by W Heisenberg
In 1792, the German Richter discovered that chemical elements always combine in chemical compounds in definite quantitative proportions. It is not possible for just any arbitrary quantity of hydrogen to combine with just any arbitrary quantity of oxygen to form water: hydrogen and oxygen must always combine in the proportion of 1: 8 to form water. Otherwise, there remains an unconverted residue of hydrogen or oxygen. This law of constant proportions was then raised by Dalton to the status of a fundamental law of chemistry, and within a fairly short time it led to the union of chemistry with atomic theory. Dalton stated this law in a more precise form, and gave it a geometrical interpretation.
It is this very geometrical interpretation that is of paramount importance. We shall try to make it more intelligible by an example. When hydrogen combines with oxygen to form water, we must visualize this process as a mutual combination of the smallest particles—the atoms—of both elements in a higher, more complex unit, a water molecule, according to our modern terminology. We are now in a position to visualize a molecule as a geometrical structure composed of individual atoms, and a water molecule as a structure composed of two hydrogen atoms and one oxygen atom. This view makes the law of multiple proportions directly understandable. The compound which we call water is thus characterized by the 1:2 ratio of oxygen and hydrogen atoms.
This theory of Dalton, advanced in 1803, of atoms combining in molecules in a manner capable of geometrical illustration, was developed further and raised, within a few years, to the status of an established scientific postulate. As early as 1811, Avogadro announced a daring hypothesis, by which he laid the corner stone of what we know to-day as the chemical theory of atoms. He maintained that at the same temperature and pressure, equal volumes of all gases contained the same number of molecules. Although this hypothesis was still in need of experimental proof, it soon turned out to be the clue to the determination of atomic weights, and it also provided a solid, permanent foundation for Dalton’s atomic theory. If the number of atoms or molecules contained in a specific quantity of gas is known, the composition of an individual molecule can be stated exactly—for instance, whether a water molecule actually consists of one oxygen atom and two hydrogen atoms.
Thus the way was paved for a quantitative determination of the weight or mass ratios of atoms. Although the absolute number of atoms present at any one time was not known, it was known for a certainty that at the same temperature and pressure, the number of molecules contained in equal volumes of gases was the same. This was sufficient, since it furnished information concerning the mass ratios of atoms and molecules.
Not much later, the Swedish scientist Berzelius determined the atomic weights of a great many molecules, and succeeded in developing very definite theories about the way in which molecules are built from individual atoms. Berzelius also studied the nature of the forces binding atoms together in molecules. It was he who introduced the notion of valency in connection with the force binding an atom of one element to an atom of another. In studying this force, he came to the conclusion that it must be of electrical nature.
The status of atomic theory about 120 years ago can be summed up as follows: It was known that the prodigious number of chemical compounds could be reduced to a relatively small number of chemical elements, a great many—although by far not all—of which were known. The mass ratios of the atoms of these elements were also known fairly accurately—as, for instance, that one oxygen atom was roughly 16 times, and a nitrogen atom roughly 14 times heavier than a hydrogen atom. However, there were still considerable gaps to be filled. Nothing at all was known about the absolute size of atoms, or the order of magnitude of their number within. a given volume of space. All that was known was that in gases at the same temperature and pressure, the number of molecules was the same. So far as accurate knowledge was concerned, an atom might still, as Democritus had believed, be approximately the same size as one of the motes dancing in a sunbeam, or infinitely smaller. Just as little was known about the shape of atoms, or about the forces operating between them. As to the latter question, nothing but extremely hypothetical conjectures was possible. Furthermore, although it was known that, chemically, the atoms must be the ultimate building blocks of matter—in other words, the smallest units demonstrable by chemical means and methods—no one knew whether or not these chemical atoms might be capable of being further subdivided and transmuted into each other by the application of other methods.
A discovery, from which Prout was the first to draw conclusions in 1815, actually spoke against the theory of the absolute indivisibility of atoms. Prout (1785–1850) based his deductions on the fact that the atomic weights known in those days—these were mainly only those of the lighter elements—were nearly integral multiples of the atomic weight of hydrogen. This fact is the basis of his view, that all atoms were built up of hydrogen atoms. Since one carbon atom was roughly twelve times, and one oxygen atom roughly sixteen times as heavy as one hydrogen atom, the carbon atom had to be composed of twelve hydrogen atoms, and the oxygen atoms of sixteen hydrogen atoms. The hydrogen atom would thus be the only, ultimate building block of all matter. The hypothesis which postulated the existence of nearly a hundred different elements, had always been regarded as rather difficult to accept. For if we really believe in homogeneity in nature, we must obviously prefer the number of basic elements to be considerably smaller.
Despite the captivating features of Prout’s hypothesis, it remained almost completely neglected for more than a hundred years. The main reason for its being discarded was that the atomic weights of the heavier atoms had not been proved to be approximately whole numbers. Nevertheless, this hypothesis did actually contain a grain of truth of considerable importance. We shall see later on that, in a modified form, it plays a fundamental part in modern nuclear physics.
A new era in atomic theory was introduced by Faraday (1791–1867), who combined atomic theory with the theory of electricity. Atomic theory is indebted to him for the formulation of a law of prime importance: In chemical changes induced electrically—by electrolysis—there is always a relationship between the matter transformed and a definite quantity of electricity. Moreover, Faraday discovered that the masses of the substances transformed by a certain definite quantity of electricity, are related to the so-called ‘equivalent weights,’ and thus in the simplest cases—those of univalent substances—to the atomic weights of the substances concerned. This discovery indicated that electricity, too, possessed an atomic structure, of such nature that each atom, or each molecule, of a chemical compound was always associated with one or more atoms of electricity, even though in some manner then still unknown. This was pointed out by Weber as early as 1848. It explains logically why the same quantity of electricity was always associated with the same quantity—in other words, the same number of atoms—of a substance. To-day, the mol (also written mole) and the gramme-atom are customarily employed as basic mass units. One mol of any substance is that quantity which weighs as many grammes as the numerical value of its molecular weight; one gramme-atom of an element is a quantity equal in grammes to the numerical value of its atomic weight. Thus one mol of oxygen gas, O2, (molecular weight, 32) is equal to 32 grammes of oxygen gas, and one gramme-atom of oxygen, 0, (atomic weight, 16) is equal to 16 grammesof oxygen.b Every gramme-atom of a univalent element is associated with a certain quantity of electricity, 96,520 coulombs, and one gramme-atom of a multivalent element is associated with the appropriate multiple of this quantity.
The next advances were made in the domain of the theory of gases, raised to the status of an exact science as a result of the efforts of Maxwell, Boltzmann and, above all, Clausius. It was through the work of these investigators that the concept of a gas as something consisting of molecules in rapid motion—comparable in a way to a swarm of midges—gained a solid foundation in conformity with strict mathematical principles.
The year 1865 brought a new achievement of considerable importance: The first, and as yet only approxi
mate, determination by Loschmidt of the size of atoms, and hence of the number of molecules contained in a given volume. Like Robert Mayer before him, Loschmidt investigated the internal friction of gases, and as a result of the preliminary researches of his precursor, he obtained a first clue to the size of an atom. His conclusions were still rather inaccurate, but he arrived at the right order of magnitude. The size of the atom has been known accurately for about forty years only. To give some idea of it, let it be mentioned that approximately ten million atoms placed next to each other in a straight line would form a line of one millimetre in length. Therefore, individual atoms are completely invisible, and it is impossible to observe them directly. They are infinitely smaller than those motes in a sunbeam which Democritus regarded as comparable with atoms with respect to order of magnitude.
The following years produced another step forward in the field of our knowledge of electricity. Through Faraday’s discoveries, the existence of atoms of electricity had become a probability, but they were still known solely in association with atoms of the chemical elements, and not in a free state. Free atoms of electricity, atoms not bound to atoms of ordinary matter, were discovered by Hittorf in cathode rays, which are a consequence of electrical discharges in highly attenuated gases. Hittorf (1824–1914) studied the deflection of cathode rays in magnetic fields, and found that on the ground of the magnitude of this deflection it was possible to calculate the ratio of the charge to the mass of those particles moving in the cathode rays. As the mass of an individual atom had been known since Loschmidt’s time, and as on the ground of Faraday’s discoveries the size of the atoms of electricity could be computed to a fair approximation, the magnitude of the mass with which the atom of electricity was associated in its free state—in the cathode rays—was now determined in connection with the ratio just mentioned. As a result of more recent measurements, it is now known that this mass is about one 1,840th part of the mass of the lightest of all atoms, the hydrogen atom.
These atoms of free electricity are called electrons, a name first suggested by Stoney.
Of major importance is the fact that the wide range of masses like those of the atoms of the chemical elements is absent in the case of the atoms of electricity. Electrons are always associated with the same mass, which circumstance is in excellent conformity with the demand for homogeneity in nature. The view that electrons might be, in some way or another, constituent parts of atoms, gradually developed during the years that followed. An amazing fact was that only negative electricity could be observed in a free state, as electrons, while positive electricity would always appear in association with atoms of matter. This fact of experience indicated that atoms contained negative electrons as component parts, and therefore, free negative electricity could manifest itself only when an electron was torn off an atom, with the result that an equivalent quantity of positive electricity remained bound to the remainder of the atom. But fifty years ago it was totally impossible to arrive at a clear notion of these phenomena. The weights of atoms were approximately known, and so was the volume occupied by them. It was known also that atoms possessed electrical properties, and that they contained one or more electrons. But little or nothing at all was known about their structure, and the question as to their shape could not even be asked.
The solution of this problem was reserved for the twentieth century, the threshold of which we are now approaching in our survey of the history of atomic theory. The further course of this history is so closely linked with the topic proper of this book that in the following chapters it may be presented in connection with the latter only.
2. MOLECULES AND ATOMS
I. MOLECULAR STRUCTURE
In order to prepare the way for the actual subject of this book, the second lecture will deal first with the structure of molecules, and then with the structure of atoms.
Visualize a piece of silver. You can cut it up, first, with coarse mechanical tools, and then with a file you can reduce these fragments to almost invisibly minute specks of dust. But neither of these operations has enabled you to reach the smallest component particles. If you rub the silver with your hand, a minute quantity of the metal will stick to your hand. But even this hardly at all visible quantity contains an enormous number of silver atoms. Finally, you can heat the silver until it melts and finally evaporates, in other words, until it becomes a gas. This process breaks it up into its ultimate, smallest particles, the atoms. At any rate, it cannot be broken up further either mechanically or by chemical means. Silver is a pure element.
But if a drop of water is caused to vaporize, it is not broken down into water atoms. The smallest particles which can be obtained in this manner, the water molecules, can still be broken down further by chemical means. A water molecule consists of two hydrogen atoms and one oxygen atom. Water is not an element.
Modern physics has established a definite geometrical picture of the structure of such a molecule. The hydrogen atom is denoted by the symbol H, the oxygen atom by the symbol O. With these symbols, the water molecule can be represented by the following schematic formula:
For certain reasons, which cannot be discussed further here, the water molecule is imagined as the triangular structure shown diagrammatically in Figure 1. In this sketch, shading indicates the average distribution of the electric charge of the atoms.
Now, proceeding from the individual molecule to matter in its various states of aggregation—for instance, from the water molecule to water vapour, water and ice—we can extend this visual presentation as follows: In water vapour, the molecules dart about erratically, in all directions, like a swarm of midges, at considerable distances from each other, and in a state of complete disorder. Their movement is closely dependent upon the temperature of the vapour; heat is always associated with a disorderly motion of the molecules. In the case of the larger particles, a powerful microscope will enable us to discern the so-called Brownian movement, which becomes always more and more marked as the temperature of the substance increases. In liquids, the molecules are likewise in a state of disorder, but they are closely packed and move in between each other, in a manner comparable to the movement of ants in an ant-hill. In crystalline, solid matter, the atoms, or molecules, are likewise tightly packed, but here they constitute a completely orderly pattern. Figure 2 shows the model of a rock salt crystal. Rock salt is a chemical compound of the elements chlorine and sodium. In this model, the black dots stand for chlorine atoms, the white dots for sodium atoms. They alternate in the crystal in a perfectly regular pattern. Actually, these atoms are in a state of more or less violent movement, according to the temperature of the crystal; they vibrate about their positions of equilibrium. Since the atoms are actually packed tightly, without any empty space between them, the above model does not exactly correspond to reality.
Figure 1.—Model of the molecule of water.
Figure 2.—Model of a common salt crystal.
The question now is: What do such schematic models actually mean, and have we no reason for viewing them with a certain mistrust? For if atoms are supposed to be the smallest units of matter, they cannot be expected to behave in every respect like the visually perceptible objects of our daily experience—like the actual black and white dots in the spatial model of a crystal, for instance. One is indeed quite justified in suspecting that here, in a region where we are approaching the ultimate, fundamental component parts of matter, there is a limit to our power of perception, too. Hence, we must ask, first of all, what the actual size of the atoms is, and what magnification would be required to make a molecule appear to us the size, say, of a billiard ball. Secondly, we must ask, to what extent such a visual model can be justified at all—in other words, what its intended purpose is. Does it possess such a directly perceptible import that we may expect an ideally perfect microscope of the future actually to show us such an image of a real molecule?
Let us take first the question of the size of atoms. Obviously, not all atoms are the same size, but all
atoms are more or less of the same order of magnitude. The magnification necessary to permit us to see an atom as a structure with a diameter of, roughly, 10 centimetres, is approximately that which we would have to use to magnify a ball of 1 centimetre in diameter to the size of the earth. This example will give you an approximate idea of the infinitesimal smallness of molecules.
Now, the second question, that of the significance of a molecular model: In recent years, a quite novel microscope has been developed, the electron microscope, which—unlike the ordinary optical microscope—does not utilize light rays, but electron rays. With this electron microscope, a considerably greater resolving power, and a far greater magnification, can be attained than with the optical microscope, so that it enables us, even at the present stage of its development, to see particularly large molecules as discrete particles. If it should ever become possible to increase this magnifying power to twenty or thirty times its present degree—to be sure, a difficult problem—an individual water molecule may conceivably be made visible through such a microscope.
But the important question is whether we would then see anything in any way resembling the model shown in Figure 1. It is true, of course, that no molecule is ever in a state of rest. It moves, as a whole, under the influence of the temperature, and its component parts vibrate, in reciprocal movement. Thus it would be necessary to take cinematographic records of molecules, in which case one would actually obtain a snapshot of the kind shown in Figure 1. This cannot be doubted in the light of all our present knowledge of atomic physics—and this realization is at the same time a recognition of the visual-perceptual significance of models of the kind shown in Figure 1. However, as a result of thermal movement, minor changes would be constantly taking place in this picture.
