Nuclear Physics

by W Heisenberg

  And so on further. After a certain number of elements, we always find a completed shell, as in helium. The chemical significance of this fact is that these elements—the inert gases, helium, neon, argon, krypton, xenon—do not react chemically at all. They always represent the end of a period, as shown in Table III at the end of this book.

  As we have stated before, the first period consists of only two elements: hydrogen and helium. The second period contains eight elements: lithium, beryllium, boron, carbon, nitrogen, oxygen, fluorine and neon. Since the element fluorine contains seven electrons in its outermost shell, one more is needed to complete this shell. This fact gives a clue to the chemical properties of fluorine: The fluorine atom always tends to complete this outermost shell by taking up an eighth electron, and thus to have an electro-negative character, and to occur in solutions negatively charged, as a rule. Obviously, those elements which occur at the beginning of a period (hydrogen and the alkali metals), and which therefore will readily give up an electron, combine particularly readily with one of the penultimate elements of the periods, the halogens, which will readily take up an electron. Examples of these combinations are hydrogen fluoride (HF) and sodium chloride, ordinary table salt (NaCl).

  Figure 8.—Model of (a) the helium atom; (b) the lithium atom.

  The third period, which begins with sodium and ends with argon, again consists of eight elements. Thereafter, the periodic system becomes a little more complicated. Both the fourth period (from potassium to krypton) and the fifth one (from rubidium to xenon) contain eighteen elements each, and the sixth period (from caesium to the inert gas radon) consists of thirty-two elements. The final period is evidently an incomplete one, which for the time being ends with curium. The numbers of elements contained in the various periods—2, 8, 18, 32, i.e. 2 × 12, 2 × 22, 2 × 32, 2 × 42—obviously follow a simple mathematical sequence. The latter can be explained by the quantum numbers of the individual states of vibration, already mentioned. But we cannot discuss the details of this explanation here.

  We have now obtained a general, although merely superficial, survey of our current knowledge of the extranuclear atomic structure. This knowledge enables the physicist to understand the chemical properties of the individual elements, in their general outlines at least. Theoretically, with the aid of quantum mechanics, it would be possible to calculate, quantitatively, every chemical magnitude, such as emission of heat, affinities, etc. But the mathematical difficulties are, as a rule, so great that such calculations have only been actually carried out in some of the simplest of cases.

  This brings us to the conclusion of our discussions of the extranuclear structure of the atom. We shall now turn our attention to our principal topic, the nucleus of the atom.

  3. RADIOACTIVITY AND THE BUILDING BLOCKS OF THE NUCLEUS

  I. RADIOACTIVITY

  When investigating the internal physical properties of any system, we must endeavour, on the one hand, to discover its effects on the outside world and, on the other hand, try to approach it in some way that will show us how it behaves during this process. In certain cases, it becomes necessary to dissect it into its component parts, by means of interference from outside. This principle applies to the atomic nucleus, too. Thus there arises the question whether there are any nuclear phenomena which furnish us with the desired knowledge of their internal structure without our having to resort to such interference. The radioactivity (a phenomenon already mentioned) of certain heavy elements is actually such a phenomenon. For this reason, let us discuss it first.

  We have already discussed the fact that in radioactivity three distinct types of radiation can be observed: alpha, beta and gamma radiation. A few years after the first observation of radioactivity, Rutherford and Soddy made the discovery, of decisive importance for the development of atomic theory, that the emission of alpha and beta rays is associated with a transmutation of the chemical elements. An atom which has emitted either of these radiations is no longer an atom of the same original element.

  This discovery was of paramount importance for atomic theory. The old notion of atoms had now to be discarded; the atoms of chemistry were, evidently, no longer the ultimate, indivisible building blocks of matter. To be sure, it was still not possible to change one element into another by chemical means, yet the existence of a natural process producing this very result appeared to be a certainty. The hopes and aspirations of the alchemists of past ages were thus given new life. For if in certain cases, nature itself effected a transmutation of the elements, it was bound to be possible to perform this process artificially, once the proper tools were discovered. It was bound to be possible, theoretically at least, to turn mercury into gold!

  In view of our present knowledge, in the first place that the alpha and beta particles carry electric charges, and secondly, that the chemical properties of the atom depend on the number of elementary charges of electricity on its nucleus, this discovery of Rutherford and Soddy is easily understandable to-day. The alpha and beta particles originate in the nucleus of the atom, and not in its outer structure. The alpha particles are helium nuclei, identified as such by their mass and charge. Their mass is 4 atomic mass units, and they carry two elementary charges of electricity. We express this shortly by saying that their mass number is 4, and their atomic number is 2. Accordingly, the helium atom is represented by the symbol 2He4, where the superscript denotes the mass number and the subscript the atomic number. This kind of symbolism is applied to the atoms of all the elements. When an alpha particle is ejected by an atomic nucleus, it carries with it not only its own mass, but also its own charge. The nucleus loses both this mass and charge; its atomic number (the number of elementary quanta of electricity present on it) is reduced by 2, whereas its mass number is reduced by 4. On the other hand, a beta particle is a negative electron. Its mass number is approximately 0, and its atomic number is −1. Accordingly, if e stands for ‘electron’ in general, the symbol of the negative electron may be written as -1e0. Thus, when an electron is emitted, the mass of the nucleus remains practically unchanged, whereas its positive charge increases by 1, due to the loss of one elementary quantum of negative electricity. Hence, both the emission of an alpha particle and the emission of a beta particle result in a change in the atomic number. Since the chemical properties of the elements are determined by the nuclear charge number, the atomic number, it is evident that both alpha and beta radiation must result in a transmutation of elements.

  Let us now examine these facts more closely, using radium as our example. The mass number of radium is 226, its atomic number is 88, and consequently, its symbol is 88Ra226. The radium atom contains 88 extranuclear electrons; since 86 electrons form completed shells, the chemical properties of radium are determined largely by the two electrons which revolve around the nucleus in the outermost, incomplete shell. Therefore, the chemical properties of radium are similar to those of one of the alkaline earth metals, such as barium or strontium. The radium nucleus is an emitter of alpha rays, and as a result of this radiation, its mass is reduced to 222, and its nuclear charge, its atomic number, to 86. A new element—likewise radioactive—is formed: the inert gas radon, the symbol of which is 86Rn222. Due to its nuclear charge number, the radon atom contains only 86 electrons, which are arranged in completed shells. This atom is therefore chemically inactive—this element is an inert gas. The process of the emission of an alpha particle by the radium atom and the formation of a radon atom are indicated by the following formula:

  The symbol to the left of the arrow is that of the radiating atom; the symbols following the arrow show what has become of this atom as a result of the emission of the alpha particle. In such a formula, the sum total of the superscripts must be equal on both sides of the arrow; in this particular case, 226 = 222 + 4. This follows from the law of the conservation of mass. The same rule applies to the subscripts; in this case, 88 = 86 + 2. This follows from the law of the conservation of electric charges. Analogous formulae are used for proc
esses in which beta radiation occurs.

  All—or nearly all—of the alpha particles emitted by a homogeneous radioactive substance have exactly the same range. This is evident in the cloud chamber photograph shown in Figure 3 (a). It shows the successive decay of two radioactive elements; therefore, we see two groups of alpha rays. The range in air of the alpha particles of different radioactive substances is between 1 and 9 centimetres, and the range is evidently dependent on the energy with which the particles emerge from the nucleus. The greater the energy, the longer is the range.

  The various radioactive substances show great differences in their respective speeds of transmutation. Some of these substances are very short-lived, whilst others last very long and show no noticeable lessening in radioactivity over long periods of time. Obviously, for the atoms of every radioactive substance there exists a probability, capable of being expressed numerically, of their radioactive decay. The reciprocal of this probability is the average life of the substance. The decay probability, and hence also the average life, is independent of the number of atoms already decayed. This means that the same percentage of the number of atoms still intact will decay per unit time. This law is expressed by the following equation:

  dN = − λ N dt

  with the following solution for N:

  N = N0e−λt

  where N0 is the number of the intact atoms present at the time t = 0, N is their number at the time t, e is the base of natural logarithms, and λ is the decay probability, and hence 1/λ is the average life. Instead of the latter, the half-life period, T (that period of time during which exactly one-half of the original number of atoms decays) is frequently used. The half-life is slightly less than the average life; it differs from the latter by the factor log nat 2, the natural logarithm of 2. (If we write t = nat 2, then N = N0 × e−log nat 2 = ).This law applies to both alpha and beta radiation.

  Thus the radioactive properties of a homogeneous substance are determined principally by two factors: the nature of the emitted particles and the average life or half-life of the substance.

  The gamma rays play a somewhat different part. We must point out, first of all, that in natural radioactivity gamma rays do not appear alone, but only in combination with one of the other two types of radiation. Gamma rays have an even greater penetrating power than either the x-rays (to which they are essentially analogous in other respects) or the alpha and beta rays. To give an approximate idea of their power of penetration, let it be said that while an alpha ray is absorbed by a single sheet of paper, 100 such sheets would be required to absorb a beta ray, and several thick volumes to absorb the gamma radiation. As already mentioned, gamma rays cannot be deflected, nor—unlike the alpha and beta rays—can they be made visible in the cloud chamber. For although the gamma rays too cause ionization in air, this is not a direct, primary process, but an indirect ionization through the agency of the electrons which the gamma rays dislodge. In the cloud chamber, we can see only the tracks of the secondary particles generated by them; the tracks of the gamma rays themselves are not visible. These two facts are quite compatible with each other, since both can be attributed to the absence of an electric charge in gamma rays.

  Actually, gamma rays differ from x-rays, and even from visible light, too, merely in that the wavelength of the gamma rays is much shorter. They are a species of electro-magnetic waves, among which the radio waves have the longest wavelength. At any rate, we know that the already mentioned wave-particle duality applies to all these types of radiation. Hence, while we have just referred to gamma rays as an electromagnetic wave issuing forth from the atomic nucleus, we may just as well look at them under their particle aspect and speak of particles, extremely energetic photons, ejected from the nucleus and speeding through space with the velocity of light.

  The fact that under certain conditions atomic nuclei can emit gamma rays, is quite understandable. We already know that the extranuclear structure of the atom can emit light when—for example—the atom is excited due to a gaseous discharge. Atoms emit x-rays also when particles are dislodged from their inner electron shells by extremely fast electrons. This follows clearly from the fact that the extranuclear structure of the atom constitutes an electrical system, and when any such system is disturbed, electromagnetic waves are emitted. But the atomic nucleus, too, is an electrical system, as is shown by its charge, and so it can be reasonably expected that in conjunction with certain internal processes within the nucleus, the nucleus, too, will emit electromagnetic waves—gamma radiation.

  In natural radioactivity, beta particles make an appearance always as carriers of a negative charge only, in other words, only as negative electrons. Let us jump ahead for a moment and mention that in the radiation of artificially produced radioactive substances positively charged electrons are observed also; they are particles having the same mass as the negative electrons, but each of them carries an elementary quantum of positive electricity (Anderson). To-day, these particles are known as positrons, and electrons are usually regarded merely as a negative variety of them. The question now arises, why these positrons were not observed a long time ago, and why they do not occur in the extranuclear structure of the atom. The answer to ·this question is based on experiments which have established that positrons are very short-lived. As soon as a positron approaches an electron—usually after a very brief interval of time—it combines with the latter, to form an electrically neutral structure; the product of this union is one or two gamma-ray photons, i.e. photons of an extremely short wavelength. These constitute what is known as annihilation radiation. Both the existence of positrons and of annihilation radiation were predicted by Dirac, and subsequently confirmed by experiments. The annihilation radiation has its counterpart, too; a photon entering the powerful field in the immediate vicinity of an atomic nucleus, can change into an electron and a positron. This formation of a pair of charged particles can be observed in the cloud chamber, and is shown in the photograph reproduced here as Figure 9. In the cloud chamber, a very strong magnetic field deflects the electrons to one side, and the positrons to the other, so that they describe circular tracks (Figure 9). In the upper half of our photograph, such a pair formation has just taken place, and the two tracks of the electron and positron thus formed can be clearly seen. Since this photograph is considerably enlarged, the individual cloud droplets along the tracks can also be recognized. Another electron, the track of which is slightly blurred, is visible, too. The rest of the droplets are due partly to impurities.

  Figure 9.—Pair production in the cloud chamber

  However, this phenomenon of pair formation must not be regarded as indicating that a photon is actually composed of an electron and a positron. A photon is a true elementary particle, in the strictest sense of the word. But it is capable of changing, when it enters into interaction with other particles or with powerful fields. Generally speaking, the concept of ‘elementary particles’ in modern physics has undergone a change; these elementary particles may be described as the ‘ultimate, indivisible building blocks of matter’ in a very limited sense only. For it has been proved that these elementary particles can change into each other practically without restriction, so long as it is compatible with the laws of conservation of mass, energy, etc. But just for this very reason, it is meaningless to describe any of them as being composed of some of the others.

  Beta particles have a far longer range than alpha rays. The explanation is not that the former have more energy, but principally that due to their smaller charge and greater velocity, they have a considerably smaller capacity to produce ionization, and therefore they lose their energy much more slowly along their path.

  But there is another very characteristic difference between alpha and beta rays. All alpha rays of a homogeneous radioactive substance have exactly the same range, and therefore, the same energy. This is to be expected, for as the energy released in any chemical reaction is determined both by the initial and end states of the system, so must also the ene
rgy released by radioactive decay—in other words, essentially, the energy of the alpha particle—depend solely upon the initial and end states of the atomic nucleus. Generally speaking, all nuclei of the same kind have the same energy, but in the case of beta rays the situation is different from that of the alpha rays. Any homogeneous radioactive substance will emit beta particles with all possible velocities, from an upper limiting velocity down to quite low speeds. It seems that the energy corresponding to this upper limit is identical with the difference between the energies of the atom in its initial and end states. The occurrence of slower particles would, however, contradict the energy principle, unless the energy missing from the individual beta particles were removed from the nucleus in some other way. This brings us to the theory of Pauli, that with every beta particle another particle leaves the nucleus, carrying the difference in energy. The sum total of the energy is always constant, and this total energy is shared by the beta particle and this new particle, in accordance with definite statistical laws.

  This new particle must be devoid of all electric charge, for otherwise it would be impossible to explain the fact—confirmed experimentally in every instance—that when a beta radiation takes place, the nuclear charge increases by one unit. The absence of an electric charge on this new particle is indicated also by the fact that these particles cannot be observed in the cloud chamber. Since this new particle is electrically neutral, and its mass is certainly very small, it is called the neutrino. According to the evidence of every experiment hitherto performed, the mass of the neutrino is smaller than the mass of an electron. But whether it is actually 0, like the rest mass of the photon, cannot be stated with any certainty as yet.