Atoms and electrons

§ 1. The Atom

THE theory that any piece of matter may be divided up into small particles which are themselves indivisible was a speculation familiar to the ancient Greeks. It is a theory which, unless it be enunciated with some care, has been found by some people to be ambiguous. For the indivisibility attributed to the ultimate particle or atom may have reference either to practical or to mental operations. There are philosophers who have worried themselves as to how it is possible to conceive any particle of matter, however small, as ultimately indivisible. For, they argue, if the small particle exists at all it must occupy space and have a shape. Something still smaller, therefore, something occupying only half the space, could be imagined: the atom could be pictured as divided into halves or quarters and so on. And yet, although it seems impossible for thought to stop at any point in the process of dividing up a piece of matter, it is also very difficult, as can be shown by ingenious arguments, for thought to go on with the process indefinitely. And so an interesting impasse is arrived at.

Now it must be clearly understood from the beginning that this is not the sort of indivisibility with which science is concerned. The scientific use of the term has reference purely to practical scientific methods. The indivisibility ascribed to the atom was merely an enunciation of the fact that smaller particles than atoms were not found to occur in any of the processes known to science. Nothing whatever was asserted about any supposed “inherent indivisibility” of the atom. An atom of a substance was merely the smallest part of that substance which took part in any known chemical processes. The whole conception of the atom was first made really definite and fruitful by John Dalton in 1803. He asserted that every irreducible substance, or “element,” was composed of atoms indivisible in the sense described above. All the atoms of every given element were precisely similar, and, in particular, had the same weight. The atoms of different elements were different and, in particular, had different weights. But besides the chemical elements, that is, substances which cannot be dissociated into other substances, there are chemical compounds. The atoms of the elements constituting a compound unite with one another in a perfectly definite way, and Dalton gave the laws according to which these combinations are effected.

The Atomic Theory of Dalton was a tremendous success. The whole of chemistry since his time has been based on it. To describe even a small part of the consequences of the atomic theory would be beyond our scope, but we must here call attention to one very important classification to which the atomic theory led. By very careful measurements, undertaken by many men and extending over many years, the weights of the atoms of all the different primary substances, or elements, known to science have been determined. The weights, as usually given, are, of course, relative weights. If we denote the weight of an atom of oxygen by 16, then helium, for example, will have the atomic weight 4, copper will be 63·57, and hydrogen will be a little greater than unity, viz., 1·008. The heaviest element known, uranium, has an atomic weight of 238·2.

Now when all the elements known are arranged in order of increasing atomic weight the highly interesting fact emerges that their properties are not just chaotically independent of one another. They fall into similar groups, recurring at definite intervals. These relations, although they are not of mathematical definition, are quite unmistakable, and show that there is a connection between chemical properties and atomic weights. Such a connection is quite inexplicable if each atom is regarded as a perfectly simple and irreducible structure having no essential relations to the atoms of any other elements. If the atom be regarded as something possessing a structure, then the similarities between different elements may be attributed to similarities in their atomic structures, the heavier atoms being, as it were, more complicated versions of the same ground plan. We shall see that there is much truth in this view.

Even as early as 1815 the idea had been put forward by Prout that all the chemical elements were really combinations of one primordial substance. Prout supposed this primordial substance to be hydrogen. On comparing different atomic weights he was led to the conclusion that they were all whole multiples of the atomic weight of hydrogen, so that if the weight of hydrogen be represented by 1, then all the other atomic weights would be whole numbers. Every atom, in this case, could be considered as built up from a definite number of hydrogen atoms. The determinations of atomic weights in Prout’s day were not sufficiently accurate to warrant this conclusion, and when more accurate measurements showed that a large number of atomic weights are not whole multiples of hydrogen, Prout’s hypothesis was abandoned. But recent work, as we shall see, has shown that Prout’s hypothesis is much closer to reality than had been supposed.

§ 2. Elements and Compounds

The theory that all matter is built up out of atoms was invented, as a scientific theory, to explain certain phenomena which belong to the science of Chemistry. The universe of the chemist is, at first sight, a very bewildering universe. He is concerned to find out what he can about the properties of all the substances that exist. Now there are hundreds of thousands of such substances. Gold, lead, iron, table salt, air, water, gum, leather, etc., etc., is the mere beginning of a list that it would take months simply to write down. The chemist is concerned with every one of these substances. And if he found that all these substances were quite independent of one another, that there were no relations between them, then he would probably give up his task in disgust. For, in that case, he could do nothing but draw up a gigantic catalogue which would, at most, be of some practical use, but which would possess no scientific interest. But even before the rise of a true science of chemistry, men had become aware that all the different substances on earth are not wholly unrelated to one another. The old alchemists, chiefly by mixing different substances together and then heating them, found that they could change some substances into others. Some of their results were perfectly genuine; they did affect some of the transformations they claimed to have effected. In other cases, they were either mistaken or else imposing on the credulity of their disciples. Many of them claimed, for instance, that certain “base” metals, on being mixed with other substances and then heated, could be turned into gold. We know that this is impossible. But one main idea emerged from their work. They learned to distinguish between the simple substance and the compound substance. It is true that this idea emerged in a very curious form; they did not think so much of simple substances as of primary principles, such as maleness and femaleness, which were somehow incorporated in different substances in different degrees. But the idea of the simple and compound substance, although in a vastly different form, is the basis of the science of chemistry.

Out of all the substances known to exist, the chemist distinguishes a certain number as being “elements.” An element is a substance which cannot be decomposed into anything else. It happens that there are remarkably few of them. Nearly every one of the hundreds of thousands of substances known can be decomposed into other substances. When this decomposition is carried as far as it will go, we find that the substance in question is really built up out of a certain number of the substances called elements. There are about ninety of these elementary substances. In the little list of substances we have just given, for instance, gold, lead, and iron are elements. Table salt is a compound of two elements called sodium and chlorine. Air is a mixture of various elements of which nitrogen and oxygen are the chief. Water is a compound of two elements, hydrogen and oxygen. Gum and leather are more complicated compounds.

Now it is interesting enough to know that all substances are either elements or can be decomposed into two or more elements. But the most interesting aspect of this fact, and what makes it of great scientific importance, is that when elements combine to form a substance they always do so in exactly the same proportions. When hydrogen combines with oxygen to form water, for instance, exactly the same proportions of hydrogen and oxygen are concerned. We will illustrate this very important law by considering the decomposition of that well-known substance sal ammoniac. It is a pure solid substance. If it be heated it turns into a mixture of two gases. These two gases can be separated from one another and are found to be ammonia gas and hydrochloric acid gas. Now the ammonia gas can in its turn be decomposed into a mixture of the two gases, nitrogen and hydrogen, and these two gases can be separated from one another. The hydrochloric acid gas can also be decomposed. It can be decomposed into chlorine and hydrogen. We have now decomposed our sal ammoniac into three substances, nitrogen, hydrogen and chlorine. Each of these three substances is an element; no one of them can be decomposed into anything else. And we can find in what proportions they combine to make sal ammoniac. If we began our experiment with 100 grammes of sal ammoniac we should have at the end 26·16 grammes of nitrogen, 7·50 grammes of hydrogen, and 66·34 grammes of chlorine, the combined weight of these substances making up exactly 100 grammes. And in whatever way we perform the decomposition of sal ammoniac we always get these three substances and always in exactly the same proportions. By starting with nitrogen, hydrogen, and chlorine in the above proportions we can, of course, make sal ammoniac. And there is no way of making sal ammoniac except with just those proportions. No specimen of sal ammoniac ever has slightly more chlorine or nitrogen or slightly less hydrogen, for example, than any other specimen. The same remarks apply to every other compound. The general law may be enunciated thus: the same compound is always formed of the same elements in exactly the same proportions.

In the above example we obtained, in our preliminary dissociation of sal ammoniac, two substances each of which contained hydrogen. We obtained ammonia gas, which is made up of nitrogen and hydrogen, and we obtained hydrochloric acid gas, which is made up of chlorine and hydrogen. We might ask the question whether there is any simple relation between the amount of nitrogen which combines with, say, one gramme of hydrogen, and the amount of chlorine which combines with one gramme of hydrogen. But before dealing with this question we will deal with another which has some bearing on it. Can two elements combine in different proportions to form different substances, and, if so, what is the relation between the proportions? The answer is that two substances can combine in different proportions to form different substances, but that, when this occurs, the proportions are simple multiples of one another. Thus, 3 grammes of carbon can unite with 8 grammes of oxygen to produce a substance called carbon dioxide. But 3 grammes of carbon can unite with 4 grammes of oxygen to produce a different substance called carbon monoxide. It will be noticed that the amount of oxygen in the first case is just twice that in the second. This example is typical. Whenever there is more than one compound of two elements the ratio by weight of the elements in the two compounds is always a simple number. This fact is very suggestive, as we shall see.

We can now deal with our first question, and we can make it more general. Consider, for instance, hydrogen, oxygen, and carbon. We can take 2 grammes of hydrogen and combine them with 16 grammes of oxygen. The result is water. Again, if we take 16 grammes of oxygen and combine them with 12 grammes of carbon we shall obtain carbon monoxide. Here the 16 grammes of oxygen is the common factor. The appetite of this amount of oxygen for combination can be satisfied, apparently, either with 2 grammes of hydrogen or 12 grammes of carbon. And the interesting fact is that we can combine hydrogen and carbon in precisely this proportion. Two grammes of hydrogen combine with 12 grammes of carbon to form a substance called olefiant gas.

Now these are the facts that the atomic theory so beautifully explains. Let us see how it is done. Dalton’s atomic theory is to the effect that every element is built up of small equal particles. These particles are indivisible in the sense that less than one of them cannot take part in any chemical reaction. They are called atoms. The smallest part of a compound substance is called a molecule. It is built up out of atoms of the elements which unite to form that compound, and it is the smallest part of the compound which can exist as that definite substance. If a molecule were split up we should simply get the constituent elements again; the compound substance itself would have ceased to exist. Consider, for instance, a molecule of carbon monoxide. We know that this molecule is formed from one atom of carbon and one atom of oxygen. We write it CO. The carbon dioxide molecule, on the other hand, is formed from one atom of carbon and two atoms of oxygen. We write it CO₂. A carbon dioxide molecule contains exactly twice as much oxygen as does a carbon monoxide molecule. It cannot possibly contain 1¹⁄₂ times as much or 1³⁄₄ times as much, since the amount of oxygen present in a molecule must vary by at least one atom. Thus we see how it is that the proportions are whole multiples.

The atomic theory gave so clear and simple an account of the laws of combination that there could be little doubt of its truth. The ordinary chemical methods, however, did not enable one to decide unambiguously what were the exact relative weights of the atoms of the different elements. This question is obviously of great importance, but the law discovered by Avogadro, called Avogadro’s hypothesis, enabled the matter to be cleared up. This hypothesis asserts that equal volumes of different gases, under the same conditions of temperature and pressure, contain equal numbers of molecules. We may mention here that many elements normally exist in a molecular form, that is, their atoms unite together in twos or threes to form molecules.

§ 3. Relative Weights of Atoms

We will now give the reasoning by which, from Avogadro’s hypothesis, the relative weights of atoms may be deduced. Suppose we have a number of precisely similar vessels, each having the same volume V, and each filled with a gas at the same temperature and pressure. Then, according to Avogadro’s hypothesis, they each contain the same number of molecules. Suppose we take two of these vessels, one containing hydrogen and the other oxygen, and compare the weights of the two quantities of gas. Since they have the same number of molecules, the relative weights of the two quantities of gas is the same as the relative weights of their molecules. But is this sufficient to determine the relative atomic weights of hydrogen and oxygen? Obviously not, for the molecule of hydrogen, for all we know, may contain two or more atoms, and so may the molecule of oxygen. This method will not give us the desired result.

But we have said that the atom is the smallest part of an element that takes part in any chemical combination. What we really mean by that is that the smallest part of an element which takes part in any known chemical reaction is called an atom. Suppose, therefore, we consider all the compounds into which hydrogen enters. Amongst these compounds there will be one whose molecules contain a minimum amount of hydrogen. The molecules of this compound contain, therefore, one atom of hydrogen. The volume V of this compound, in the gaseous state, and at a certain pressure and temperature, contains a mass of hydrogen which can be measured. Call this mass H. Now, of all the oxygen compounds, select that compound which contains the minimum weight of oxygen. The molecules of this compound contain one atom of oxygen. The volume V of this compound, in the gaseous state, and at the same pressure and temperature as the hydrogen compound, has a known weight of oxygen. Call this mass O. Both the oxygen and the hydrogen compounds have the same number of molecules, by Avogadro’s hypothesis. Corresponding to each molecule of the hydrogen compound is one atom of hydrogen, and corresponding to each molecule of the oxygen compound is one atom of oxygen. We have, therefore, the same number of atoms of hydrogen in the one vessel that we have of oxygen in the other. The ratio of the weights of the hydrogen and the oxygen—that is, the ratio of H and O—is therefore the ratio of their atomic weights. By a similar process we find the relative atomic weights of other elements, carbon, chlorine, etc. For the purpose of comparing these relative weights, oxygen is taken as the standard, simply because oxygen occurs so frequently in chemical combinations. It is nearly 16 times heavier than hydrogen, the lightest atom. Its weight is therefore taken as exactly 16. Compared with this hydrogen is 1·008. On this standard carbon’s atomic weight is 12, and chlorine 35·456.

It is evident, from Avogadro’s hypothesis, that 1·008 grammes of hydrogen contain as many atoms as 16 grammes of oxygen or 12 grammes of carbon or 35·456 grammes of chlorine, and so on. The number of grammes of an element which is equal to its relative atomic weight is called a gramme-atom of the element. All gramme-atoms contain the same number of atoms. This number is known. It is 660,000 times a million billion. This is the number of atoms in 1 gramme of hydrogen, 12 grammes of carbon, 16 grammes of oxygen, etc. The actual weight of an atom, therefore, is to be obtained by dividing its gramme-atom by this number.

§ 4. Some Experimental Evidence

The figure we have just given for the weight of an atom is evidently exceedingly minute. Such small quantities are, of course, altogether below the limits of observation. Nevertheless, there is a series of experiments which enables us to see that the ultimate particles of matter must be extremely minute. Gold-leaf, for instance, can be prepared of a thickness of one ten-thousandth of a millimetre. In this state, gold-leaf is transparent and transmits a greenish light. It cannot be beaten out more thinly merely because of the difficulty of manipulating such thin sheets without tearing them. It is certain, therefore, that the diameter of a gold atom is less than the thickness of one of these sheets, that is, is less than 10^-5 cm. The weight of a cube of gold, having this length for the length of its side, would be 10^-14 gramme. The hydrogen atom is about 200 times lighter than the gold atom. On this showing, therefore, the mass of a hydrogen atom is certainly less than ¹⁄₂ × 10^-16 gramme. The study of thin films takes us very much further. The black spots so familiar to us on soap bubbles are the thinnest part of the soapy film. The blacker they are the thinner they are. The thickness of these extremely thin films can be measured, and is found to be about 4·5 × 10^-7 cm. The films produced by letting oil drops spread on water are even thinner. Films no thicker than 1·1 × 10^-7 cm. have been obtained. The maximum possible diameter for an oil molecule, therefore, would be about 1 × 10^-7 cm. A hydrogen atom would weigh nearly a thousand times less than one of these oil molecules, and we can calculate, on this basis, that the mass of a hydrogen atom would be of the order of 10^-24 gramme. The actual mass of a hydrogen atom, as can be shown by other calculations, is 1·65 × 10^-24 gramme. By actual experiment, therefore, we can obtain films so thin that they are not much more than one molecule in thickness.

§ 5. Molecular Movements

If two liquids are taken and one is placed on top of the other, we know that they will begin to mix. In some cases the mixing process may take a long time and may seem to be incomplete, as when water and ether are superposed, for example. But even in this case we would find, after a time, that every part of the layer of ether contained some water, and that in every part of the water there was some ether. With most pairs of liquids the diffusion is more rapid and obvious. Even solids diffuse very slightly. With pairs of metals which have been kept in contact for years, it is found that the bottom layer of one and the top layer of the other have become, to some extent, intermingled. In the case of gases, diffusion is rapid and complete. Berthollet took a globe containing carbon dioxide, a heavy gas, and put it in communication by means of a stop-cock with another globe containing hydrogen, the lightest of gases. The globe of hydrogen was above the globe of carbon dioxide, and in each globe the gas was at the same pressure. When the stopcock was opened it was found that, after a little time, each globe contained as much carbon dioxide as hydrogen. With any pair of gases the result is the same.

This range of phenomena obviously points to the existence of molecular motions. We must imagine that each tiny particle of a liquid or a gas is in incessant movement. Even in the case of solids, there is some movement of the molecules, although here the movement is much more restricted. In a gas, in particular, the molecules must be moving about in all directions, perpetually colliding and changing their directions. A rise in temperature increases the velocity of these movements. All phenomena of diffusion take place at a greater rate the higher the temperature. What affects our senses as heat is, in fact, the energy due to these molecular movements. The hotter the body the greater the energy of motion of its molecules. Thus there is no such thing as a greatest possible temperature. The temperature of the outer layers of the sun is some thousands of degrees; the temperature of the innermost parts may be some millions of degrees. But there is an absolute zero of temperature; no body can be colder than the absolute zero. As the temperature of a body decreases its molecular movements become feebler and feebler until, at a sufficiently low temperature, they cease altogether. This lowest possible temperature is the same for all bodies. It is −273°C.

The hypothesis that a gas consists of a large number of molecules moving about in all directions with all velocities is called the Kinetic Theory of Gases, and its mathematical development enabled us to account for the known laws of gases and to predict other phenomena which have since been observed. At first sight the problem appears to be a very complicated one. We have to assume that the molecules are moving at random; some are moving slowly, some fast, some very fast, and so on. They are moving in all directions; they are perpetually colliding. Their motions are completely chaotic. But this very fact, which seems to make the problem insoluble, was shown by James Clerk Maxwell to lead to its solution. If we imagine our gas to be enclosed in a box, for instance, then we may suppose that some of the molecules, at a given instant, are moving towards one of the sides of the box with a certain velocity—say 100 yards per second. But besides having this motion, these molecules will also, in general, be moving towards a side at right angles to the first one and also, it may be, towards the floor or ceiling of the box. What do we know about these other motions from the fact that these molecules are moving towards one side at 100 yards per second? According to Maxwell, we know nothing whatever about these other motions. They might be anything. And from this mere fact he was able to deduce how different velocities are distributed amongst the molecules of the gas by applying the theory of probabilities. The pressure exerted by a gas is due to the incessant bombardment of its containing vessel by its molecules. At a given temperature there is a simple connection between the pressure and the volume of the same mass of gas. If the volume is halved the pressure is doubled; similarly, if the volume is doubled the pressure is halved. The general relation is that, at constant temperature, the volume multiplied by the pressure is constant. In virtue of their motion, the molecules possess energy, and Maxwell showed that, for a given mass of gas, the product of the pressure and volume of that mass of gas is equal to two-thirds of the energy of translation of its molecules. At the same temperature, therefore, it does not matter whether the same mass of gas occupies a large volume or a small one; the energy due to its molecular motions is the same. This energy is considerable. If the molecular energy of 2 grammes of hydrogen could be utilised it would be sufficient to raise a weight of 350 kilogrammes through 1 metre. The speed of these flying molecules is very considerable. At the temperature of melting ice the average velocity of oxygen molecules is about 425 metres per second, which is nearly that of a rifle bullet. At the same temperature, the hydrogen molecule is moving four times as fast, namely, 1700 metres per second. These velocities are the average velocities. Some molecules are moving more slowly, and some faster. The molecules are constantly colliding. The average distance between successive collisions is called the mean free path, and can be calculated. For air at normal temperature and pressure, the mean free path is about one ten-thousandth part of a millimetre. Collisions occur, therefore, about 5,000 million times a second.

§ 6. The Brownian Movement

We now come to a remarkable discovery which gives us actual visible evidence of the reality of these molecular movements. An English botanist named Brown, using the improved microscope objectives which had just been introduced, noticed, in 1827, that very small particles suspended in water were in a state of constant movement. This phenomenon was at first dismissed as being due to vibration or to convection currents in the water. More careful experiments showed that the motion certainly was not due to such causes. It does not occur only in water. It occurs in all fluids, although the more viscous the fluid the less active is the motion. The size of the small particles is an important factor—the smaller the particles the more lively the movement—but the substance or density of the particles seems to be without effect. The movement never ceases. It has been observed in liquid which has been shut up in quartz for thousands of years.

These movements have been very thoroughly observed, under a variety of conditions, by Perrin, and their theory has been worked out by Einstein. The correspondence between theory and observation is remarkably satisfactory, and there can now be no doubt that the Brownian movement is a direct manifestation of the chaotic molecular movements of the fluid. We must imagine each small particle as being constantly bombarded by the molecules of the fluid surrounding it. If the particle be fairly large, these molecular impacts, occurring irregularly and on every side of the particle, cancel out. No resultant motion is given to the particle. But if the particle be small the chances are less that the irregular impacts will cancel out. It may happen that, for a time sufficient to produce visible motion in a very small particle, the majority of the impacts are in one direction. A moment afterwards, of course, the direction has changed. So we get this incessant and extremely irregular motion called the Brownian movement. The way in which the agitation depends on the molecular energy of the fluid, on its viscosity, and on the dimensions of the particles has been worked out by Einstein, and his results have received experimental confirmation.

Chapter III: Constituents of the Atom