structure of hydrogen. The ideas of Bohr, founded as they were on the quantum theory, were startling and revolutionary, but their immense success in explaining the facts of experience after a time won for them the wide recognition of the scientific world, and stimulated work by other investigators along similar lines. The past decade has witnessed an enormous development at the hands of scientists in all parts of the world of Bohr’s original conceptions; but through it all Bohr has remained the leading spirit, and the theory which, at the present time, gives the most comprehensive view of atomic structure may, therefore, most properly bear the name of Bohr.

It is the object of this book to give the reader a glimpse of the fundamental conceptions of this theory, together with some of the most significant results it has attained. The book is designed to meet the needs of those who wish to keep abreast of modern developments in science, but have neither time nor inclination to delve into the highly mathematical abstract literature in which the developments are usually concealed. It is with this in mind that the first four chapters have been devoted to a general survey of those parts of physics and chemistry which have close connection with atomic theory. No attempt has been made at a mathematical development, and the physical meaning of such mathematical formulæ as do occur has been clearly emphasized in the text. It is hoped, however, that even those readers whose acquaintance with atomic theory is more than casual, will find the book a stimulus to further study of the Bohr theory.

Here we wish to record our best thanks to Mr. and Mrs. Lindsay for the ability and the great care with which they have carried out the translation from the Danish original.

FOREWORD

During the last decade there has been a great advance in our knowledge of the structure of the atom and of the relation between the atoms of the chemical elements. In the later stages, science owes much to the remarkable achievements of Professor Niels Bohr and his co-workers in Copenhagen. For the first time, we have been given a consistent theory to explain the arrangement and motion of the electrons in the outer atom. The theory of Bohr is not only able to account in considerable detail for the variation in the properties of the elements exemplified by the periodic law, but also for the main features of the spectra, both X-ray and optical, shown by all elements.

This volume, written by Dr. Kramers and Mr. Holst, gives a simple and interesting account of our knowledge of atomic structure, with special reference to the work of Professor Bohr. Dr. Kramers is in an especially fortunate position to give a first-hand account of this subject, for he has been a valued assistant to Professor Bohr in developing his theories, and has himself made important original contributions to our knowledge in this branch of inquiry.

I can confidently recommend this book to English readers as a clearly written and accurate account of the development of our ideas on atomic structure. It is written in simple language, and the essential ideas are explained without mathematical calculations. This book should prove attractive not only to the general scientific reader, but also to the student who wishes to gain a broad general idea of this subject before entering into the details of the mathematical theory.

E. RUTHERFORD.

Cavendish Laboratory,
Cambridge, 8th October 1923.

CONTENTS

THE ATOM AND
THE BOHR THEORY
OF ITS STRUCTURE

CHAPTER I
ATOMS AND MOLECULES

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.

Fig. 1.—The four elements and the four fundamental characteristics.

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.

Simple

Binary

Ternary

Quaternary

Fig. 2.—Representation of a part of Dalton’s atomic table (of 1808) where the atom of each element has its own symbol, and chemical compounds are indicated by the union of the atoms of the elements into groups by 2, 3, 4 ... (binary, ternary, quaternary ... atoms). Below are given the designations of the different atoms, and in parentheses the atomic weight given by Dalton with that of hydrogen as unity and the designations of the indicated atomic groups.

Atoms of the Elements.—1. Hydrogen (1); 2. Azote (5); 3. Carbon (5); 4. Oxygen (7); 5. Phosphorus (9); 6. Sulphur (13); 7. Magnesia (20); 8. Lime (23); 9. Soda (28); 10. Potash (42); 11. Strontites (46); 12. Barytes (68); 13. Iron (38); 14. Zinc (56); 15. Copper (56); 16. Lead (95); 17. Silver (100); 18. Platina (100); 19. Gold (140); 20. Mercury (167).

Chemical Compounds.—21. Water; 22. Ammonia; 23. 26. 27. and 30. Oxygen compounds of Azote; 24. 29. and 33. Hydrogen compounds of Carbon; 25. Carbon monoxide; 28. Carbon dioxide; 31. Sulphuric acid; 32. Hydro-sulphuric acid.

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.

Fig. 3.—Rough illustrations of the valences of the elements.

A. Hydrogen chloride (HCl); B. Water (H₂O); C. Methane (CH₄); D. Ethylene (C₂H₄).

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.

CHAPTER II
LIGHT WAVES AND THE SPECTRUM

The Wave Theory of Light.

There have been several theories about the nature of light. The great English physicist, Isaac Newton (1642-1727), who was a pioneer in the study of light as well as in that of mechanics, favoured an atomic explanation of light; i.e., he thought that it consisted of particles or light corpuscules which were emitted from luminous bodies like projectiles from a cannon. In contrast to this “emission” theory was the wave theory of Newton’s contemporary, the Dutch scientist, Huygens. According to him, light was a wave motion passing from luminous bodies into a substance called the ether, which filled the otherwise empty universe and permeated all bodies, at least all transparent ones. In the nineteenth century the wave theory, particularly through the work of the Englishman, Young, and the Frenchman, Fresnel, came to prevail over the emission theory. Since the wave theory plays an important part in the following chapters, a discussion of the general characteristics of all wave motions is appropriate here. The examples will include water waves on the surface of a body of water, and sound waves in air.

Fig. 4.—Photograph of the interference between two similar wave systems.

Fig. 5.—A section of the same picture enlarged.

(From Grimsehl, Lehrbuch der Physik.)

Let us suppose that we are in a boat which is anchored on a body of water and let us watch the regular waves which pass us. If there is neither wind nor current, a light body like a cork, lying on the surface, rises with the wave crests and sinks with the troughs, going forward slightly with the former and backward with the latter, but remaining, on the whole, in the same spot. Since the cork follows the surrounding water particles, it shows their movements, and we thus see that the individual particles are in oscillation, or more accurately, in circulation, one circulation being completed during the time in which the wave motion advances a wave-length, i.e., the distance from one crest to the next. This interval of time is called the time of oscillation, or the period. If the number of crests passed in a given time is counted, the oscillations of the individual particles in the same time can be determined. The number of oscillations in the unit of time, which we here may take to be one minute, is called the frequency. If the frequency is forty and the wave-length is three metres, the wave progresses 3 × 40 = 120 metres in one minute. The velocity with which the wave motion advances, or in other words its velocity of propagation, is then 120 metres per minute. We thus have the rule that velocity of propagation is equal to the product of frequency and wave-length ([cf. Fig. 8]).

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.

Fig. 6.—Schematic representation of an interference.

In [Fig. 6] there is a schematic representation of an interference of the same nature. Let us examine the situation at points along the lower boundary line. At 0, which is equidistant from the two wave centres, there is evidently a wave crest in each system; therefore there is a resultant crest of double the amplitude of a single crest if the two systems have the same amplitude. Half a period later there is a trough in each system with a resultant trough of twice the amplitude of a single trough. Thus higher crests and deeper troughs alternate. The same situation is found at point 2, a wave-length farther from the left than from the right wave centre; in fact, these results are found at all points such as 2, 2′, 4 and 4′, where the difference in distance from the two wave centres is an even number of wave-lengths. At the point 1, on the other hand, where the difference between the distance from the centres is one-half a wave-length, a crest from one system meets a trough from the other, and the resultant is neither crest nor trough but zero. There is the same result at points 1′, 3, 3′, 5, 5′, etc., where the difference between the distances from the two wave centres is an odd number of half wave-lengths. By throwing a stone into the water in front of a smooth wall an interference is obtained, similar to the one described above. The waves are reflected from the wall as if they came from a centre at a point behind the wall and symmetrically placed with respect to the point where the stone actually falls.

Fig. 7.—Waves which are reflected by a board and pass through a hole in it.

When a wave system meets a wall in which there is a small hole, this opening acts as a new wave centre, from which, on the other side of the wall, there spread half-rings of crests and troughs. But if the waves are small and the opening is large in proportion to the wave-length, the case is essentially different. Let us suppose that wave rings originate at every point of the opening. As a result of the co-operation of all these wave systems the crests and troughs will advance, just as before, in the original direction of propagation, i.e., along straight lines drawn from the original wave centre through the opening; lines of radiation, we may call them. It can be shown, however, that as these lines of radiation deviate more and more from the normal to the wall, the interference between wave systems weakens the resultant wave motion. If the deviation from the normal to the wall is increased, the weakening varies in magnitude, provided that the waves are sufficiently small; but even if the wave motions at times may thus “flare up” somewhat, still on the whole they will decrease as the deviation from the normal to the wall is increased. The smaller the waves in comparison to the opening, the more marked is the decrease of the wave motions as the distance from the normal to the wall is increased, and the more nearly the waves will move on in straight lines. That light moves in straight lines, so that opaque objects cast sharp shadows, is therefore consistent with the wave theory, provided the light waves are very small; though it is reasonable to expect that on the passage of light through narrow openings there will be produced an appreciable bending in the direction of the rays. This supposition agrees entirely with experiment. As early as the middle of the seventeenth century, the Italian Grimaldi discovered such a diffraction of light which passes through a narrow opening into a dark room.

Fig. 8.—Schematic representation of a wave.

A and B denote crests; C denotes a trough.
λ = wave-length. α = amplitude of wave.

If T denotes the time the wave takes to travel
from A to B, and ν = 1/T the frequency, the
wave velocity v will be equal to λ/T = λν.

Points P and P′ are points in the same phase.

In both light and sound the use of such terms as wave and wave motion is figurative, for crests and troughs are lacking. But this choice of terms is commendable, because sound and light possess an essential property similar to one possessed by water waves. What happens when a tuning-fork emits sound waves into the surrounding air, is that the air particles are set in oscillation in the direction of the propagation of sound. All the particles of air have the same period as the tuning-fork, and the number of oscillations per second determines the pitch of the note produced; but the air particles at different distances from the tuning-fork are not all simultaneously in the same phase or condition of oscillation. If one particle, at a certain distance from the source of sound and at a given time, is moving most rapidly away from the source, then at the same time there is another particle, somewhat farther along the direction of propagation, which is moving towards the source most rapidly. This alternation of direction will exist all along the path of the sound. Where the particles are approaching each other, the air is in a state of condensation, and where the particles are drawing apart, the air is in a state of rarefaction. While the individual particles are oscillating in approximately the same place, the condensations and rarefactions, like troughs and crests in water, advance with a velocity which is called the velocity of sound. If we call the distance between two consecutive points in the same phase a wave-length, and the number of oscillations in a period of time the frequency, then, as in the case of water waves, the velocity of propagation will be equal to the product of frequency and wave-length.

Light, like sound, is a periodic change of the conditions in the different points of space. These changes which emanate from the source of light, in the course of one period advance one wave-length, i.e., the distance between two successive points in the same phase and lying in the direction of propagation. As in the cases of sound and water waves, the velocity of propagation or the velocity of light is equal to the product of frequency and wave-length. If this velocity is indicated by the letter c, the frequency by ν and the wave-length by λ, then

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 Rømer (1676) by observations of the moons of Jupiter. According to the measurements of the present day the velocity of light is about 1,000,000,000 feet or 300,000 kilometres per second. In centimetres it is thus about 3 × 10¹⁰.

Efforts have been made to consider light waves, like sound waves, as produced by the oscillations of particles, not of the air, but of a particular substance, the “ether,” filling and permeating everything; but all attempts to form definite representations of the material properties of the ether and of the movements of its particles have been unsuccessful. The electromagnetic theory of light, enunciated about fifty years ago by the Scottish physicist, Maxwell, has furnished information of an essentially different character concerning the nature of light waves.

Let us suppose that electricity is oscillating in a conductor connecting two metal spheres, for instance. The spheres, therefore, have, alternately, positive and negative charges. Then according to Maxwell’s theory we shall expect that in the surrounding space there will spread a kind of electromagnetic wave with a velocity equal to that of light. Wherever these waves are, there should arise electric and magnetic forces at right angles to each other and to the direction of propagation of the waves; the forces should change direction in rhythm with the movements of electricity in the emitting conductor. By way of illustration let us assume that we have somewhere in space an immensely small and light body or particle with an electric charge. If, in the region in question, an electromagnetic wave motion takes place, then the charged particle will oscillate as a result of the periodically changing electrical forces. The particle here plays the same rôle as the cork on the surface of the water ([cf. p. 35]); the charged body thus makes the electrical oscillations in space apparent just as the cork shows the oscillations of the water. In addition to the electrical forces there are also magnetic forces in an electromagnetic wave. We can imagine that they are made apparent by using a very small steel magnet instead of the charged body. According to Maxwell’s theory, the magnet exposed to the electromagnetic wave will perform rapid oscillations. Maxwell came to the conclusion that light consisted of electromagnetic waves of a similar nature, but much more delicate than could possibly be produced and made visible directly by electrical means.

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.

In this respect also light may be compared with sound. In whatever way a sound is produced, it is in general of a complicated nature, composed of many distinct notes, each with its characteristic wave-length and frequency. Naturally the air particles cannot oscillate in several different ways simultaneously. At a given time, however, we can think of the condensation and rarefactions of the air or the oscillations of the particles corresponding to different tones, as compounded with each other in a way similar to that in which the resultant crests and troughs are produced on a body of water with several coexistent wave systems. When we say that the complicated wave-movement emitted from some sound-producing instrument consists of different tones, this does not only mean that we may imagine it purely mathematically as resolved into a series of simpler wave systems. The resolution may also take place in a more physical way. Let us assume that we have a collection of strings each of which will produce a note of particular pitch. Now, if sound waves meet this collection of strings, each string is set in oscillation by the one wave in the compound sound wave which corresponds to it. Each string is then said to act as a resonator for the note in question. The notes which set the resonator strings in oscillation sound more loudly in the neighbourhood of the resonators; but, as the wave train continues on its journey the tones taken out by the strings will become weak in contrast to those notes which found no corresponding strings. The resonator is said to absorb the notes with which it is in pitch.

Light which is composed of different colours, i.e., of wave systems with different wave-lengths, can also be resolved or dispersed, but by a method different from that in the case of sound.

When light passes from one medium to another, as from air to glass or vice versa, it is refracted, i.e., the direction of the light rays is changed; but if the light is composed of different colours the refraction is accompanied by a “spreading” of the colours which is called dispersion. If we look through a glass prism so that the light from the object examined must pass in and out through two faces of the prism which make not too great an angle with each other, the light-producing object is not only displaced by the refraction, but has coloured edges. Newton was the first to explain the relation of the production of the colours to refraction. He made an experiment with sunlight, which he sent through a narrow opening into a dark room. The sunlight was then by a glass prism transformed or dispersed into a band of colour, a spectrum consisting of all the colours of the rainbow, red, yellow, green, blue and violet, in the order named, and with continuous transition stages between neighbouring colours.

Fig. 9.—Prism spectroscope. To the right is seen the collimator,
to the left the telescope, in the foreground a scheme for
illuminating the cross-wire.

(From an old print.)

In Newton’s original experiment the different wave-lengths were but imperfectly separated. A spectrum with pure wave-lengths can be obtained with a spectroscope ([cf. Fig. 9]). The light to be investigated illuminates an adjustable vertical slit in one end of a long tube, called the collimator, with a lens in the other end. If the slit is in the focal plane of the lens, the light at any point in the slit goes in parallel rays after meeting the lens. It then meets a prism, with vertical edges, placed on a little revolving platform. The rays, refracted by the prism, go in a new direction into a telescope whose objective lens gives in its focal plane, for every colour, a clear vertical image of the slit. These images can be examined through the ocular of the telescope; but since the different colours are not refracted equally, each coloured image of the slit has its own place. The totality of the slit images then forms a horizontal spectrum of the same height as the individual images. By revolving the collimator different parts of the spectrum can be put in the middle of the field of view. To facilitate measurements in the spectrum there is in the focal plane of the collimator a sliding cross-wire with an adjusting screw or a vertical strand of spider web.

Fig. 10.—The mode of operation of a grating.

A, grating; C, D, E ... H, slits; M M, incident rays. When D D′, E E′ ... are a whole number of wave-lengths, the light waves which move in the direction indicated by C N and are collected by a lens, at the focal point will all be in the same phase and therefore will reinforce each other. In other directions the light action from one slit is compensated by that from another.

Instead of using the refraction of light in a prism to separate the wave-lengths, we can use the interference which arises when a bundle of parallel light waves passes through a ruled grating, consisting of a great many very fine parallel lines, equidistant from each other; such a grating can be made by ruling lines with a diamond point on the metal coating of a silvered plate of glass. From each line there are sent out light waves in all directions; but if we are considering light of one definite colour (a given wave-length, monochromatic light), the interference among the waves from all the slits practically destroys all waves except in the direction of the original rays and in the directions making certain angles with the former, dependent upon the wave-length and the distance between two successive lines (the grating space). Monochromatic light can be obtained by using as the source of light a spirit flame, coloured yellow with common salt (sodium chloride). If the slit in a spectroscope is lighted with a yellow light from such a flame, and if a grating normal to the direction of the rays is substituted for the prism, then in the telescope there is seen a yellow image of the slit, and on each side of it one, two, three or more yellow images. If sunlight is used the central image is white, since all the colours are here assembled. The other images become spectra because the different colours are unequally refracted. In these grating spectra, which according to their distance from the central line are called spectra of the first, second or third order, the violet part lies nearest to the central line, the red part farthest away. Since the deflection is the greater the greater the wave-length, then violet light must have the shortest wave-length and red the greatest. From the amount of the refraction and the size of the grating space the wave-length of the light under investigation can be calculated.

For the yellow light from our spirit flame the wave-length is about 0·000589 mm. or 0·589 μ or 589 μμ. In centimetres the wave-length is 0·0000589 cm.; from the formula ν = c/λ, ν = 526 × 10¹². The frequency is thus almost inconceivably large. For the most distant red and violet in the spectrum the wave-lengths are respectively about 800 μμ and 400 μμ, and the frequencies 375 × 10¹² and 750 × 10¹² oscillations per second.

In scientific experiments a grating of specular metal with parallel rulings is substituted for the transparent grating. The spectrum is then given by the reflected light from the parts between the rulings. Specular gratings can be made by ruling on a concave mirror, which focuses the rays so that a glass lens is unnecessary. Gratings with several hundred lines or rulings to the millimetre give excellent spectra, with strength of light and marked dispersion. The preparation of the first really good gratings is due to the experimental skill of the American, Rowland, who in 1870 built a dividing engine from which the greater part of the good gratings now in use originate. The contribution which Rowland thereby made to physical science can hardly be over-estimated.

Spectral Lines.

In the early part of the nineteenth century Wollaston, in England, and later Fraunhofer in Germany, discovered dark lines in the solar spectrum, a discovery which meant that certain colours were missing. The most noticeable of these so-called “Fraunhofer Lines” were named with the letters A, B, C, D, E, F, G, H, from red to violet. It was later discovered that some of the lines were double, that the D-line, for instance, can be resolved into D₁ and D₂; other letters, such as b and h, were introduced to denote new lines. With improvements in the methods of experiment and research the number of lines has increased to hundreds and even thousands. The light from a glowing solid or liquid element forms, on the other hand, a continuous spectrum, i.e. a spectrum which has no dark lines. An illustration of the solar spectrum with the strongest Fraunhofer lines is given at the end of the book.

In contrast to the solar spectrum with dark lines on a bright background are the so-called line spectra, which consist of bright lines on a dark background. The first known line spectrum was the one given by light from the spirit flame coloured with common salt, mentioned in connection with monochromatic light. As has been said, this spectrum had just one yellow line which was later found to consist of two lines close to each other. It is sodium chloride which colours the flame yellow. The colour is due, not to the chlorine, but to the sodium, for the same double yellow line can be produced by using other sodium salts not compounded with chlorine. The yellow light is therefore called sodium light. [No. 7 in the table of spectra at the end of the book] shows the spectrum produced by sodium vapour in a flame. (On account of the small scale in the figure it is not shown that the yellow line is double.)

Another interesting discovery was soon made, namely, that the sodium line has exactly the same wave-length as the light lacking in the solar spectrum, where the double D-line is located. About 1860 Kirchhoff and Bunsen explained this remarkable coincidence as well as others of the same nature. They showed by direct experiment that if sodium vapour is at a high temperature it can not only send out the yellow light, but also absorb light of the same wave-length when rays from a still warmer glowing body pass through the vapour. This phenomenon is something like that in the case of sound waves where a resonator absorbs the pitch which it can emit itself. The existence of the dark D-line in the solar spectrum must then mean that in the outer layer of the sun there is sodium vapour present of lower temperature than the white-hot interior of the sun, and that the light corresponding to the D-line is absorbed by the vapour. Several ingenious experiments, which cannot be described here, have given further evidence in favour of this explanation.

In the other line spectra, just as in that from the common salt flame, definite lines correspond to definite elements and not to chemical compounds. The emission of these lines is then not a molecular characteristic, but an atomic one. The line spectra of metals can often be produced by vaporizing a metallic salt in a spirit flame or in a hot, colourless gas flame (from a Bunsen burner). It is even better to use an electric arc or strong electric sparks. The atoms from which gaseous molecules are formed can also be made to emit light which by means of the spectroscope is shown to consist of a line spectrum. These results are obtained by means of electric discharges of various kinds, arcs, and spark discharges through tubes where the gas is in a rarefied state.

The other Fraunhofer lines in the solar spectrum correspond to bright lines in the line spectra of certain elements which exist here on earth. These Fraunhofer lines must then be assumed to be caused by the absorption of light by the elements in question. This may be explained by the presence of these elements as gases in the solar atmosphere, through which passes the light from the inner layer. This inner surface would in itself emit a continuous spectrum.

The work of Kirchhoff and Bunsen put at the disposal of science became a new tool of incalculable scope. First and foremost, spectrum examinations were taken into the service of chemistry as spectrum analysis. It has thus become possible to analyse quantities of matter so small that the general methods of chemistry would be quite powerless to detect them. It is also possible by spectrum analysis to detect minute traces of an element; several elements were in this way first discovered by the spectroscope. Moreover, chemical analysis has been extended to the study of the sun and stars. The spectral lines have given us answers to many problems of physics—problems which formerly seemed insoluble. Last but not least spectrum analysis has given us a key to the deepest secrets of the atom, a key which Niels Bohr has taught us how to use.

In the discussion of the spectrum we have hitherto restricted ourselves to the visible spectrum limited on the one side by red and on the other by violet. But these boundaries are in reality fortuitous, determined by the human eye. The spectrum can be studied by other methods than those of direct observation. The more indirect methods include the effect of the rays on photographic plates and their heating effect on fine conducting wires for electricity, held in various parts of the spectrum. It has thus been discovered that beyond the visible violet end of the spectrum there is an ultra-violet region with strong photographic activity and an infra-red region producing marked heat effects. There are both dark and light spectral lines in these new parts of the spectrum. The fact that glass is not transparent to ultra-violet or infra-red rays has been an obstacle in the experiments, but the difficulty can be overcome by using other substances, such as quartz or rock salt, for the prisms and lenses, or by substituting concave gratings. By special means it has been possible to detect rays with wave-lengths as great as 300 μ and as small as about 0·02 μ, corresponding to frequencies between 10¹², and 15 × 10¹⁵ vibrations per second, while the wave-lengths of the luminous rays lie between 0·8 and 0·4 μ. The term “light wave” is often used to refer to the ultra-violet and infra-red rays which can be shown in the spectra produced by prisms or gratings.

Fig. 11.—Photographic effect of X-rays, which are
passed through the atom grating in a magnesia crystal.

The electrically produced electromagnetic waves, as already mentioned, have wave-lengths much greater than 300 μ. In wireless telegraphy there are generally used wave-lengths of one kilometre or more, corresponding to frequencies of 300,000 vibrations per second or less. By direct electrical methods it has, however, not been possible to obtain wave-lengths less than about one-half a centimetre, a length differing considerably from the 0·3 millimetre wave of the longest infra-red rays. Wave-lengths much less than 0·02 μ or 20 μμ exist in the so-called Röntgen rays or X-rays with wave-lengths as small as 0·01 μμ corresponding to a frequency of 30 × 10¹⁸. These rays cannot possibly be studied even with the finest artificially made gratings, but crystals, on account of the regular arrangement of the atoms, give a kind of natural grating of extraordinary fineness. With the use of crystal gratings success has been attained in decomposing the Röntgen rays into a kind of spectrum, in measuring the wave-lengths of the X-rays and in studying the interior structure of the crystals. The German Laue, the discoverer of the peculiar action of crystals on X-rays (1912), let the X-rays beams pass through the crystal, obtaining thereby photographs of the kind illustrated in [Fig. 11]. Later on essential progress was due to the Englishmen, W. H. and W. L. Bragg, who worked out a method of investigation by which beams of X-rays are reflected from crystal faces. The greatest wave-length which it has been possible to measure for X-rays is about 1·5 μμ, which is still a long way from the 20 μμ of the furthermost ultra-violet rays.

It may be said that the spectrum since Fraunhofer has been made not only longer but also finer, for the accuracy of measuring wave-lengths has been much increased. It is now possible to determine the wave-length of a line in the spectrum to about 0·001 μμ or even less, and to measure extraordinarily small changes in wave-lengths, caused by different physical influences.

In addition to the continuous spectra emitted by glowing solids or liquids, and to the line spectra emitted by gases, and to the absorption spectra with dark lines, there are spectra of still another kind. These are the absorption spectra which are produced by the passage of white light through coloured glass or coloured fluids. Here instead of fine dark lines there are broader dark absorption bands, the spectrum being limited to the individual bright parts. There are also the band spectra proper, which, like the line spectra, are purely emission spectra, given by the light from gases under particular conditions; these seem to consist of a series of bright bands which follow each other with a certain regularity ([cf. Fig. 12]). With stronger dispersion the bands are shown to consist of groups of bright lines.

Fig. 12.—Spectra produced by discharges of different character
through a glass tube containing nitrogen at a pressure of ¹/₂₀
that of the atmosphere. Above, a band spectrum;
below, a line spectrum.

Since the line spectra are most important in the atomic theory, we shall examine them here more carefully.

The line spectra of the various elements differ very much from each other with respect to their complexity. While many metals give a great number of lines (iron, for instance, gives more than five thousand), others give only a few, at least in a simple spectroscope. With a more powerful spectroscope the simplicity of structure is lost, since weaker lines appear and other lines which had seemed single are now seen to be double or triple. Moreover, the number of lines is increased by extending the investigation to the ultra-violet and infra-red regions of the spectrum. The sodium spectrum, at first, seemed to consist of one single yellow line, but later this was shown to be a double line, and still later several pairs of weaker double lines were discovered. The kind and number of lines obtained depends not only upon the efficiency of the spectroscope, but also upon the physical conditions under which the spectrum is obtained.

The eager attempts of the physicists to find laws governing the distribution of the lines have been successful in some spectra. For instance, the line spectra of lithium, sodium, potassium and other metals can be arranged into three rows, each consisting of double lines. The difference between the frequencies of the two “components” of the double lines was found to be exactly the same for most of the lines in one of these spectra, and for the spectra of different elements there was discovered a simple relationship between this difference in frequency and the atomic weight of the element in question. But this regularity was but a scrap, so to speak; scientists were still very far from a law which could exactly account for the distribution of lines in a single series, not to mention the lines in an entire spectrum or in all the spectra.

The first important step in this direction was made about 1885 by the Swiss physicist, Balmer, in his investigations with the hydrogen spectrum, the simplest of all the spectra. In the visible part there are just three lines, one red, one green-blue and one violet, corresponding to the Fraunhofer lines C, F and h. These hydrogen lines are now generally known by the letters Hα, Hᵦ and Hᵧ. In the ultra-violet region there are many lines also.

Balmer discovered that wave-lengths of the red and of the green hydrogen line are to each other exactly as two integers, namely, as 27 to 20, and that the wave-lengths of the green and violet lines are to each other as 28 to 25. Continued reflection on this correspondence led him to enunciate a rule which can be expressed by a simple formula. When frequency is substituted for wave-length Balmer’s formula is written as

ν = K		1	-	1		,
		4		n²

where ν is the frequency of a hydrogen line, K a constant equal to 3·29 × 10¹⁵ and n an integer. If n takes on different values, ν becomes the frequency for the different hydrogen lines. If n = 1 ν is negative, for n = 2 ν is zero. These values of n therefore have no meaning with regard to ν. But if n = 3, then ν gives the frequency for the red hydrogen line Hα; n = 4 gives the frequency of the green line Hᵦ and n = 5 that of the violet line Hᵧ. Gradually more than thirty hydrogen lines have been found, agreeing accurately with the formula for different values of n. Some of these lines were not found in experiment, but were discovered in the spectrum of certain stars; the exact agreement of these lines with Balmer’s formula was strong evidence for the belief that they are due to hydrogen. The formula thus proved itself valuable in revealing the secrets of the heavens.

As n increases 1/n² approaches zero, and can be made as close to zero as desired by letting n increase indefinitely. In mathematical terminology, as n = ∞, 1/n² = 0 and ν = K/4 = 823 × 10¹², corresponding to a wave-length of 365 μμ. Physically this means that the line spectrum of hydrogen in the ultra-violet is limited by a line corresponding to that frequency. Near this limit the hydrogen lines corresponding to Balmer’s formula are tightly packed together. For n = 20 ν differs but little from K/4, and the distance between two successive lines corresponding to an increase of 1 in n becomes more and more insignificant. [Fig. 13], where the numbers indicate the wave-lengths in the Ångström unit (0·1 μμ), shows the crowding of the hydrogen lines towards a definite boundary. [The following table], where K has the accurate value of 3·290364 × 10¹⁵, shows how exactly the values calculated from the formula agree with experiment.

Fig. 13.—Lines in the hydrogen spectrum corresponding to the Balmer series.

Table of some of the Lines of the Balmer Series

From arguments in connection with the work of the Swedish scientist, Rydberg, in the spectra of other elements, Ritz, a fellow countryman of Balmer’s, has made it seem probable that the hydrogen spectrum contains other lines besides those corresponding to Balmer’s formula. He assumed that the hydrogen spectrum, like other spectra, contains several series of lines and that Balmer’s formula corresponds to only one series. Ritz then enunciated a more comprehensive formula, the Balmer-Ritz formula:

ν = K		1	-	1		,
		n″ ²		n′ ²

where K has the same value as before, and both n′ and n″ are integers which can pass through a series of different values. For n″ = 2, the Balmer series is given; to n″ = 1, and n′ = 2, 3 ... ∞ there corresponds a second series which lies entirely in the ultra-violet region, and to n″ = 3, n′ = 4, 5 ... ∞ a series lying entirely in the infra-red. Lines have actually been found belonging to these series.

Formulæ, similar to the Ritz one, have been set up for the line spectra of other elements, and represent pretty accurately the distribution of the lines. The frequencies are each represented by the difference between two terms, each of which contains an integer, which can pass through a series of values. But while the hydrogen formula, except for the n′s, depends only upon one constant quantity K and its terms have the simple form K/n², the formula is more complicated with the other elements. The term can often be written, with a high degree of exactness, as K/(n + α)², where K is, with considerable accuracy, the same constant as in the hydrogen formula. For a given element α can assume several different values; therefore the number of series is greater and the spectrum is even more complicated than that of hydrogen.

All these formulæ are, however, purely empirical, derived from the values of wave-lengths and frequencies found in spectrum measurements. They represent certain more or less simple bookkeeping rules, by which we can register both old and new lines, enter them in rows, arrange them according to a definite system. But from the beginning there could be no doubt that these rules had a deeper physical meaning which it was not yet possible to know. There was no visible correspondence between the spectral line formulæ and the other physical characteristics of the elements which emitted the spectra; not even in their form did the formulæ show any resemblance to formulæ obtained in other physical branches.

CHAPTER III
IONS AND ELECTRONS

Early Theories and Laws of Electricity.

The fundamental phenomena of electricity, which were first made the subject of careful study about two centuries ago, are that certain substances can be electrified by friction so that somehow they can attract light bodies, and that the charges of electricity may be either “positive” or “negative.” Bodies with like charges repel each other, while those with unlike charges attract each other, and either partially or entirely neutralize each other when they are brought close together. Moreover, it had long ago been discovered that in some substances electricity can move freely from place to place, while in others there is resistance to the movement. The former bodies are now called conductors and include metals, while the latter are called insulators, glass, porcelain and air being members of this class.

In order to explain the phenomena some imagined that there were two kinds of “electric substances” or “fluids”; and since no change in weight could be discovered in a body when it was electrified, it was, in general, assumed that the electric fluids were weightless. In the normal, neutral body it was believed that these fluids were mixed in equal quantities, thereby neutralizing each other; on this account they were supposed to be of opposite characteristics, so one was called positive and the other negative. According to a second theory, there was assumed to be just one kind of electricity, which was present in a normal amount in neutral bodies; positive electricity was caused by a superfluity of the fluid; negative, by a deficit. In both theories it was possible to talk of the amount of positive or negative electricity which a body contained or with which it was “charged,” because the supporters of the one-fluid idea understood by the terms positive and negative a superfluity and a deficit, respectively, of the one fluid. In both theories it was possible to talk about the direction of the electric current in a conductor, since the supporters of the two-fluid theory understood by “direction” that in which the electric forces sent the positive electricity, or the opposite to that in which the negative would be sent. It could not be decided whether positive electricity went in the one direction or the negative in the other, or whether each simultaneously moved in its own direction. Both theories were quite arbitrary in designating the electric charge in glass, which was rubbed with woollen cloth, as positive. On the whole, neither theory seemed to have any essential advantage over the other; the difference between them seemed to lie more in phraseology than in actual fact.

That the positive and negative states of electricity could not be taken as “symmetric” seemed, however, to follow from the so-called discharge phenomena, in which electricity, with the emission of light, streams out into the air from strongly charged (positive or negative) bodies, or passes through the air between positive and negative bodies in sparks, electric arcs or in some other way. In a discharge in air between a metal point and a metal plate, for instance, a bush-shaped glow is seen to extend from the point when the charge there is positive, while only a little star appears when the charge is negative.

Naturally, we cannot discuss here the many electric phenomena and laws, and must be satisfied with a brief description of those which are of importance in the atomic theory.

In this latter category belongs Coulomb’s Law, formulated about 1785. According to this law, the repulsions or attractions between two electrically charged bodies are directly as the product of the charges and inversely as the square of the distance between them (as in the case of the gravitational attraction between two neutral bodies, according to Newton’s Law). The unit in measuring electric charges can be taken as that amount which will repel an equal amount of electricity of the same kind at unit distance with unit force. If we use the scientific or “absolute” system, in which the unit of length is one centimetre, that of time one second and that of mass one gram, then the unit of force is one dyne, which is a little greater than the earth’s attraction on a milligram weight. Let us suppose that two small bodies with equal charges of positive (or negative) electricity are at a distance of one centimetre from each other. If they repel each other with a charge of one dyne, then the amount of electricity with which each is charged is called the absolute electrostatic unit of electricity. If one body has a charge three times as great and the other has a charge four times as great, the repulsion is 3 × 4 = 12 times greater. If the distance between the bodies is increased from one to five, the repulsion is twenty-five times as small, since 5² = 25. If the charge of one body is substituted by a negative one of same magnitude the repulsion becomes an attraction of the same magnitude.

In the early part of the nineteenth century methods were found for producing a steady electric current in metal wires. In 1820, the Danish physicist, H. C. Ørsted, discovered that an electric current influences a magnet in a characteristic way, and that, conversely, the current is affected by the forces emanating from the magnet, by a magnetic field in other words. The French scientist, Ampère, soon afterwards formulated exact laws for the electromagnetic forces between magnets and currents. In 1831, the English physicist, Faraday, discovered that an electric current is induced in a wire when currents or magnets in its neighbourhood are moved or change strength. Faraday’s views on electric and magnetic fields of force around currents and magnets were further of fundamental importance to the electromagnetic wave theory as developed by Maxwell. The branch of physics dealing with all these phenomena is now generally known as electrodynamics.

Fig. 14.—Picture of electrolysis of hydrogen chloride.

A, anode; K, cathode;
H, hydrogen atoms;
Cl, chlorine atoms.

Electrolysis.

Faraday also studied the chemical effects which an electric current produces upon being conducted between two metal plates, called electrodes, which are immersed in a solution of salts or acids. The current separates the salt or acid into two parts which are carried by the electric forces in two opposite directions. This separation is called electrolysis. If the liquid is dilute hydrochloric acid (HCl), the hydrogen goes with the current to the negative electrode, the cathode, and takes the positive electricity with it, while the chlorine goes against the current and takes the negative electricity to the positive electrode, the anode. We must then assume with the Swedish scientist, Arrhenius, that, under the influence of the water, the molecules of hydrogen chloride always are separated into positive hydrogen atoms and negative chlorine atoms, and that the electric forces from the anode and the cathode carry these atoms respectively with and against the current. The electrically charged wandering atoms are called ions, i.e. wanderers. The positive electricity taken by the hydrogen atoms to the cathode goes into the metal conductor, while the anode must receive from the metal conductor an equal amount of positive electricity to be given to the chlorine atoms to neutralize them. The negative charge of a chlorine atom must then be as large as the positive charge of a hydrogen atom. These assumptions imply that equal numbers of the two kinds of atoms are present in the whole quantity of atoms transferred in any period of time.

Faraday found that the quantity of hydrogen which in the above experiment is transferred to the cathode in a given time is proportional to the quantity of electricity transferred in the same time. A gram of hydrogen always takes the same amount of electricity with it. By experiment this amount of electricity can be determined, and, since the weight in grams of the hydrogen atom is known, it is possible to calculate the amount of one atom. In electrostatic units it is 4·77 × 10⁻¹⁰, i.e., 477 billionth[1] parts. A chlorine atom then carries with it 4·77 × 10⁻¹⁰ electrostatic units of negative electricity. Since its atomic weight is 35·5, then 35·5 grams of chlorine will take as much electricity as 1 gram of hydrogen. The ratio e/m between the charge e and the mass m is then 35·5 times as great for hydrogen as for chlorine.

[1] Billion used here to mean one million million, and trillion to mean one million billion.

We have temporarily restricted ourselves to the electrolysis of hydrogen chloride. Let us now assume that we have chloride of zinc (ZnCl₂), which, by electrolysis, is separated into chlorine and zinc. Each atom of chlorine will, as before, carry 4·77 × 10⁻¹⁰ units of negative electricity to the anode; but since zinc is divalent ([cf. p. 17]) and one atom of zinc is joined to two of chlorine, therefore one atom of zinc must carry a charge of 2 × 4·77 × 10⁻¹⁰ units of positive electricity to the cathode. An atom or a group of atoms, with valence of three, in electrolysis carries 3 × 4·77 × 10⁻¹⁰ units, etc.

We see then, that the quantity of electricity which accompanies the atoms in electrolysis is always 4·77 × 10⁻¹⁰ electrostatic units or an integral multiple thereof. This suggests the thought that electricity is atomic and that the quantity 4·77 × 10⁻¹⁰ units is the smallest amount of electricity which can exist independently, i.e., the elementary quantum of electricity or the “atom of electricity.” The atom of a monovalent element, when charged or ionized, should have one atom of electricity; a divalent, two, etc. On the two-fluid theory it was most reasonable to assume that there were two kinds of atoms of electricity representing, respectively, positive and negative electricity. In [Fig. 15] there is given, in accordance with the two-fluid theory, a rough picture of a chlorine ion and a hydrogen ion and their union into a molecule.

Fig. 15.—Provisional representation
(according to the two-fluid theory) of

A, a hydrogen ion; and
B, a chlorine ion; and
C, a molecule of hydrogen chloride.

The atoms of electricity seemed to differ essentially from the usual atoms of the elements in their apparent inability to live independently; they seemed to exist only in connection with the atoms of the elements. They would seem much more real if they could exist independently. That such existence really is possible, has been discovered by the study of the motion of electricity in gases.

Vacuum Tube Phenomena.

Fig. 16.—Vacuum tube with cathode rays and a shadow-producing cross.

P and N, conducting wires for the electric current;
a, cathode; b, anode and shadow-producer; c, d, the shadow.

Fig. 17.—Vacuum tube, where a bundle of
cathode rays are deviated by electric forces.

A, anode; K, cathode.

It has previously been said that air is an insulator for electricity, a statement which is, in general, true; however, as has also been said, electric sparks and arcs can pass through air. Moreover, it has been discovered that exhausted air is a very good conductor, so that a strong current can pass between two metal electrodes in a glass tube where the air is exhausted, if the electrodes are connected to an outer conductor by metal wires fused into the glass. In these vacuum tubes there are produced remarkable light effects, at first inexplicable. When the air is very much exhausted, to a hundred thousandth of the atmospheric pressure or less, strong electric forces (large difference of potential between the electrodes) are needed to produce an electric discharge. Such a discharge assumes an entirely new character; in the interior of the glass tube there is hardly any light to be seen, but the glass wall opposite the negative electrode (the cathode) glows with a greenish tint (fluorescence). If a small metal plate is put in the tube between the cathode and the glass wall, a shadow is cast on the wall, just as if light were produced by rays, emitted from the cathode at right angles to its surface (c[f. Fig. 16]). The English physicist, Crookes, was one of the first to study these cathode rays. He assumed that they are not ether waves like the light rays, but that they consist of particles which are hurled from the cathode with great velocity in straight lines; they light the wall by their collisions with it. There was soon no doubt as to the correctness of Crookes’ theory. The cathode rays are evidently particles of negative electricity, which by repulsions are driven from the cathode (the negative electrode). A metal plate bombarded by the rays becomes charged negatively. Let us suppose that we have a small bundle of cathode rays, obtained by passing the rays from the cathode K ([cf. Fig. 17]) through two narrow openings S₁ and S. It can then be shown that the bundle of rays is deviated not only by electric forces, but also by magnetic action from a magnet which is held near the glass. In the figure there is shown a deviation of the kind mentioned, caused by making the plates at B and C respectively positive and negative; since B attracts the negative particles and C repels them, the light spot produced by the bundle of rays is moved from M to M₁. The magnetic deviation is in agreement with Ørsted’s rules for the reciprocal actions between currents and magnets, if we consider the bundle of rays produced by moving electric particles as an electric current. (Since the electric particles travelling in the direction of the rays are negative, and since it is customary by the expression “direction of current” to understand the direction opposite to that in which the negative electricity moves, then, in the case of the cathode rays just mentioned, the direction of the current must be opposite to that of the rays.)

From measurements of the magnetic and electric deviations it is possible to find not only the velocity of the particles, but also the ratio e/m between the charge e of the particle and its mass m. The velocity varies with the potential at the cathode, and may be very great, 50,000 km. per second, for instance (about one-sixth the speed of light), or more. It has been found that e/m always has the same value, regardless of the metal of the cathode and of the gas in the tube; this means that the particles are not atoms of the elements, but something quite new. It has also been found that e/m is about two thousand times as large as the ratio between the charge and the mass of the hydrogen atom in electrolysis. If we now assume that e is just the elementary quantum of electricity 4·77 × 10¹⁰, which in magnitude amounts to the charge of the hydrogen atom in electrolysis (but is negative), then m must have about ¹/₂₀₀₀ the mass of the hydrogen atom. This assumption as to the size of e has been justified by experiments of more direct nature. The experiments with charge and mass of electrons which have in particular been carried out by the English physicist, J. J. Thomson, give reason then to suppose these quite new and unknown particles to be free atoms of negative electricity; they have been given the name of electrons. Gradually more information about them has been acquired. Thus it has been possible in various ways to determine directly the charge on the electron, independently of its mass. Special mention must be made of the brilliant investigations of the American, Millikan, on the motion of very small electrified oil-drops through air under the influence of an electric force. To Millikan is due the above-mentioned value of e, which is accurate to one part in five hundred. Further, the mass of the electron has been more exactly calculated as about ¹/₁₈₃₅ that of the hydrogen atom. Their magnitude has also been learned; the radius of the electron is estimated as 1·5 × 10⁻¹³ cm. or 1·5 × 10⁻⁶ μμ, an order of magnitude one ten-thousandth that of the molecule or atom.

After the atom of negative electricity had been isolated, in the form of cathode rays, the next suggestion was that corresponding positive electric particles might be discharged from the anode in a vacuum tube. By special methods success has been attained in showing and studying rays of positive particles. In order to separate them from the negative cathode ray particles the German scientist, Goldstein, let the positive particles pass through canals in the cathode; they are therefore called canal rays. The velocity of the particles is much less than that of the cathode rays, and the ratio e/m between charge and mass is much smaller and varies according to the gas in the tube. In experiments where the tube contains hydrogen, rays are always found for which e/m, as in electrolysis, is about ¹/₂₀₀₀ of the ratio in the cathode rays. Therefore there can be scarcely any doubt that these canal rays are made up of charged hydrogen atoms or hydrogen ions. The values found with other gases indicate that the particles are atoms (or molecules sometimes) of the elements in question, with charges one or more times the elementary quantum of electricity (4·77 × 10⁻¹⁰ electrostatic units). Research in this field has also been due in particular to J. J. Thomson. From his results, as well as from those obtained by other methods, it follows that positive electricity, unlike negative, cannot appear of its own accord, but is inextricably connected to the atoms of the elements.

The Nature of Electricity.

The earlier conceptions of a one or two-fluid explanation of the phenomena of electricity appear now in a new light. We are led to think of a neutral atom as consisting of one mass charged with positive electricity together with as many electrons negatively charged as are sufficient to neutralize the positive. If the atom loses one, two or three electrons, it becomes positive with a charge of one, two or three elementary quanta of electricity, or for the sake of simplicity and brevity we say that the atom has one, two or three “charges.” If, on the other hand, it takes up one, two or three extra electrons it has one, two or three negative charges. [Fig. 18] can give help in understanding these ideas, but it must not be thought that the electrons are arranged in the way indicated. The substances, which appear as electropositive in electrolysis—i.e. hydrogen and metals—should then be such that their atoms easily lose one or more electrons, while the electronegative elements should, on the other hand, easily take up extra electrons. Elements should be monovalent or divalent according as their atoms are apt to lose or to take up one or two electrons. From investigations with the vacuum tube it appears, however, that the atoms of the same element can in this respect behave in more ways than would be expected from electrolysis or chemical valence.

Fig. 18.—Provisional representation (according to the electron theory) of

A, a neutral atom; B, the same atom with two positive charges (a divalent positive ion)
and C, the same atom with two negative charges (a divalent negative ion).

When an electric current passes through a metal wire, it must be assumed that the atoms of the metal remain in place, while the electrical forces carry the electrons in a direction opposite to that which usually is considered as the direction of the current ([cf. p.70]). The motion of the electrons must not be supposed to proceed without hindrance, but rather as the result of a complicated interplay, by no means completely understood, whereby the electrons are freed from and caught by the atoms and travel backwards and forwards, in such a way that through every section of the metal wire a surplus of electrons is steadily passing in the direction opposite to the so-called direction of the current. The number of surplus electrons which in every second passes through a section of the thin metal wire in an ordinary twenty-five candle incandescent light, at 220 volts, amounts to about one trillion (10¹⁸), or 1000 million (10⁹) in 0·000,000,001 of a second. If the metal conducting wire ends in the cathode of a vacuum tube, the electrons carried through the wire pass freely into the tube as cathode rays from the cathode.

This motion of electricity agrees best with the one-fluid theory, since the electrons, which here alone accomplish the passage of the electricity, may be considered as the fundamental parts of electricity. In this respect the choice of the terms positive and negative is very unfortunate, since a body with a negative charge actually has a surplus of electrons. Moreover, the electrons really have mass; but since the mass of a single electron is only ¹/₁₈₃₅ that of the atom of the lightest element, hydrogen, and since in an electrified body which can be weighed by scale there is always but an infinitesimal number of charged atoms, it is easy to understand that, formerly, electricity seemed to be without weight.

In electrolysis, where the motion of electricity is accomplished by positive and negative ions, we have a closer connection with the two-fluid theory. In motions of electricity through air the situation suggests both the one-fluid and the two-fluid theories, since the passage of electricity is sometimes carried on exclusively by the electrons, and sometimes partly by them and partly by larger positive and negative ions, i.e., atoms or molecules with positive and negative charges.

The Electron Theory.

Proceeding on the assumption that the electric and optical properties of the elements are determined by the activity of the electric particles, the Dutch physicist Lorentz and the English physicist Larmor succeeded in formulating an extraordinarily comprehensive “electron theory,” by which the electrodynamic laws for the variations in state of the ether were adapted to the doctrine of ions and electrons. This Lorentz theory must be recognized as one of the finest and most significant results of nineteenth century physical research.

It was one of the most suggestive problems of this theory to account for the emission of light waves from the atom. From the previously described electromagnetic theory of light ([cf. p. 42]) it follows that an electron oscillating in an atom will emit light waves in the ether, and that the frequency ν of these waves will naturally be equal to the number of oscillations of the electron in a second. If this last quantity is designated as ω, then

ν = ω

It may then be supposed that the electrons in the undisturbed atom are in a state of rest, comparable with that of a ball in the bottom of a bowl. When the atom in some way is “shaken,” one or more of the electrons in the atom begins to oscillate with a definite frequency, just as the ball might roll back and forth in the bowl if the bowl was shaken. This means that the atom is emitting light waves, which, for each individual electron have a definite wave-length corresponding to the frequency of the oscillations, and that, in the spectrum of the emitted light, the observed spectral lines correspond to these wave-lengths.

Strong support for this view was afforded by Zeeman’s discovery of the influence of a magnetic field upon spectral lines. Zeeman, a Dutch physicist, discovered, about twenty-five years ago, that when a glowing vacuum tube is placed between the poles of a strong electromagnet, the spectral lines in the emitted light are split so that each line is divided into three components with very little distance between them. It was one of the great triumphs of the electron theory that Lorentz was able to show that such an effect was to be expected if it was assumed that the oscillations of light were produced by small oscillating electric particles within the atom. From the experiments and from the known laws concerning the reciprocal actions of a magnet and an electric current (here the moving particle), the theory enabled Lorentz to find not only the ratio e/m between the electric charge of each of these particles and its mass, but also the nature of the charge. He could conclude from Zeeman’s experiment that the charge is negative and that the ratio e/m is the same as that found for the cathode rays. After this there could not well be doubt that the electrons in the atoms were the origin of the light which gives the lines of the spectrum. It seemed, however, quite unfeasible for the theory to explain the details in a spectrum—to derive, for instance, Balmer’s formula, or to show why hydrogen has these lines, copper those, etc. These difficulties, combined with the great number of lines in the different spectra, seemed to mean that there were many electrons in an atom and that the structure of an atom was exceedingly complicated.

Ionization by X-rays and Rays from Radium. Radioactivity.

As has been said, the electrons in a vacuum tube cause its wall to emit a greenish light when they strike it. Upon meeting the glass wall or a piece of metal (the anticathode) placed in the tube the electrons cause also the emission of the peculiar, penetrating rays called Röntgen rays in honour of their discoverer, or more commonly X-rays. They may be described as ultra-violet rays with exceedingly small wave-lengths ([cf. p. 54]). When, further, the electrons meet gas molecules in the tube they break them to pieces, separating them into positive and negative ions (ionization). The positive ions are the ones which appear in the canal rays. The ions set in motion by electrical forces can break other gas molecules to pieces, thus assisting in the ionization process. At the same time the gas molecules and atoms are made to produce disturbances in the ether, and thus to cause the light phenomena which arise in a tube which is not too strongly exhausted.

The free air can be ionized in various ways; this ionization can be detected because the air becomes more or less conducting. In fact, electric forces will drive the positive and negative ions through the air in opposite directions, thus giving rise to an electric current. If the ionization process is not steadily continued, the air gradually loses its conductivity, since the positive and negative ions recombine into neutral atoms or molecules. Ionization can be produced by flames, since the air rising from a flame contains ions. A strong ionization can also be brought about by X-rays and by ultra-violet rays. In the higher strata of the atmosphere the ultra-violet rays of the sun exercise an ionizing influence. Most of all, however, the air is ionized by rays from the so-called radioactive substances which in very small quantities are distributed about the world.

The characteristic radiation from these substances was discovered in the last decade of the nineteenth century by the French physicist, Becquerel, and afterwards studied by M. and Mme. Curie. From the radioactive uranium mineral, pitchblende, the latter separated the many times more strongly radioactive element radium. The proper nature of the rays was later explained, particularly through the investigations of the English physicists, Rutherford, Soddy and Ramsay. These rays, which can produce heat effects, photographic effects and ionization, are of three quite different classes, and accordingly are known as α-rays, β-rays, and γ-rays. The last named, like the X-rays, are ultra-violet rays, but they have often even shorter wave-lengths and a much greater power of penetration than the usual X-rays. The β-rays are electrons which are ejected with much greater velocity than the cathode rays; in some cases their velocity goes up to 99·8 per cent. that of light. The α-rays are positive atomic ions, which move with a velocity varying according to the emitting radioactive element from ¹/₂₀ to almost ¹/₁₀ that of light. It has further been proved that the α-particles are atoms of the element helium, which has the atomic weight 4, and that they possess two positive charges, i.e., they must take up two electrons to produce a neutral helium atom.

There is no doubt that the process which takes place in the emission of radiation from the radioactive elements is a transformation of the element, an explosion of the atoms accompanied by the emission either of double-charged helium atoms or of electrons, and the forming of the atoms of a new element. The energy of the rays is an internal atomic energy, freed by these transformations. The element uranium, with the greatest of all known atomic weights (238), passes, by several intermediate steps, into radium with atomic weight 226; from radium there comes, after a series of steps, lead, or, in any case, an element which, in all its chemical properties, behaves like lead. We shall go no further into this subject, merely remarking that the transformations are quite independent of the chemical combinations into which the radioactive elements have entered, and of all external influences.

When α-particles from radium are sent against a screen with a coating of especially prepared zinc sulphide, on this screen, in the dark, there can be seen a characteristic light phenomenon, the so-called scintillation, which consists of many flashes of light. Each individual flash means that an α-particle, a helium atom, has hit the screen. In this bombardment by atoms the individual atom-projectiles are made visible in a manner similar to that in which the individual raindrops which fall on the surface of a body of water are made visible by the wave rings which spread from the places where the drops meet the water. This flash of light was the first effect of the individual atom to be available for investigation and observation. The incredibility of anything so small as an atom producing a visible effect is lessened when, instead of paying attention merely to the small size or mass of the atom, its kinetic energy is considered; this energy is proportional to the square of the velocity, which is here of overwhelming magnitude. For the most rapid α-particles the velocity is 2·26 × 10⁹ cm. per second; their kinetic energy is then about ⁴/₃₀ of the kinetic energy of a weight of one milligram of a substance at a velocity of one centimetre per second. This energy may seem very small, but, at least, it is not a magnitude of “inconceivable minuteness,” and it is sufficient under the conditions given above to produce a visible light effect. We must here also consider the extreme sensitiveness of the eye.

Fig. 19.—Photograph of paths described by
α-particles (positive helium ions) emitted
from a radioactive substance.

More practical methods of revealing the effects of the individual α-particles and of counting them are founded on their very strong ionization power. By strengthening the ionization power of α-particles, Rutherford and Geiger were able to make the air in a so-called ionization chamber so good a conductor that an individual α-particle caused a deflection in an electrical apparatus, an electrometre.

Fig. 20.—Photograph of the path of a
β-particle (an electron).

(Both 19 and 20 are photographs by C. T. R. Wilson.)

With a more direct method the English scientist C. T. R. Wilson has shown the paths of the α-particles by making use of the characteristic property of ions, that in damp air they attract the neutral water molecules which then form drops of water with the ions as nuclei. In air which is completely free of dust and ions the water vapour is not condensed, even if the temperature is decreased so as to give rise to supersaturation, but as soon as the air is ionized the vapour condenses into a fog. When Wilson sent α-particles through air, supersaturated with water vapour, the vapour condensed into small drops on the ions produced by the particles; the streaks of fog thus obtained could be photographed. [Fig. 19] shows such a photograph of the paths of a number of atoms. When a streak of fog ends abruptly it does not mean that the α-particles have suddenly halted, but that their velocity has decreased so that they can no longer break the molecules of air to pieces, producing ions. The paths of the β-particles have been photographed in the same way, although an electron of the β-particles has a mass about 7000 times smaller than that of a helium atom; the electron has, however, a far greater velocity than the helium atom. This velocity causes the ions to be farther apart, so that each drop of water formed around the individual ions can appear in the photograph by itself ([cf. Fig. 20]).

CHAPTER IV
THE NUCLEAR ATOM

Introduction.

We are now brought face to face with the fundamental question, hardly touched upon at all in the previous part of this work, namely, that of the construction and mode of operation of the atomic mechanism itself. In the first place we must ask: What is the “architecture” of the atom, that is, what positions do the positive and negative particles take up with respect to each other, and how many are there of each kind? In the second place, of what sort are the processes which take place in an atom, and how can we make them interpret the physical and chemical properties of the elements? In this chapter we shall keep essentially to the first question, and consider especially the great contribution which Rutherford made in 1911 to its answer in his discovery of the positive atomic nucleus and in the development of what is known as the Rutherford atomic model or nuclear atom.

Rutherford’s Atom Model.

Rutherford’s discovery was the result of an investigation which, in its main outlines, was carried out as follows: a dense stream of α-particles from a powerful radium preparation was sent into a highly exhausted chamber through a little opening. On a zinc sulphide screen, placed a little distance behind the opening, there was then produced by this bombardment of atomic projectiles, a small, sharply defined spot of light. The opening was next covered by a thin metal plate, which can be considered as a piece of chain mail formed of densely-packed atoms. The α-particles, working their way through the atoms, easily traversed this “piece of mail” because of their great velocity. But now it was seen that the spot of light broadened out a little and was no longer sharply limited. From this fact one could conclude that the α-particles in passing among the many atoms in the metal plate suffered countless, very small deflections, thus producing a slight spreading of the rays. It could also be seen that some, though comparatively few, of the α-particles broke utterly away from the stream, and travelled farther in new directions, some, indeed, glancing back from the metal plate in the direction in which they had come ([cf. Fig. 21]). The situation was approximately as if one had discharged a quantity of small shot through a wall of butter, and nearly all the pellets had gone through the wall in an almost unchanged direction, but that one or two individual ones had in some apparently uncalled for fashion come travelling back from the interior of the butter. One might naturally conclude from this circumstance that here and there in the butter were located some small, hard, heavy objects, for example, some small pellets with which some of the projectiles by chance had collided. Accordingly, it seemed as if there were located in the metal sheet some small hard objects. These could hardly be the electrons of the metal atoms, because α-particles, as has been stated before, are helium atoms with a mass over seven thousand times that of a single electron; and if such an atom collided with an electron, it would easily push the electron aside without itself being deviated materially in its path. Hardly any other possibility remained than to assume that what the α-particles had collided with was the positive part of the atom, whose mass is of the same order of magnitude as the mass of the helium atom ([cf. Fig. 21]). A mathematical investigation showed that the large deflections were produced because the α-particles in question had passed, on their way, through a tremendously strong electric field of the kind which will exist about an electric charge concentrated into a very small space and acting on other charges according to Coulomb’s Law. When, in the foregoing, the word “collision” is used, it must not be taken to mean simply a collision of elastic spheres; rather the two particles (the α-particle and the positive particle of the metal atom) come so near to each other in the flight of the former that the very great electrical forces brought into play cause a significant deflection of the α-particles from their original course.

Fig. 21.—Tracks of α-particles in the interior of matter. While 1 and 3 undergo small deflections by collisions with electrons, 2 is sharply deflected by a positive nucleus.

Rutherford was thus led to the hypothesis that nearly all of the mass of the atom is concentrated into a positively charged nucleus, which, like the electrons, is very small in comparison with the size of the whole atom; while the rest of the mass is apportioned among a number of negative electrons which must be assumed to rotate about the nucleus under the attraction of the latter, just as the planets rotate about the sun. Under this hypothesis the outer limits of the atom must be regarded as given by the outermost electron orbits. The assumption of an atom of this structure makes it at once intelligible why, in general, the α-particles can travel through the atom without being deflected materially by the nuclear repulsion, and why the very great deflections occur as seldom as is indicated by experiment. This latter circumstance has, on the other hand, no explanation in the atomic model previously suggested by Lord Kelvin and amplified by J. J. Thomson, in which the positive electricity was assumed to be distributed over the whole volume of the atom, while the electrons were supposed to move in rings at varying distances from the centre of the atom.

Fig. 22.—Photograph of the paths of two α-particles
(positive helium ions).

One collides with an atomic nucleus.

The same characteristic phenomenon made evident in the passage of α-particles through substances by the investigations of Rutherford appears in a more direct way in Wilson’s researches discussed on [p. 81]. His photographs of the paths of α-particles through air supersaturated with water vapour ([see Fig. 22]) show pronounced kinks in the paths of individual particles. Thus in the figure referred to, there are shown the paths of two α-particles. One of these is almost a straight line (with a very slight curvature), while the other shows a very perceptible deflection as it approaches the immediate neighbourhood of the nucleus of an atom, and finally a very abrupt kink; at the latter place it is clear that the α-particle has penetrated very close to the nucleus. If one examines the picture more closely, there will be seen a very small fork at the place where the kink is located. Here the path seems to have divided into two branches, a shorter and a longer. This leads one at once to suspect that a collision between two bodies has taken place, and that after the collision each body has travelled its own path, just as if, to return to the analogy of the bombardment of the butter wall, one had been able to drive two pellets out of the butter by shooting in only one. Or, to take perhaps a more familiar example, when a moving billiard ball collides at random with a stationary one, after the collision they both move off in different directions. So, when the α-particle hits at random the atomic nucleus, both particle and nucleus move off in different directions; though in this case, since the nucleus has the much greater mass of the two, it moves more slowly, after the collision, than the α-particle, and has, therefore, a much shorter range in the air than the lighter, swifter α-particle. Had the gas in which the collisions took place been hydrogen, for example, the recoil paths of the hydrogen nuclei would have been longer than those of the α-particles, because the mass of the hydrogen nucleus is but one quarter the mass of the α-particle (helium atom).

The collision experiments on which Rutherford’s theory is founded are of so direct and decisive a character that one can hardly call it a theory, but rather a fact, founded on observation, showing conclusively that the atom is built after the fashion indicated. Continued researches have amassed a quantity of important facts about atoms. Thus, Rutherford was able to show that the radius of the nucleus is of the order of magnitude 10⁻¹² to 10⁻¹³cm. This means really that it is only when an α-particle approaches so near the centre of an atom that forces come into play which no longer follow Coulomb’s Law for the repulsion between two point charges of the same sign (in contrast to the case in the ordinary deflections of α-particles). It should be remarked, however, that in the case of the hydrogen nucleus theoretical considerations give foundation for the assumption that its radius is really many times smaller than the radius of the electron, which is some 2000 times lighter; experiments by which this assumption can be tested are not at hand at present.

The Nuclear Charge; Atomic Number; Atomic Weight.

It is not necessary to have recourse to a new research to determine the masses of the nuclei of various atoms, because the mass of the nucleus is for all practical purposes the mass of the atom. Accordingly, if the mass of the hydrogen nucleus is taken as unity, the atomic mass is equal to the atomic weight as previously defined. The individual electrons which accompany the nucleus are so light that their mass has relatively little influence (within the limits of experimental accuracy) on the total mass of the atom.

On the other hand, a problem of the greatest importance which immediately suggests itself is to determine the magnitude of the positive charge of the nucleus. This naturally must be an integral multiple of the fundamental quantum of negative electricity, namely, 4·77 × 10⁻¹⁰ electrostatic units, or if we prefer to call this simply the “unit” charge, then the nuclear charge must be an integer. Otherwise a neutral atom could not be formed of a nucleus and electrons, for in a neutral atom the number of negative electrons which move about the nucleus must be equal to the number of positive charges in the nucleus. The determination of this number is, accordingly, equivalent to the settling of the important question, how many electrons surround the nucleus in the normal neutral state of the atom of the element in question.

The answer to the question is easiest in the case of the helium atom. For when this is expelled as an α-particle, it carries, as Rutherford was able to show, a positive charge of two units—in other words, two electrons are necessary to change the positive ion into a neutral atom. At the same time there is every reason to suppose that the α-particle is simply a helium nucleus deprived of its electrons; it follows, therefore, that the electron system of the neutral helium atom consists of two electrons. Since the atomic weight of helium is four, the number of electrons is consequently one-half the atomic weight. Rutherford’s investigation of the deflections of α-particles in passing through various media had already led him to believe that for many other elements, to a considerable approximation, the nuclear charge and hence the number of electrons was equal to half the atomic weight. Hydrogen, of course, must form an exception, since its atomic weight is unity. The positive charge on the hydrogen nucleus is one elementary quantum, and in the neutral state of the atom, only one electron rotates about it. [Fig. 23] gives a representation of the structure of the hydrogen atom, and the structures of the two types of hydrogen ions formed respectively by the loss and gain of an electron. In the picture, the position of the electron is, of course, arbitrary, and for the sake of simplicity its path is supposed to be circular.

Fig. 23.—Schematic representation of the nuclear atom.

A, a neutral hydrogen atom;
B, a positive, and C, a negative hydrogen ion;
K, atomic nuclei; E, electrons.

As has just been indicated, Rutherford’s rule for the number of electrons is only an approximation. A Dutch physicist, van den Broek, conceived in the meantime the idea that the number of electrons in the atom of an element is equal to its order number in the periodic table (its “atomic number,” as it is now called). Especially through a systematic investigation of the X-ray spectra characteristic of the different elements this has proved to be the correct rule. In fact, using Bragg’s reflection method of X-rays from crystal surfaces ([cf. p. 54]), the Englishman, Moseley, made in 1914 the far-reaching discovery that these spectra possess an exceptionally simple structure, which made it possible in a simple way to attach an order number to each element ([given on p. 23]). On the basis of Bohr’s theory, established a year before, it could be directly proved that this order number must be identical with the number of positive elementary charges on the nucleus.

The number which formerly indicated simply the position of an element in the periodic system has thus obtained a profound physical significance, and in comparison the atomic weight has come to have but a secondary meaning. The inversion of argon and potassium in the periodic system [(mentioned on p. 21]), which seemed to be an exception to the regularity displayed by the system as a whole, obtains an easy explanation on the van den Broek rule; for to explain the inversion we need only assume that potassium has one electron more than argon, though its atomic weight is less than that of argon. We see at once that the atomic weight and number of electrons (or what is the same thing—the nuclear charge) are not directly correlated to each other. And since the periodic system based on the atomic number represents the correct arrangement of the elements according to their respective properties (especially their chemical properties), we are led naturally to the conclusion that it is the atomic number and not the atomic weight that determines chemical characteristics.

The conception of the relatively great importance of the atomic number as compared with the atomic weight has in recent years received overwhelming support from the researches of Soddy, Fajans, Russell, Hevesy and others who have discovered the existence of so-called isotope elements (from the Greek isos = same, and topos = place), substances with different nuclear masses (atomic weights) and different radioactive properties (if there are any), but with the same nuclear charge, the same number of electrons and, consequently, occupying the same place in the periodic system. Two such isotopes are practically equivalent in all their chemical properties as well as in most of their physical characteristics. One of the oldest examples of isotopes is provided by ordinary lead with the atomic weight 207·2 and the substance found in pitchblende with the atomic weight 206, but identical, chemically, with ordinary lead. This latter form of lead has already been [referred to on p. 79] as the end product of radioactive disintegrations, and hence it is sometimes called radium lead.

By his investigations of canal rays the English physicist Aston has just recently shown that many substances which have always been assumed to be simple elements, are in reality mixtures of isotopes. The atomic weight of chlorine determined in the usual way is 35·5, but in the discharge tube two kinds of chlorine atoms appear, having atomic weights 35 and 37 respectively; and it must be assumed that these two kinds of chlorine are present in all the compounds of chlorine known on the earth in the ratio of, roughly, three to one. To separate such mixtures into their constituent parts is extremely difficult, precisely because the constituents have identical properties apart from a small difference in density, which stands in direct connection with the atomic weight. Such a separation was first carried out successfully by the Danish chemist, Brønsted, in collaboration with the Hungarian chemist, Hevesy (1921). These two scientists were able to separate a large quantity of mercury of density 13·5955 into two portions of slightly different densities. All the different isotopes of which mercury is a mixture were, indeed, not wholly separated; they were represented in the two portions in different proportions. Thus, in one of the first attempts, the density of the one part was 13·5986 and of the other 13·5920 (at 0° C).

It is a perfectly reasonable supposition that it is the electron system which determines the external properties of the atom, that is, those properties which depend on the interplay of two or more atoms. For the electron, rotating about the nucleus at a considerable distance, separates, so to speak, the nucleus from the surrounding space, and must therefore be assumed to be the organ which connects the atom with the rest of the universe. One might also expect the structure of the electron system to depend wholly on the nuclear charge, i.e. on the atomic number and not on the mass of the nucleus, since it is the nuclear electrical attraction which holds the electrons in their orbits and not the relatively insignificant gravitational attraction.

It thus becomes intelligible that the properties of the elements can be divided into two sharply defined classes, namely: (1) properties of the nucleus, and (2) properties of the electron system in the atom. The credit for first recognizing the sharp distinction between these two classes, a distinction fundamental for a detailed study of the atom, is due to Niels Bohr.

The properties of the nucleus determine—(a) the radioactive processes, or explosions of the nucleus, and related processes; (b) collisions, where two nuclei approach extremely near to each other; and (c) weight which, as mentioned above, stands in direct connection with atomic weight. The properties of the electron system are, on the other hand, the determining factors in all other physical and chemical activities, and, as has been stated, are functions, we may say, of the atomic number of the given element. The Bohr theory may be said to concern itself with the chemical and physical properties of the atom with the exception of those which have to do with the nucleus. We shall consequently devote our attention in the next chapters to the electron system. But before turning to this we shall dwell a little further upon the atomic nucleus.

The Structure of the Nucleus.

That the nucleus is not an elementary indivisible particle but a system of particles, is clearly shown by the radioactive processes in which α-particles and β-particles (electrons) are shot out of the nuclei of radioactive elements. Bohr was the first to see clearly that not only the α-particles emitted in such cases come from the nucleus, but that the β-particles also have their source there. There is now no doubt that, in addition to the outer electrons of the atom, which are the determining factor in the atomic number, there must also be, in the radioactive substances at any rate, special nuclear electrons which lead a more hidden existence in the interior of the nucleus. One can easily understand that isotopes may result as products of radioactive disintegration. For example, let us suppose that a nucleus emits first an α-particle (i.e. a helium nucleus with two positive charges), and thereafter sends out two electrons, each with its negative charge, in two new disintegrations. The nuclear charge in the resultant atom will then obviously be the same as before, because the loss of the two electrons exactly neutralizes that of the α-particle. But the atomic weight will be diminished by four units (i.e. the weight of the helium nucleus, remembering also that the electrons have but very negligible masses). Among the radioactive substances are recognized many examples of isotope elements, with atomic weights differing precisely by four. The radioactive element uranium is the element with the greatest atomic weight (238), and atomic number (92), and consequently with the greatest nuclear charge. Almost all the other radioactive substances are those with high atomic numbers in the periodic system. The cause of radioactivity must be sought in the hypothesis that the nuclei of the radioactive elements are very complicated systems with small stability, and therefore break down rather easily into less complicated and more stable systems with the emission of some of their constituent particles; the corpuscular rays thus produced possess a considerable amount of kinetic energy.

Accordingly, by analogy, the nuclei of the non-radioactive elements may be assumed to be composed of nuclear electrons and positive particles; hydrogen alone excepted. The simplest assumption is that the hydrogen nucleus is the real quantum or atom of positive electricity, just as the electron is the atom of negative electricity. On this theory all substances are built up of two kinds only of fundamental particles, namely, hydrogen nuclei and electrons. That these particles may themselves consist of constituent parts is, of course, an open possibility, but such speculation is beyond our experience up to the present. In every nucleus there are more positive hydrogen nuclei than there are negative electrons, so that the nucleus has a residual positive charge of a magnitude equal to the difference between the number of hydrogen nuclei and nuclear electrons.

If we now pass from hydrogen which has the atomic weight, atomic number and nuclear charge of unity, we next encounter helium with the atomic weight 4, atomic number and nuclear charge 2. The helium nucleus should therefore consist of 4 hydrogen nuclei, which would together account for the atomic weight of 4. But since these represent 4 positive charges, there must also be present in the nucleus 2 negative electrons to make the resultant nuclear charge equal to 2. We could indeed hardly conceive of a system composed of 4 positive hydrogen nuclei alone; for the forces of repulsion would soon drive the separate parts asunder. The two electrons can, so to speak, serve to hold the system together. [Fig. 24] gives a rough representation of the helium atom. It must be carefully noted that the picture is purely schematic and the distances arbitrary. The helium nucleus, composed of 4 hydrogen nuclei and 2 electrons, seems to possess extreme stability, and it is not improbable that helium nuclei occur as higher units in the structure of the nuclei of not only the radioactive substances but also the other elements. We shall perhaps be very near the truth in saying that all nuclei are built up of combinations of hydrogen nuclei, helium nuclei and electrons.

Fig. 24.—Schematic representation of a helium atom.
K, nuclear system with four hydrogen nuclei and two nuclear
electrons; E, electrons in the outer electron system.

In nitrogen, with the atomic weight 14 and atomic number 7, the nucleus should consist of 14 hydrogen nuclei (with 12 of them compounded, perhaps, into 3 helium nuclei) and 7 nuclear electrons, reducing the resultant positive nuclear charge from 14 to 7. Uranium, with atomic number 92 and atomic weight 238, should have a nucleus composed of 238 hydrogen nuclei and 146 electrons, and so on for the others. We see at once that the conception of the nucleus here propounded leads us back to the old hypothesis of Prout ([see p. 15]) that all atomic weights should be integral multiples of that of hydrogen. This hypothesis apparently disagreed with atomic weight measurements, but the isotope researches have vanquished this difficulty; thus it has been mentioned before that chlorine with an atomic weight of 35·5 appears to be a mixture of isotopes with atomic weights 35 and 37, and other cases have a similar explanation. Yet the rule cannot be wholly and completely exact. For, in the first place, the mass of the electrons must contribute something, though this contribution is far too small to be measured. But there is also a second matter which plays a part here. This is the law enunciated by Einstein in his relativity theory, that every increase or decrease in the energy of a body is correlated with an increase or decrease in the mass of the body, proportional to the energy change. We must, therefore, expect that the masses of the various atomic nuclei will depend not only on the number of hydrogen nuclei (and electrons), but also on the energy represented in the attractions and repulsions between the particles of the system, and in their mutual motions, or the energy which comes into play in the formation and disintegration of nuclear systems. This is presumably closely connected, although in a way which is not clearly understood, with the fact, that if the atomic weights of the elements are to come out integers, that of hydrogen must not be taken as 1 but as 1·008; that is, the atomic weight unit must be chosen a little smaller than the atomic weight of hydrogen ([cf. table, p. 23]).

Transformation of Elements and Liberation of Atomic Energy.

We shall now treat very briefly two questions which have profoundly interested many people, because they are concerned with possible practical applications of our new knowledge of atoms.

The first question is this: Can one not, from this knowledge, bring about the transformation of one element into another? In answering this, it can, of course, be said immediately that among the radioactive substances such transformations are constantly taking place without human interference, and we certainly have no right to state offhand that it will be impossible for man ever to bring about such a transformation artificially. For example, if we could succeed in getting one hydrogen nucleus loose from the nucleus of mercury, the latter would thereby be changed into a gold nucleus. Such a thing is not only conceivable, but in the last few years it has become a reality, though, to be sure, not with the substances here mentioned. In 1919 Rutherford, by bombarding nitrogen (N = 14) with α-particles, was able to knock loose some hydrogen nuclei from the nitrogen nucleus; perhaps he succeeded thereby in changing the nitrogen nuclei into carbon nuclei (C = 12) by the breaking off of two hydrogen nuclei from each nitrogen nucleus. But to disintegrate very few nitrogen nuclei, Rutherford had to employ a formidable bombardment with hundreds of thousands of projectiles (α-particles); and even if he had ended with gold instead of carbon, this would have been, from the economic point of view, a very foolish way of making gold; and at the present time we know of no other artificial method for the transformation of elements. That Rutherford’s investigation has, in any case, extraordinarily great interest and scientific value is another matter.

The second question is whether one cannot liberate and utilize the energy latent in the interior of the atom. This question, which was suggested in the first instance by the discovery of radium, has recently attracted considerable attention because of reports that, according to Einstein’s relativity theory, one gram of any substance by virtue of its mass alone must contain a quantity of energy equal to that produced by the burning of 3000 tons of coal. The meaning of this statement is this: it has already been mentioned that according to the relativity theory a decrease in the energy of a body brings about a decrease in its mass; it is immaterial in what form the energy is given up, whether as heat, elastic oscillations, or the like; all that is said is, that to a certain decrease in mass, will correspond a perfectly definite emission of energy in some form. If we now could imagine the whole mass of one gram of a substance to be “destroyed” (i.e. caused to disappear utterly as a physical substance), and to reappear as heat energy, for example, then we could compute from the known relation between mass and energy, that the heat energy thus brought about would be equivalent to that obtained by the burning of 3000 tons of coal. But in order that all this energy should be developed, even the hydrogen nuclei and the electrons would have to be “destroyed,” and no phenomenon is known, supporting the supposition that such a “destruction” of the fundamental particles of a substance is possible, or that it is possible to transform these particles into other types of energy. A thought like this must rather be stamped as fantasy, the origin of which is to be found in a misunderstanding of a purely scientific mode of expression.

The case is essentially different with those quantities of energy which must be assumed to be freed or absorbed in the transformation of one nuclear system into another, that is, in elemental transformations. Though these are far smaller in amount, the radioactive processes indicate that they are not wholly to be despised. For one gram of radium will upon complete disintegration to non-radioactive material give off as much energy as is equivalent to 460 kg. of coal. But even here we must confess that it will take about 1700 years for only half of the radium to be transformed. It is not at all impossible that other elemental transformations might lead to just as great energy developments as appear in the disintegration of radioactive substances. Let us imagine that four hydrogen nuclei, which together have a mass of 4 × 1·008 = 4·032, and two electrons could join together to form a helium nucleus with atomic weight very close to 4. This process would thus result in a loss of mass which must be assumed to appear in another form of energy. The amount of energy obtainable in this way from one gram of hydrogen would be considerably more than that given off by the disintegration of one gram of radium.

There can hardly exist any doubt that in nature there occur not only disintegrations, but also (perhaps in the interior of the stars) building-up processes in which compound nuclei result from simple ones. It is therefore natural to suppose that by exerting on hydrogen exceptional conditions of temperature, pressure, electrical changes, etc., we could succeed by experiments here on earth in forming helium from it with the development of considerable energy. But at the same time it is very likely that even under favourable circumstances such a process would take place with very great slowness, because the formation of a helium nucleus might well be a very infrequent occurrence; it would probably be the result of a certain succession of collisions between hydrogen nuclei and electrons, a combination whose probability of occurrence in a certain number of collisions is infinitely less than the probability of winning the largest prize in a lottery with the same number of chances. Nature has time enough to wait for “wins,” while mankind unfortunately has not. We know concerning the disintegration of the radioactive substances that it is of the character here indicated; of the great number of atoms to be found in a very small mass of a radioactive substance, now one explodes and now another. But why fortune should pick out one particular atom is as difficult to understand as why in a lottery one particular number should prove to be the lucky one rather than any other. Our only understanding of the whole matter rests on the law of averages, or probability as we may call it. We know that of a billion radium atoms (10¹²) on the average thirteen explode every second; and even if in any single collection of a billion a few more or a few less may explode, the average of thirteen per second per billion will always be maintained in dealing with larger and larger numbers of atoms, as, for example, with a thousand billion or a million billion. For other radioactive substances we get wholly different averages for the number of atoms disintegrating per second; but in no case are we able to penetrate into the inner character of the process of disintegration itself. And what holds true of the radioactive substances will also hold true probably for elemental changes of all kinds; Rutherford with his hundreds of thousands of α-particle projectiles was able to make sure of but a few lucky “shots.” The whole matter must at this stage be looked upon as governed wholly by chance.

One interested in speculating on what would happen if it were possible to bring about artificially a transformation of elements propagating itself from atom to atom with the liberation of energy, would find food for serious thought in the fact that the quantities of energy which would be liberated in this way would be many, many times greater than those which we now know of in connection with chemical processes. There is then offered the possibility of explosions more extensive and more violent than any which the mind can now conceive. The idea has been suggested that the world catastrophes represented in the heavens by the sudden appearance of very bright stars may be the result of such a release of sub-atomic energy, brought about perhaps by the “super-wisdom” of the unlucky inhabitants themselves. But this is, of course, mere fanciful conjecture.

It seems clear, however, that we need have no fear that in investigating the problem of atomic energy we are releasing forces which we cannot control, because we can at present see no way to liberate the energy of atomic nuclei beyond that which Nature herself provides, to say nothing of a practical solution of the energy problem. The time has certainly not yet come for the technician to follow in the theoretical investigator’s footsteps in this branch of science. One hesitates, however, to predict what the future may bring forth.

Interesting and significant as is the insight which Rutherford and others have opened up into the inner workings of the nucleus, the study of the electron system of the atom bears more intimately upon the various branches of physical and chemical science, and hence presents greater possibilities of attaining, in a less remote future, to discoveries of practical significance.

CHAPTER V
THE BOHR THEORY OF THE
HYDROGEN SPECTRUM

The Nuclear Atom and Electrodynamics.

Even if Rutherford had not yet succeeded in giving a complete answer to the first of the questions propounded in the [previous chapter], namely, that concerning the positions of the positive and negative particles of the atom, one might at any rate hope that his general explanation of the structure of the atom—that is, the division into the nucleus and surrounding electrons, and the determination of the number of electrons in the atoms of the various elements—would furnish a good foundation for the answer to the second question about the connection between the atomic processes and the physical and chemical properties of matter. But in the beginning this seemed so far from being true that it appeared almost hopeless to find a solution of the problem of the atom in this way.

We shall best understand the meaning of this if we consider the simplest of the elemental atoms, namely, the atom of hydrogen with its positive nucleus and its one electron revolving about the nucleus. How could it be possible to explain from such a simple structure the many sharp spectral lines given by the Balmer-Ritz formula ([p. 57])? As has previously been mentioned, the classical electron theory seemed to demand a very complicated atomic structure for the explanation of these lines. According to the electron theory, the atoms may be likened to stringed instruments which are capable of emitting a great number of tones, and in these atoms the electrons are naturally supposed to correspond to the “strings.” But the hydrogen atom has only one electron, and it hardly seems credible that in a mass of hydrogen the individual atoms would be tuned for different “tones,” with definite frequencies of vibration.

Now, it certainly cannot be concluded from the analogy with the stringed instrument that a single electron can emit light of only a single frequency at one time, corresponding to a single spectral line. For a plucked string will, as we know, give rise to a simple tone only if it vibrates in a very definite and particularly simple way; in general it will emit a compound sound which may be conceived as made up of a “fundamental” and its so-called “overtones,” or “harmonies” whose frequencies are 2, 3, ... times that of the fundamental (i.e. integral multiples of the latter). These overtones may arise even separately because the string, instead of vibrating as a whole, may be divided into 2, 3, ... equally long vibrating parts, giving respectively 2, 3, ... times as great frequencies of vibration. We call such vibrations “harmonic oscillations.” The simultaneous existence of these different modes of oscillation of the string may be thought of in the same way as the simultaneous existence of wave systems of different wave-lengths on the surface of water. Corresponding to the possibility of resolving the motion of the string into its “harmonic components,” the compound sound waves produced by the string can be resolved by resonators ([cf. p. 44]) into tones possessing the frequencies of these components.

According to the laws of electrodynamics the situation with the electron revolving about the hydrogen nucleus might be expected to be somewhat similar to that described above in connection with the vibrating string. If the orbit of the electron were a circle, it should emit into the ether electromagnetic waves of a single definite wave-length and corresponding frequency, ν, equal to ω, the frequency of rotation of the electron in its orbit; that is, the number of revolutions per second. But just as a planet under the attraction of the sun, varying inversely as the square of the distance, moves in an ellipse with the sun at one focus, so the electron, under the attraction of the positive nucleus, which also follows the inverse square law, will in general be able to move in an ellipse with the nucleus at one focus. The electromagnetic waves which are emitted from such a moving electron may on the electron theory be considered as composed of light waves corresponding to a series of harmonic oscillations with the frequencies:

ν₁ = ω, ν₂ = 2ω, ν₃ = 3ω ... and so on,

where ω, as before, is the frequency of revolution of the electron. According as the actual orbit deviates more or less from a circle, the frequencies ν₂, ν₃ ... will appear stronger or weaker in the compound light waves emitted. But the actual distribution of spectral lines in the real hydrogen spectrum presents no likeness whatever to this distribution of frequencies.

From this it is evident that no agreement can be reached between the classical electron theory on the one hand and the Rutherford atom model on the other. Indeed, the disagreement between the two is really far more fundamental than has just been indicated. According to Lorentz’s explanation of the emission of light waves, the electrons in a substance ([see again p. 75]) should have certain equilibrium positions, and should oscillate about these when pushed out of them by some external impulse. The energy which is given to the electron by such an impulse is expended in the emission of the light waves and is thus transformed into radiation energy in the emitted light, while the electrons fall to rest again unless they receive in the meantime a new impulse. We can get an understanding of what these impulses in various cases may be by thinking of them, in the case of a glowing solid, for example, as due to the collisions of the molecules; or in the case of the glowing gas in a discharge tube, from the collisions of electrons and ions. The oscillating system represented by the electron (the “oscillator”) will possess under these circumstances great analogy with a string which after being set into vibration by a stroke gradually comes back to rest, while the energy expended in the stroke is emitted in the form of sound waves. Although the vibrations of the string become weaker after a while, the period of the vibrations will remain unchanged; the string vibrations like pendulum oscillations have an invariable period, and the same will be the case with the frequency of the electron if the force which pulls it back into its equilibrium position is directly proportional to the displacement from this position (the “harmonic motion” force).

Rutherford’s atomic model is, however, a system of a kind wholly different from the “oscillator” of the electron theory. The one revolving hydrogen electron will find a position of “rest” or equilibrium only in the nucleus itself, and if it once becomes united with the latter it will not easily escape; it will then probably become a nuclear electron, and such a process would be nothing less than a transformation of elements ([see p. 79]). On the other hand, it follows necessarily from the fundamental laws of electrodynamics that the revolving electron must emit radiation energy, and, because of the resultant loss of energy, must gradually shrink its path and approach nearer the nucleus. But since the nuclear attraction on the electron is inversely proportional to the square of the distance, the period of revolution will be gradually decreased and hence the frequency of revolution ω, and the frequency of the emitted light will gradually increase. The spectral lines emitted from a great number of atoms should, accordingly, be distributed evenly from the red end of the spectrum to the violet, or in other words there should be no line spectrum at all. It is thus clear that Rutherford’s model was not only unable to account for the number and distribution of the spectral lines; but that with the application of the ordinary electrodynamic laws it was quite impossible to account for the existence even of spectral lines. Indeed, it had to be admitted that an electrodynamic system of the kind indicated was mechanically unstable and therefore an impossible system; and this would apply not merely to the hydrogen atom, but to all nuclear atoms with positive nuclei and systems of revolving electrons.

However one looks at the matter, there thus appears to be an irremediable disagreement between the Rutherford theory of atomic structure and the fundamental electrodynamic assumptions of Lorentz’s theory of electrons. As has been emphasized, however, Rutherford founded his atomic model on such a direct and clear-cut investigation that any other interpretation of his experiments is hardly possible. If the result to which he attained could not be reconciled with the theory of electrodynamics, then, as has been said, this was so much the worse for the theory.

It could, however, hardly be expected that physicists in general would be very willing to give up the conceptions of electrodynamics, even if its basis was being seriously damaged by Rutherford’s atomic projectiles. Surmounted by its crowning glory—the Lorentz electron theory—the classical electrodynamics stood at the beginning of the present century a structure both solid and spacious, uniting in its construction nearly all the physical knowledge accumulated during the centuries, optics as well as electricity, thermodynamics as well as mechanics. With the collapse of such a structure one might well feel that physics had suddenly become homeless.

The Quantum Theory.

In a field completely different from the above the conclusion had also been reached that there was something wrong with the classical electrodynamics. Through his very extended speculations on thermodynamic equilibrium in the radiation process, Planck (1900) had reached the point of view expressed in his quantum theory, which was just as irreconcilable with the fundamental electrodynamic laws as the Rutherford atom.

A complete representation of this theory would lead us too far; we shall merely give a short account of the foundations on which it rests.

By a black body is generally understood a body which absorbs all the light falling upon it, and, accordingly, can reflect none. Physicists, however, denote by the term “perfect black body” in an extended sense, a body which at all temperatures absorbs all the radiation falling upon it, whether this be in the form of visible light, or ultra-violet, or infra-red radiation. From considerations which were developed some sixty years ago by Kirchhoff, it can be stated that the radiation which is emitted by such a body when heated does not depend on the nature of the body but merely on its temperature, and that it is greater than that emitted by any other body whatever at the same temperature. Such radiation is called temperature radiation or sometimes “black” radiation, though the latter term is apt to be misleading, since a “perfect black body” emitting black radiation may glow at white heat. It may be of interest to note here the fundamental law deduced by Kirchhoff, which may best be illustrated by saying that good absorbers of radiation are also good radiators. An instructive experiment illustrating this is performed by painting a figure in lampblack on a piece of white porcelain. The lampblack surface is clearly a better absorber of radiant energy than the white porcelain. When the whole is heated in a blast flame, the lampblack figure glows much more brightly than the surrounding porcelain, thus showing that at the same temperature it is also the better radiator. Following the same law we conclude that highly reflecting bodies are not good radiators, a fact that has practical significance in house heating. The perfect black body, then, being the best absorber of radiation, is also the best radiator.