by W Heisenberg
How does the physicist know that a water molecule consists just exactly of two hydrogen atoms and one oxygen atom, instead of—let us say—four hydrogen and two oxygen atoms, which would still represent the same mass ratio? In order to answer this question, we must make reference again to the theory of gases, and to Avogadro’s hypothesis in particular, which states—as mentioned above—that at the same temperature and pressure, equal volumes of all gases contain the same number of molecules. There exists an exact proof of this hypothesis, but here we shall confine ourselves merely to elucidating it. The pressure on the sides of a vessel filled with a gas, is due to the impacts of the gas molecules, which hammer against those sides like drops of a steady rain, only to be bounced back from them again. The sum total of the forces of these impacts exerts a pressure against the sides. The magnitude of this pressure, obviously, depends on the kinetic energy of the molecules, which, in turn, depends on the temperature of the gas. Since the days of Maxwell, we have known that at the same temperature the molecules of all gases always have the same average kinetic energy. Thus, if equal volumes of gases contain the same number of molecules, it follows that at the same temperature their pressure, too, must be the same. This is the real meaning of Avogadro’s hypothesis.
Moreover, at this point, we must refer to certain chemical facts. The fact, already mentioned, that 2 grammes of gaseous hydrogen and 16 grammes of gaseous oxygen combine to form 18 grammes of water vapour, can be expressed by the following equation:
Instead of the ratio by mass, we may investigate also the ratio by volume present when hydrogen and oxygen combine at the same temperature. Experiments show, for instance, that 1 litre of hydrogen and litre of oxygen combine to form 1 litre of water vapour. Thus, we get the following equation:
From these two equations, it is easy to deduce the mass ratios of these three kinds of molecules. Since 1 litre always contains the same number of gas molecules, all we have to do is determine the ratio of the above-mentioned masses and volumes of the three gases, to obtain numbers proportionate to the masses of their molecules. Thus we get:
Hydrogen gas, 2 gm. litre;
Oxygen gas, 32 gm. litre;
Water vapour, 18 gm. litre.
Accordingly, the relative masses of the various molecules in question are:
Hydrogen gas: oxygen gas: water vapour = 2: 32: 18
The hypothesis which expresses these facts most simply, and which has been confirmed by other experiments, is that a hydrogen molecule consists of two hydrogen atoms of atomic weight 1, and consequently, has the molecular weight 2. Similarly, an oxygen molecule consists of two oxygen atoms, of atomic weight 16, and consequently, has the molecular weight 32. And, finally, a water molecule consists of two hydrogen atoms and one oxygen atom, and consequently, has the molecular weight 2 × 1 + 16 = 18. This compound can be described by the following formula:
The atomic weights of all elements, as well as the molecular weights of all chemical compounds, can be determined in analogous manner. The unit of atomic weight is chosen so as to be equal exactly to of the chemical atomic weight of oxygen, so that the atomic weight of oxygen is exactly 1600000. Similarly, the molecular weight is the standard measure of the mass of a molecule measured in terms of the same unit.
We have already mentioned the unit called mol (or mole). One mol represents that quantity of a substance which weighs as many grammes as equal numerically the molecular weight of that substance. Thus, one mol of hydrogen gas (H2) is 2 grammes, one mol of oxygen gas (O2) is 32 grammes, and 1 mol of water (H2O) is 18 grammes. Thus the masses of 1 mol of different substances are to each other exactly as their respective molecular weights, and consequently, as the masses of their individual molecules. It follows, therefore, that 1 mol of any substance always contains exactly the same number of molecules. Quite analogously, a gramme-atom is defined as that quantity of an element which weighs as many grammes as equal numerically the atomic weight of that element. Thus 1 gramme-atom of hydrogen (H) is 1 gramme, one gramme-atom of oxygen (O) is 16 grammes. It is evident that 1 gramme-atom of any element contains always the same number of atoms—namely, as many atoms as there are molecules in 1 mol. A knowledge of these concepts is very important, for they enable us to count molecules, or atoms, by weighing them, as it were, and for this reason it is absolutely necessary to know the exact number of molecules contained in a mol. As we have stated before, this number was first computed correctly—as regards the order of magnitude at least—by Loschmidt in 1865. But the first really reliable calculation was made in 1900 only, on the basis of Planck’s radiation law. To-day, the most reliable numerical value of this important Loschmidt’s number (L) is: 6·024 × 1023.
This means that 1 mol of a substance—for instance, 32 grammes of oxygen gas—contains almost 1 quadrillion molecules.
Furthermore, Loschmidt’s number gives us an exact knowledge of the masses of the individual atoms and molecules in terms of the customary unit of 1 gramme. Since 1 mol of hydrogen gas weighs 2 grammes, we can easily find—dividing by Loschmidt’s number—that the mass of a hydrogen molecule (H2) is 3·34 × 10−24 gramme, and therefore, the mass of a hydrogen atom (H) is 1·67 × 10−24 gramme. The masses of all other atoms and of all kinds of molecules (when their atomic structure is known) can be computed.
Now let us turn our attention to the magnitude of the electric charge which is linked, through electrolysis, with an atom or molecule—the atom of electricity, the electron. We have already stated that a certain quantity of electricity, namely:
F = 96,520 coulombs
is always linked to 1 gramme-atom of a univalent substance. But it is very difficult to appreciate the magnitude of this charge. It is much greater than any electric charge that can be produced in any single substance in the laboratory. If both the moon and the earth were to carry, each, a charge of this magnitude, they would attract or repel each other—despite the great distance between them—with a force equivalent to several hundreds of kilogrammes. This is the charge carried by 1 gramme-atom of a univalent substance. But since 1 gramme-atom always contains the same number of atoms (Loschmidt’s number), the charge carried by an individual univalent atom is determined by dividing the equivalent charge F by Loschmidt’s number; this charge is e = 1·6 × 10−19 coulombs, or 4·8 × 10−10 electrostatic units, and is therefore exceedingly small. This charge of an atom of electricity is called the elementary quantum of electricity, for any electric charge can be only an integral multiple—either positive or negative—thereof.c This number and several other important constants of nuclear physics, are given in Table 1 at the end of this book.
We have already pointed out that the ratio of the charge to the mass of electrons, both in electric and magnetic fields, was determined on the basis of the deflection of the cathode rays—of electrons, in other words. Once the magnitude of their charge is known, the electronic mass can be computed. It is only about 1/1,840 of the mass of the hydrogen atom, viz.: 9·1 × 10−28 gramme. In Table 1 it is designated rest mass, because the mass of every body increases with its velocity.
Up till not so very long ago, only electrons with a negative electric charge were known. Positively charged electrons were only discovered during the past decade. Under normal conditions, this positive electron is very short lived; as a rule, it vanishes soon after it comes into being. Otherwise a positive charge also occurs invariably in magnitudes equal to one or more elementary quanta of electricity, in association with masses of the atomic order of magnitude. This fact in itself suggests that the mass of the atom is associated with a positive electric charge which is neutralized by negative electrons, and that ions are produced either by a loss or gain of electrons. But it was still a long way from this concept to the creation of the correct atom model.
II. RUTHERFORD’S ATOM MODEL
Shortly before the end of the nineteenth century, the way was opened for new decisive developments in nuclear physics. They were introduced by a discovery not directly related to nuclear
physics at all: the discovery of x-rays by Wilhelm Röntgen in 1895. The first effect of this discovery was merely the knowledge of a new type of radiation which, although not perceptible directly by human sense organs, could be measured by instruments in the physical laboratory, and which amazed the entire world by its power to penetrate dense layers of matter.
c
In the following year, as a result of his attempt to discover other rays of a similar nature, the Frenchman Henri Becquerel proved that certain substances, notably the compounds of uranium, emitted certain rays of a similar penetrating power, and that this emission took place independently of any external agency. This phenomenon became known as radioactivity, and the entire modern theory of atoms owes its development to this discovery. A series of other important developments then followed in rapid succession. The two Curies succeeded as early as 1898 in obtaining from uranium a much more strongly radioactive substance, and because of its extremely strong radioactive properties they named it radium—that which radiates.
Just about that time, Ernest Rutherford, the real father of modern atomic physics, began to take a hand in its development. He was born in Nelson, New Zealand, in 1871, and died in Cambridge, England, in 1937. Shortly after the announcement of the phenomenon of radioactivity, he found that rays of various types were emitted by radioactive substances, and these rays were distinguished by their different absorbabilities in matter. They are called alpha, beta and gamma rays. The alpha and beta rays are deflected by a magnetic field, which fact indicates that they carry an electric charge—the alpha ray a positive charge, the beta ray a negative one. Gamma rays cannot be deflected—they carry no electric charge.
A more precise study of the alpha rays led to the conclusion that they consisted of particles in rapid movement, each carrying two elementary quanta of positive electricity, and having a mass equal to that of a helium atom (atomic weight 4). The particles which constitute the beta radiation carry only one elementary quantum of negative electricity each, and the mass of each such particle is equal to that of an electron. In other words, beta rays consist of negative electrons in rapid movement. Finally, the gamma rays are identical with x-rays as regards their general properties.
An excellent method was developed by Wilson to make these rays visually detectable. Air containing saturated aqueous vapour is caused to expand suddenly within a chamber, called a cloud chamber; it is cooled in consequence and the water vapour therefore becomes supersaturated and has a tendency to condense; though it may remain supersaturated for some time. If now at this moment an alpha particle passes through the chamber, it will tear electrons off the atoms of air along its entire path, leaving positively charged air molecules in its wake. These positively charged air molecules are called positive ions. These ions further the condensation of the supersaturated water vapour; in fact, they form ‘condensation nuclei’, around which the water vapour condenses to small droplets. Thus, all along the path of the particle, a very fine track of water droplets is formed, similar to the condensation bands left behind by an aeroplane at high altitudes, thus producing a picture of its path. This phenomenon is shown in Figures 3 (a) and (b).
The radioactive preparation is under the visible section of the cloud chamber. The tracks of the individual alpha particles can easily be seen and constitute groups of approximately the same length. In Figure 3 (a), two groups of different ‘ranges’ are easily discernible.
One of the tracks in Figure 3(b) shows a sharp deflection. Obviously, something out of the ordinary has happened here to the alpha particle. It has come into the vicinity of the nucleus of an atom and been deflected by it. But, as a rule, the particles move in a straight line, and their range varies mostly between 2 and 10 centimetres.
It is very remarkable that the alpha particles are capable of covering such great distances in a straight line. For it is easy to calculate that on their way they must encounter an enormous number of atoms. This is an obvious inference from the large number of water droplets formed. It seems therefore as if the atoms were not impermeable to particles of such small size, as if, in fact, the latter were able to penetrate the atoms without hindrance. Evidently, they seldom encounter any serious obstacle on their way; but when they do, their tracks will show such deflections, as the one which we see in Figure 3 (b).
At an even earlier date, Lenard had investigated the passage of rapidly moving electrons through matter, and discovered that electrons were capable of penetrating extraordinarily. thick layers of matter. Thus he reached the conclusion that the space occupied by an atom is, mostly, empty, and the path of an electron is influenced by individual centres of force only, which he called dynamides. It was Rutherford who, as the result of similar studies, took the important step which eventually led to the construction of the first atom model. He studied the tracks of alpha particles through thin metal foil, and concluded, on the ground of the extreme rarity of any notable deflection, that only a very small part of the atom offered any resistance at all to the alpha particles, and that this very small part contained practically all of the mass of the atom. If this were not the case, the laws of elastic impacts would make the occurrence of those considerable deflections, which could at times be observed, quite impossible. On the basis of his observations, Rutherford was able to calculate the volume of the space actually occupied by mass, and concluded that all the rest of the space occupied by the atom must—for all practical purposes—be empty. Rutherford’s collaborators, Geiger and Marsden, succeeded in establishing, furthermore, that the deflections of the positively charged alpha particles were produced by electric forces, due to a likewise positive charge on the central part of the atom. Evidently, this central part of the atom and the alpha particles mutually repelled each other, in conformity with Coulomb’s well-known law.
Figure 3.—Alpha particles in the cloud chamber.
These findings were the foundation on which Rutherford built the following atom model: An atom consists of a positively charged nucleus, which contains practically all of the mass of the atom, but occupies only a small fraction of the total volume of the atom as a whole. The positive charge of the nucleus is offset by electrons which, held captive by the attraction exerted by the nucleus, revolve around the nucleus at relatively great distances. These electrons constitute the extranuclear structure of the atom. The number of revolving planetary electrons is determined by the nuclear charge. Since each electron carries one elementary charge of negative electricity, the number of electrons must equal the number of elementary charges of positive electricity carried by the nucleus, for the atom as a whole to be electrically neutral. Evidently, the number of electrons determines all the external properties of the atom, and thus, in particular, the forces which it is capable of exerting on other atoms—in other words, its chemical properties, which, too, are ultimately determined by the nuclear charge.
In order to obtain some idea of the orders of magnitude within an atom, imagine an atom, including its extranuclear electron structure, as a sphere with a diameter of approximately 10 centimetres. In such a model, it would hardly be possible to represent the electrons and the nucleus in their proper porportions; they are too small to allow us to do so. In such a model, the nucleus would appear as a minute particle of dust about 1/100 millimetre in diameter, and the electrons would be more or less the same size.
The lightest of all atoms, the hydrogen atom, consists of a nucleus carrying one elementary quantum of electricity, and is therefore circled by one single electron. In this case, the nucleus is said to carry the unit charge or to have the charge number 1.
Figure 4.—Model of the hydrogen atom.
If we want to obtain a visual model of this atom, we must remember that the electron must move in a path around the nucleus, like a planet around the sun, for otherwise it would fall into the nucleus. We must therefore draw the path of the electron, and we shall assume for the moment, as a working hypothesis, that it is a circular orbit.
The hydrogen atom is the simplest
of all atoms. The next one is the helium atom with its charge number 2—two elementary quanta of electricity on its nucleus and two planetary electrons in its extranuclear structure. And so forth, up to the heaviest atom known at the present time, curium, which has the nuclear charge number 96. All the necessary information on this subject is given in Table II, at the end of this book.
Once again, there arises the question, to what extent the visual representation supplied by Rutherford’s atom model may be accepted literally, at its face value. Can we expect that some day, with the aid of a supermicroscope, we shall actually be able to see electrons revolving in their orbits around a nucleus? In view of the movements of the electrons, we would have to take snapshots. According to our present knowledge, we cannot very well doubt that a snapshot of a hydrogen atom would show actually such a picture as we have described: two point charges at a distance of a few ten-millionths of a millimetre. This is the practical significance of Rutherford’s atom model. Obviously, this would not be a picture in definite colours, as our photographs would not be taken with rays of visible light, but with electron rays. But in any case such a snapshot of a hydrogen atom would show two particles: the nucleus and the single electron.
