Atoms and electrons

§ 1. The Order of the Elements

WE have already said that the various chemical elements are not entirely unrelated to one another. The different chemical elements fall naturally into groups, the members of each group greatly resembling one another in their chemical properties. This fact particularly excited the attention of an Englishman named Newlands, who, in 1864, tried to show that the chemical elements fell into sets of seven, analogous to “octaves” in music. The subsequent discovery of other elements, however, made this scheme unsatisfactory, and the first really convincing attempt at arranging the elements in this way was made by the Russian chemist Mendeléev about 1870. In this “periodic system,” as it is called, the elements are arranged in the order of their atomic weights, beginning with hydrogen and ending with uranium. If we now number the elements in the order of their atomic weights we find a curious and interesting relation between the members of the elements which have similar chemical properties. Elements numbered 3, 11, and 19 have similar properties. Elements 4, 12, and 20 have similar properties. The properties of 5, 13, and 21 are similar; so are those of 6, 14, and 22. And so on. We see that, for the elements belonging to the same group, their numbers succeed one another by the same amount, viz., 8. Thus 11 − 3 = 19 − 11 = 8, and 12 − 4 = 20 − 12 = 8, and so on. It is as if approximately the same set of chemical properties belonged to each eighth member of the table.

But the matter is not really as simple as this. The rule works well enough provided we confine our attention to the earlier part of the table, i. e., to the elements having comparatively low atomic weights. As we go farther on in the table we find the recurrence of chemical properties begins after the eighteenth instead of the eighth member, and, still later on, we have a group of no less than thirty-two elements having different chemical properties. These facts are clearly represented in the following table, where the lines join elements having similar properties.

It will be noticed that the table of the elements terminates with a row containing six members, the last of which is uranium. Uranium, as we know, is not a stable substance; it is disintegrating, and it is probable that no elements heavier than uranium are met with, not because they are theoretically impossible, but because they would be too unstable to survive.

We have seen that, neglecting the last six elements, all the other elements may be arranged in rows in the following way: One row of two elements, two rows of eight elements, two rows of eighteen elements, and one row of thirty-two elements.

Names of Elements and their Atomic Weights arranged in order of their Atomic Numbers.

Two points must be mentioned about the periodic table as we have represented it. In the first place, we have left spaces for five elements which have not yet been discovered, but whose properties and places in the table can be predicted. Such predictions have been made before, and the elements, when discovered, have completely verified the predictions. In the second place, we have not, at every place in the table, adhered to the order of the atomic weights. There are four places where a heavier element has been put before a lighter one. In such cases we allow the whole complex of the chemical properties of the element, considered as a whole, to outweigh the considerations based only on its atomic weight. In the table as now arranged each element, including the five undiscovered elements, receives a number corresponding to its position in the table. These numbers range from 1 to 92, and they are called the atomic numbers of the elements. The atomic number of an element is, in the light of the new theories, a more fundamental and important characteristic than the atomic weight of the element. There is obviously a close connection between the atomic number and the atomic weight of an element, for the order of the atomic weights is almost exactly the same as the order of the atomic numbers and, further, the atomic weight of an element is, for the early part of the table, approximately twice its atomic number, excepting, of course, hydrogen, the first member of the table. This latter property, that the atomic weight is twice the atomic number, is truer for the first part of the table than for the latter part. As we proceed along the table the atomic weights seem to depend less and less directly on the atomic number. It is obvious that we are not dealing with a case of simple proportionality, but that the atomic weight is, in reality, a quite complicated function of the atomic number.

The fact that the periodic classification of the elements is possible, that is to say, the fact that elements having different atomic weights can be arranged in groups because of the similarity of their physical and chemical properties lends great support to the theory that an atom is not a single, simple entity. There must be some similarity between the atoms of similar elements, and it is difficult to see what this similarity can be unless it be a similarity of structure.

§ 2. The Atom as a Planetary System

It is time now that we began to consider what sort of structure the atom may be supposed to possess. We have seen that the discovery of electrons, and the phenomena of radioactivity, lead us to suppose that electrons somehow form part of the constitution of the atom. We have seen further that, since atoms are electrically neutral, we must suppose the electrons to be associated with an equal positive charge. How are we to suppose the electrons and the positive charge to be distributed? We shall see that certain experimental results lead us to adopt a planetary configuration for the atom. The positive charge is imagined as placed at the centre of the system, and circulating round it are a number of electrons sufficient to balance its charge exactly. The simplest conceivable case is of a unit positive charge, and one electron circulating round it. The distance of the electron from the positive charge would be, of course, the radius of the atom. It is supposed that the hydrogen atom is built up in just this way, namely, that it consists of a nucleus containing one positive unit of charge and, circulating round this nucleus, one electron. Such a conception is extremely simple, but before it can be considered as satisfactory we must make it more definite. We have seen that an electron has a mass which is only ¹⁄₁₈₀₀ part of that of a hydrogen atom. If there is only one electron in a hydrogen atom, therefore, we must imagine that practically the whole mass of the atom is concentrated in its positive nucleus. Besides the fact, therefore, that the ultimate positive charge, the nucleus, has an equal and opposite electrical charge to that of the ultimate negative charge, the electron, we must imagine that it is about 1800 times more massive than the electron. The nucleus, deprived of its electron, would still behave, so far as mass is concerned, like a complete hydrogen atom. But it would behave like a hydrogen atom carrying one unit of positive charge. Such atoms are known. Heavier atoms, containing several electrons surrounding a nucleus having several positive units of charge, could conceivably lose one, two, three, four, or more electrons and consequently manifest as an atom carrying one, two, three, four, or more positive charges. But it would be impossible, if our simple picture is right, for the hydrogen atom ever to manifest more than one positive unit of charge. And, in fact, no hydrogen atom has ever been discovered which does manifest more than one positive unit of charge, although heavier atoms have been found which manifest several positive charges.

The element that follows on hydrogen in the order of atomic numbers is helium, and the simplest hypothesis to make concerning the structure of the helium atom is that it consists of a nucleus containing two positive charges and, circulating round it, two electrons. How these two electrons are supposed to be arranged is a problem of some difficulty. The most obvious idea would be to suppose that they were at opposite ends of a diameter and moving round the nucleus in the same circle. But there are reasons for thinking that this picture cannot be true. We shall take up this question later when we come to consider the general group of problems relating to the distribution of electrons within atoms. But, however they may be arranged, we suppose the helium atom to consist of two electrons circulating round a nucleus containing two positive charges. Now, if this picture is correct, we cannot simply suppose the helium nucleus to be composed of two hydrogen nuclei. It is true that this would give two positive charges for the nucleus, but the weight of the nucleus would be wrong. The atomic weight of helium is not 2, but 4, and we have seen that practically the whole mass of an atom is concentrated in its nucleus. Since the nucleus of a helium atom has four times the mass of a hydrogen atom, it follows that the helium nucleus must contain no less than four hydrogen nuclei. Yet its charge is only two positive units. How is this to be accounted for? We can only account for it by giving the nucleus itself a rather complicated structure. We must imagine that the helium nucleus, besides containing four hydrogen nuclei, contains also two electrons. The charge of these two electrons neutralises the charge of two of the hydrogen nuclei and leaves, for the resultant positive charge of the helium nucleus, two units. Thus we see that, if we are to consider all atoms as built up out of hydrogen nuclei and electrons, it cannot be done by simply adding hydrogen nuclei together in order to produce the nucleus of another atom.

The principle is, we see, simple. The number of hydrogen nuclei which go to make up the nucleus of an atom must be equal to the atomic weight of that atom, since it is from the hydrogen nuclei that the atom acquires its weight. The resultant positive charge on the nucleus, however, is equal to the atomic number of the atom. An atom of gold, for instance, has a mass of 197. Its atomic number is 79. Its nucleus consists, therefore, of 197 hydrogen nuclei and 118 electrons, since 197 − 118 = 79, and the resultant positive charge on the nucleus is 79. To balance this resultant positive charge of 79 there are 79 electrons circulating round the nucleus. It is this resultant positive charge, and the electrons circulating round it, which determine the physical and chemical properties of the atom. The actual mass of the atom affects these properties only to a very small degree. It is for that reason that it is not the atomic weight, but the atomic number, which is the fundamental characteristic of an atom. It is obvious, for instance, that we might obtain the same resultant positive charge with quite a different atomic weight. In the gold atom we get a charge of 79 by combining 197 hydrogen nuclei with 118 electrons. But if we had taken 198 hydrogen nuclei and 119 electrons we should have had an atom of different atomic weight, viz., 198 instead of 197, but of equal charge, namely, 79, and therefore of the same properties. We shall see that such variations in atoms exist, i. e., we can have atoms of the same substance but of different weights.

Our picture of the helium atom is perfectly compatible with the fact that the α-particles shot out by radium are found to consist of helium atoms each of which carries two positive units of charge. Each α-particle is, in fact, a helium atom which has lost both its circulating electrons and which manifests, in consequence, two positive charges. In the same way that a hydrogen atom could not manifest more than one unit of positive charge, so a helium atom cannot possibly manifest more than two units of positive charge. But it is perfectly possible for a helium atom to lose only one of its two electrons and therefore to manifest only one unit of positive charge. Such atoms are known to exist, whereas a helium atom carrying more than two positive charges has never been discovered.

Of the next element, lithium, we need only say briefly that its nucleus carries three positive charges and that, circulating round the nucleus, are three electrons. The lithium atom which has lost one electron, and consequently manifests one positive charge, is known, but the lithium atom which is minus two electrons has not yet been experimentally obtained.

Each step along the periodic table corresponds to the increase of the resultant charge on the nucleus by one positive unit and, consequently, to the addition of one electron to the circulating planetary system. By the time we get to uranium we have an atom which has 92 electrons in its planetary system, circulating round a nucleus containing a resultant positive charge of 92 units. Such a system is enormously complex. The complete mathematical treatment of such systems would lead to the elaboration of what is, at present, the practically non-existent science of mathematical chemistry. But the mathematical difficulties are enormous. They depend not only on the large number of “planets” which have to be treated, but on the peculiar difficulties offered by the very extraordinary nature of the laws which govern their motion. The further treatment of this point, also, we must leave till later.

§ 3. Experimental Evidence

When the α-particles from radium are passed through matter they suffer a certain amount of dispersion. In passing through a thin sheet of metal, for instance, the α-particles are deviated from the straight line they were pursuing when they encountered the metal. The amount of the deviation varies from one α-particle to another, but, on the whole, the deviations are very similar to those of shots round a target. The cause of these deviations must be sought in the encounters between the α-particles and the atoms of the metal. The α-particles are, as we have seen, the positively charged nuclei of helium atoms. In passing through the metal sheet they will sometimes pass near or even through a metallic atom and experience a deflection due to the attraction of the electrons of that atom. It may be that a number of such encounters will happen to deflect the α-particle in the same direction, so that the resultant deflection may be considerable. But the chances of this can be worked out, and we reach the interesting conclusion that some of the observed enormous deflections which α-particles occasionally experience cannot be explained by any such cumulative effects. Deflections of 150°, i. e., an almost complete reversal of direction, have been observed. It is true that such large deflections are not numerous (on passing through platinum, for instance, about 1 in 8000 α-particles are so affected), but the theory of successive small deviations cannot explain them. Also, the path of an α-particle through air can, in certain circumstances, actually be photographed, and the photographed path sometimes exhibits extremely abrupt changes of direction. Suddenly to deflect the massive α-particle, travelling at about 20,000 miles a second, requires an intense force. It is necessary, therefore, to consider where these intense forces could come from.

As a result of measurements of the deflections of α-particles, moving with various velocities through different substances, Rutherford came to the conclusion that the abnormal deflections were produced when an α-particle happened to approach very closely to the nucleus of an atom. To account for the observed results it was necessary to suppose that the charge on the nucleus was concentrated within a very small region. An α-particle which approached sufficiently close to this highly concentrated positive charge would experience an intense repulsive force, and would be deflected in a hyperbolic path. The deflections enabled the actual positive charges carried by the nuclei of the atoms of the different metals to be calculated, and also the maximum value for the size of these nuclei. The charge was found to be greater the greater the atomic weight of the metallic atom and to be, within the limits of experimental error, equal to the atomic number of the atom. Thus, the experimental values for platinum, silver, and copper were found to be 77·4, 46·3, and 29·3 respectively. The atomic numbers are 78, 47, and 29, and these figures agree with the experimental figures to within the limits of experimental error. Thus we have an experimental demonstration of the important law that the positive charge on the nucleus of an atom is equal to the atomic number of that atom. The experiments also showed that the maximum size that can be attributed to the nucleus of an atom is exceedingly small. Like the electron, the nucleus of an atom is very much smaller than an atom; it is of subatomic dimensions. There is reason to suppose, indeed, that the hydrogen nucleus is small compared even with an electron. It is probable that the radius of a hydrogen nucleus is not greater than 10^-16 cm., which is about ¹⁄₂₀₀₀ part of the radius of an electron.

One of the most interesting and striking confirmations of our general theory is provided by radioactive phenomena. We have said that there are about 40 radioactive substances known, and they are all substances having high atomic weights. The nuclei of such heavy atoms must be very complicated structures, built up, as the gold atom is built up, of a large number of hydrogen nuclei and several electrons. Now a radioactive substance, in the course of its disintegration, may give rise to several substances. Thus radium, in the course of disintegrating, gives rise to the following substances:—It produces Radium Emanation, Radium-A, Radium-B, Radium-C, Radium-C′, Radium-C″, Radium-D, Radium-E, Radium-F, Radium-G. Radium-F is polonium and Radium-G is lead. Two kinds of particles are shot out during this series of disintegrations, α-particles and β-particles. We have seen that α-particles are helium nuclei and β-particles are electrons. The question arises, Where do these particles come from? The answer is that they come from the nuclei of the heavy, disintegrating atoms. It may astonish us that they are helium nuclei and not hydrogen nuclei that are shot out by the disrupting atoms. But we shall see later that the helium nucleus, consisting of 4 hydrogen nuclei and 2 electrons, is a very stable affair, so stable that it enters as a sort of indivisible unit into the structure of more complicated nuclei. Now let us, remembering our general theory, trace exactly what happens in the above series of radium changes. A radium atom turns into an atom of radium emanation by losing an α-particle. The α-particle carries two units of positive charge. It is shot out from the nucleus of the radium atom, and therefore the new nucleus is minus two positive charges. That is to say, the nucleus of an atom of radium emanation carries two charges less than the nucleus of a radium atom. But the charge on the nucleus is, as we have seen, equal to the atomic number of the atom. It follows that the radium emanation atom must be placed two steps lower than the radium atom in the periodic table. But the α-particle contains four hydrogen nuclei. Therefore the atomic weight of the radium emanation atom must be four units less than that of the radium atom. The result of an atom losing an α-particle, therefore, is to give rise to a new atom whose atomic weight is less by four units, and which belongs to a place two steps back in the periodic table. What is the effect of losing a β-particle? The nucleus of every atom except a hydrogen atom contains, besides a number of hydrogen nuclei, a smaller number of electrons. These electrons neutralise an equal number of the hydrogen nuclei contained in the nucleus of the atom, leaving over a number of hydrogen nuclei equal to the charge on the nucleus, which is itself equal to the atomic number of the atom. A β-particle shot out from the nucleus, therefore, leaves one extra hydrogen nucleus unneutralised. In consequence, the charge on the atom’s nucleus increases by one unit, and therefore the atomic number increases by one. The new atom, therefore, moves one place up in the periodic table. And what happens to its atomic weight? Its atomic weight is unaffected, for we have seen that electrons play almost no part in contributing to the mass of an atom. The loss of an electron makes practically no difference to the weight of an atom. Besides, the new atom soon captures a free electron (of which there are always a large number about) to compensate for its extra positive charge. This electron does not fall into the nucleus, but joins the group of electrons which are rotating round the nucleus.

We are now in a position to understand the series of radium changes given above. Radium, with an atomic weight of 226, loses an a-particle and becomes radium emanation, with an atomic weight of 222. Radium emanation, losing an α-particle, becomes radium-A with an atomic weight of 218. The loss of α-particles continues, and radium-A gives rise to radium-B, with atomic weight 214. At radium-B the process alters. Radium-B loses a β-particle and turns into radium-C. The atomic weight is, of course, unaltered, so radium-C also has the atomic weight 214. Having got as far as radium-C, a very interesting thing happens. Some radium-C atoms, by shooting out an α-particle, pass straight to radium-C″, with an atomic weight of 210, and then, through radium-C″ losing a β-particle, to radium-D, also with an atomic weight of 210. Other radium-C atoms, however, shoot out a β-particle instead of an α-particle, and so become radium-C′, with an unchanged atomic weight of 214. Radium-C′ shoots out an α-particle and so it also becomes radium-D, atomic weight 210. Thus the two paths lead to the same result, viz., radium-D. Radium-D is not stable, however; it loses a β-particle and becomes radium-E. That also loses a β-particle and becomes radium-F, i. e., polonium. Both these substances, radium-E and polonium, have, of course, the same atomic weight, 210, as radium-D. Having reached polonium, the series has one more step to go. Polonium, by losing an α-particle, becomes lead, with an atomic weight of 206. With lead, the process of disruption seems to have stopped. There is no evidence that lead is disintegrating; if it is, it must be at an exceedingly slow rate which has hitherto avoided all means of detection. It must be noted here that the lead reached in this way has not the same atomic weight as ordinary lead. Ordinary lead has the atomic weight 207·2. By taking a different series of radioactive changes, starting from thorium, we also reach lead as the final substance. But the lead so obtained has an atomic weight of 208. These curious facts, and a number of others like them, we must now proceed to consider.

§ 4. Isotopes

The chemical and physical properties of an element depend on its atomic number, i. e., on the positive charge carried by the nucleus of an atom of that element. And this positive charge is, as we have seen, a resultant charge. It is a result of the combination of a number of unit positive charges with a smaller number of unit negative charges. We can obviously reach the same resultant figure in as many ways as we please. If the resultant charge on the nucleus is to be 5, for instance, then we could take the combinations +6 and −1, or +7 and −2, or +8 and −3, and so on. Each of these arrangements would give atoms having identical chemical and physical properties. But their atomic weights would be different. The atomic weights depend, not on the resultant positive charge, but on the actual number of positive charges present in the nucleus, including those that are compensated for by negative charges as well as those that are not. In the above case, for instance, our atoms would have atomic weights 6, 7, 8, and so on. And this is the only difference they would have. By no other chemical or physical properties could they be distinguished one from another.

It is therefore a very interesting fact, and one fitting in beautifully with our theory, that many elements have been shown to consist of a mixture of atoms having different atomic weights, but identical in every other respect. The element chlorine, for example, has the atomic weight 35·46. This number is about as far removed as it could be from being a whole number, and is therefore specially fatal to the theory that all atomic weights are simple multiples of the same unit. But it has been shown that chlorine is really a mixture of two groups of atoms, the atomic weight of the atoms of one group being 35 and the other 37. These groups are mixed together in about the proportion of 3 to 1, and the ordinary measured atomic weight of 35·46 is really the average weight of the mixture. Neon, again, whose atomic weight is ordinarily given as 20·2, is found to consist of two groups of atoms with atomic weights 20 and 22. Much more complicated groupings have been discovered. Thus krypton, whose atomic weight is put as 82·92, is made up of groups of atoms having the weights 78, 80, 82, 83, 84, 86. Such elements are called Isotopes, the name indicating that the groups of atoms belonging to these elements occupy the same place in the periodic table. It will be noticed that the atomic weights of these groups of atoms are all whole numbers. This is on the basis of oxygen taken as 16. On this basis hydrogen is not exactly unity, but is 1·008. It appears probable, then, that all atoms have atomic weights which are nearly, but not quite, whole multiples of hydrogen.

The existence of isotopes definitely destroys the great importance that chemists had always assigned to atomic weights. We have atoms of different atomic weights but of the same properties. Further, as we saw in studying the disintegration of radium into lead, we have elements of the same atomic weight but with wholly different chemical and physical properties. The atomic weight of an element, therefore, by no means suffices to determine its chemical and physical properties. We see once more that the really important quantity to be known about an element is its atomic number, i. e., its position in the periodic table. It is worth noting that the existence of isotopes was not suspected until comparatively recent times, although very delicate determinations of atomic weights have been practised for decades. The most refined measurements customary in such determinations never varied from sample to sample of the same element. Exactly the same mixture of atoms constitutes chlorine, for instance, wherever the chlorine is obtained, and always has done so ever since men began to study chlorine. The groups of atoms which make up chlorine or any other isotope must have been thoroughly and universally mixed long ages ago—in all probability before the formation of the earth’s crust, when such universal and complete diffusion would have been possible.

§ 5. Relativity and the Atom

It is necessary, now, to say a little about the Restricted Principle of Relativity, since certain points about the modern theory of atomic structure cannot be understood without it. But it is not necessary to explain the principle itself. It is only necessary to describe the relation between energy and mass that the theory shows to exist. In pre-Relativity mechanics, it was always assumed that the mass of a body was completely independent of its velocity. There was no reason to suppose otherwise. Whether a body was moving fast or slow, or whether it was at rest, its mass, when measured, was always found to be the same. But the theory of relativity asserts that the mass of a body does vary with its velocity. As the body moves faster its mass increases. The mass increases in such a way that, at the speed of light, it becomes infinite. This can only mean that the velocity of light is a natural limit, that no material body could possibly exceed this speed. If it be true that the mass of a body increases with its velocity, it might be thought that experiment would long ago have led us to suspect that fact. But the law according to which the increase occurs is such that the increase is not measurable except at very great speeds. Now we are not familiar with bodies moving at very great speeds. We know of velocities such as 100 miles per hour and even, in astronomy, of velocities which reach a few miles per second. But velocities which are a considerable fraction of the velocity of light, viz., 186,000 miles per second, are practically unknown. It is the α- and the β-particles which furnish us with examples of bodies moving at speeds comparable with that of light. And experiments on these bodies show that their mass does increase with their velocity, and precisely in the way predicted by Einstein’s theory. So that the ratio e‍/‍m, the ratio of charge to mass of an electron, varies with the velocity of the electron. As the velocity increases m increases and therefore e‍/‍m grows smaller. The value of e/m usually given, viz., 1·77 × 10⁷ (electromagnetic) units, is the value for low velocities, when m may be taken as the mass of the electron at rest. We will denote this value of m as m_o; m_o is the mass of the stationary electron. At half the velocity of light, the mass of the electron is 1·15 m_o, i. e., it is about one-seventh greater. If the electron is moving at nine-tenths the velocity of light its mass is 2·3 m_o, or nearly two and a half times greater. At ninety-nine-hundredths of the velocity of light the mass of the electron is seven times its value at rest, and at the velocity of light itself, as we have said, its mass is infinite.

This result of relativity theory must obviously be borne in mind in any attempts to ascertain in detail what goes on inside an atom. If the mass of the rotating electrons is a quantity which enters into our calculations, then obviously we must remember that the mass varies with the velocity of rotation we ascribe to the electrons. Another important aspect of this theory is that it shows we must ascribe mass to energy. This, again, is a very novel conception. We are used to thinking of energy as something to which the property of possessing mass cannot be ascribed. The two things seem to have nothing to do with one another. But it can be shown that energy certainly does possess inertia, and the property of possessing inertia is what we really mean by mass. The mass of a body is, indeed, only another way of measuring the total amount of energy it contains. Every piece of matter possesses a vast store of internal energy. If the piece of matter begins to move its energy is increased in virtue of its motion. Its mass also is increased. But the increase in mass due to increase in energy is usually extremely small. In any chemical combination which is attended by the development of heat, for instance, there is a certain loss of mass due to the energy radiated away during the process of combination. The resultant mass of the compound is less than the sum of the original masses of its constituents. But the loss which occurs in this way during any chemical process is exceedingly small, and the old law of the invariability of mass is, in all such cases, quite good enough. But there appears to be a beautiful and highly interesting exception. We have seen that there is reason to suppose that the helium nucleus, which is shot out of radioactive bodies as an α-particle, is a very stable structure. It is composed, as we have said, of four hydrogen nuclei and two electrons. The great stability of this structure suggests that its formation was attended by a great expenditure of energy, so that an enormous amount of energy would have to be communicated to it to break it up. Now the atomic weight of helium is 4, and the atomic weight of hydrogen is not 1, but 1·008. Four times the mass of the hydrogen atom would give an atomic weight of 4·032. The suggestion is that the difference between this value and the actual measured value of 4, represents the mass of the energy lost in the process of combining the four hydrogen nuclei into the helium nucleus. This gives a measure, also, of the amount of energy that would be required to split up the helium nucleus into its original components. The amount of energy represented by this figure is really enormous. It is sixty-three million times greater than the energy expended in ordinary chemical processes, and this figure is a measure of how much more stable the helium nucleus is than an ordinary chemical compound. A chemical compound can often be dissociated merely by raising its temperature a few degrees, but even the enormous energy possessed by the fastest α-particles is only about a third of that required to dissociate the helium nucleus.

Chapter V: Quantum Theory