Nuclear Physics
Page 4
But if we were to develop the electron microscope into a moving picture camera of some sort, would it then be possible to follow the movement of the electron in its orbit around the nucleus, and to determine this orbit? Here we are faced with a fundamental difficulty, which makes it quite clearly evident that with this atom model we have reached the limits of visualization. For as soon as we have taken the first exposure on our film, we find that we no longer are in the position to take a second picture of the same atom. This is due to the fact that we will never again find it in an undisturbed condition. The atom has been disrupted by the very electrons which enabled us to take the first picture. The reason is that the first impact of the electrons used to take the first photograph tore the very electron of the atom itself out of its intra-atomic bond, so that the atom appearing on the second picture would never, in any circumstances, possibly be the same, unchanged atom. At best, we would discover the electron somewhere far outside, far away from the nucleus.
It is therefore, evidently, fundamentally impossible to observe the orbit of an electron within the atom. But this impossibility is not due to any shortcoming (still remediable) of that postulated ideal microscope, assumed to be as perfect as natural laws would allow it to be, but rather a consequence of those very laws. By the operation of these self-same natural laws, extremely violent methods—as exemplified by the use of an electron microscope, where the electrons are accelerated in their orbits by a very high voltage—are our only means of getting a sharp, well focused picture of an atom which is in conformity with natural laws.
At this point, it can no longer astonish us to discover that we have reached the limits of visualization, and that the concept of electrons circling a nucleus cannot be taken literally, like the concept of a water molecule consisting of two hydrogen atoms and one ogygen atom, arranged in a triangular pattern.
The limitations imposed here on visual representation can be formulated with greater accuracy with the aid of a relationship, called the uncertainty principle, which is based on the quantum theory. It can be expressed in the simplest form as follows: One can never know simultaneously with perfect accuracy both of those two important factors which determine the movement of one of these smallest of particles—its position and its velocity. It is impossible to determine accurately both the position and the direction and speed of a particle at the same instant. If we determine experimentally its exact position at any given moment, its movement is disturbed to such a degree by that very experiment that we shall then be unable to find it at all. And conversely, if we are able to measure exactly the velocity of a particle, the picture of its position becomes totally blurred.
But by this statement I have anticipated the climax of a development which I must now attempt to describe from its very beginning.
Quite apart from the difficulties involved in obtaining a visual representation, the atom model has certain other properties which do not seem to agree at all with actual experience. For, according to all our previous knowledge, an electron revolving around an atomic nucleus should not be able to revolve in a circular or elliptical orbit for any length of time. In the first place, the electron carries an electric charge, and secondly, it vibrates in its orbit around the nucleus. As the vibrations of electrons in a radio aerial produce an electric wave, the electron vibrating in the atom must emit a wave of radiation, which in this case we should observe as ultraviolet light. But this would mean an emission of energy at the expense of the planetary electron, and the result would be that after a certain length of time, the electron would have to fall into the nucleus and come to rest there. This picture is totally different from the view presented by the atom model with its electrons circling in their orbits undisturbed. And even if it were possible in some way or other to get over this question of radiation, Rutherford’s atom model would still fail entirely to account for the stability and definiteness of the chemical properties of the atom.
The problem of co-ordinating atomic stability with Rutherford’s atom model was solved by Niels Bohr in 1913. Bohr’s views were based on a theory of Max Planck. In 1900, Planck had formulated—at first purely empirically—his radiation law, which interpreted the thermal radiation of a ‘black body’ (a body which absorbs all the radiation incident on it, and consequently—according to a law formulated by Kirchhoff—is also the most powerful emittor of radiation) in conformity with actual experience. In his subsequent attempt to give this law a physical interpretation, Planck encountered a very peculiar discontinuity in natural processes. He found that he was able to establish his radiation law solely on the foundation of the remarkable hypothesis that the smallest radiating particles, the atoms, could not assume the continuous sequence of all possible energy values of their vibrations (as they would have been expected to, according to all previous knowledge) but only a series of certain definite, specific energy values. It even appeared—and later research proved it, too—that the emitted radiation manifested this quality of discontinuity, and that light, regarded up to then as a wave process, must also consist of discrete quanta of energy. Planck realized that light of the frequency ν must be emitted as well as absorbed in discrete quanta of energy, of a magnitude proportional to the frequency and he postulated that the energy of these quanta was equal to hv. This constant, h, is called Planck’s constant (see Table 1), and has been the keynote of the entire development of physics for several decades.
As a result of this theory of energy quanta of light, a very strange situation ensued. On the one hand, it was recognized clearly that certain optical phenomena—e.g. those of interference—could only be understood by regarding light as a wave process. On the other hand, the concept of light quanta appeared to be no less necessary in order to explain other phenomena. But according to the latter view, light has no longer the characteristics of waves, propagated in space in all directions, but is a swarm of particles traversing space in straight lines. Therefore, it appears to be impossible to do without two completely different and fundamentally contradictory views of light. We can thus speak of a wave-particle duality—of a wave aspect and a corpuscular or particle aspect of light.
Bohr started out from the above-mentioned hypothesis of a discontinuity in atomic phenomena, and he advanced the theory that atoms can exist for an appreciable length of time in certain specific states only, which are characterized by specific electron orbits—in other words, by definite energy levels of their planetary electrons—and that when they are in these stationary states, they do not radiate. This theory explained the stability of atoms, but there was still a long way to go before the natural laws governing atomic structure could become known.
During the first decade of the existence of Bohr’s theory, the chemical properties of the elements were finally explained on the ground of the quantum theory. A further important step was successfully taken by the Frenchman Louis de Broglie, who realized, in 1924, that this strange duality of character which at times gave light the aspect of a wave, at times that of a swarm of particles, was a property not only of light, but of matter, too. This discovery finally led to the formulation of wave or quantum mechanics, which in a sense brought the theory of the extranuclear structure of the atom to completion.
Let us now try to elucidate this so-called duality of matter by two photographs. To begin with, let us observe once again the tracks of alpha particles in Figure 3, where their particle character is most clearly evident. After a study of these tracks, one can no longer have the slightest doubt that very small particles have actually flown through space and been deflected at some point here.
On the other hand, we have the evidence of experiments which indicate, with the same degree of certainty, that alpha rays are not particles but waves propagated from the source of radiation. I will not demonstrate this by the alpha rays, but by the beta rays, the particle character of which has been proved by numerous experiments no less convincingly than that of alpha rays. If beta rays are allowed to penetrate thin layers of matter, they show exa
ctly the same kind of interference phenomena as may be observed in the case of x-rays under the same conditions—and we are accustomed to regard x-rays as typical wave radiation. The interference phenomenon consists in the fact that a central ray which penetrates the layer of matter, is surrounded by interference rings, which can be interpreted only as a superimposition of deflected waves. For comparison, we show here two photographs, one (Figure 5) taken by x-rays, and another (Figure 6) taken by beta rays. The latter one is one of the first photographs of this kind ever taken. But for the difference in their sharpness these two photographs would be indistinguishable.
As we see, it is impossible to entertain any doubt whatsoever as to the remarkable dual character of the electron. On the one hand, electrons may be regarded quite legitimately as particles, and we can be absolutely certain that a snapshot of an atom will be a picture similar to that shown in Figure 1. But on the other hand, they appear as waves, too, and this wave nature can also be used to obtain a picture of the atom—although in this case, the picture will look considerably different.
Figure 5.—Interference rings of Rëntgen rays.
Modern physics utilizes both the wave aspect and the particle aspect, and treats both as of equal right. For we know when to use one and when the other, and we know also that neither can stand by itself, without the other.
Figure 6.—Interference rings of Beta rays.
Thus we see that it is very difficult to obtain a visual concept of an atom and at this point, we have evidently reached the limit of the possibilities of visualization. As we have seen, the most that can be observed of an atom, is the result of one single snapshot. But such a snapshot never shows the orbit of the electron, but two specific points only—the nucleus and the electron in its momentary position. If a great number of such photographs are taken, in succession, of different atoms of the same kind, the electron will be found in various locations, at a greater or lesser distance from the nucleus, more frequently in one spot, less frequently in another. In this way, we eventually obtain a general, overall picture of the probability of finding the electron at one point or another in the vicinity of the nucleus, a probability value for the distribution of electrons. But all these photographic records as a group—being collected in a single instant, as it were—can be regarded also as a picture of the average distribution of the density of electricity in the vicinity of the nucleus. Such a density distribution is comparable, in some degree, to a wave phenomenon—a stationary wave. If we conceive of stationary waves of electrically negatively charged matter, these, too, will correspond to a certain specific density distribution of this matter. Actually, the de Broglie matter waves can be interpreted so that the square of the amplitude of the waves at a certain specific point indicates the density of matter at that spot. But we can just as well say that it indicates the possibility that in a snapshot the electron will be discovered at that very point. These stationary waves in the immediate vicinity of the nucleus were investigated by Schrödinger; they represent, in fact, the object of his wave mechanics. These stationary waves also form the foundation for verifying a stationary distribution of electricity in the vicinity of the nucleus, and consequently, the existence of stationary states of the atom, in which no radiation occurs, becomes understandable. Thus one of the difficulties in connection with the atom model is eliminated.
The individual stationary waves which can possibly occur in an atom, do not form a continuous series, any more than do the individual characteristic vibrations of the strings of a musical instrument. A string can vibrate in its fundamental tone, in which case it has no nodes. On the other hand, it can vibrate also in an overtone, and in that case it has one or more nodes. Similarly, an atom can ‘vibrate’ in its ground state, in which case it has no ‘nodes’—meaning, no levels on which the density of matter disappears. But it can vibrate also in an overtone—in an ‘excited’ vibration, as it is called—and then there are several nodal levels of zero density. These various stationary vibrations correspond to the various stationary states which an atom is capable of assuming.
Let us elucidate the conditions described above by the example of the simplest of atoms, the hydrogen atom, with the aid of illustrations. The ground state of a hydrogen atom (denoted by the symbol Is) was described by Bohr in 1913 as a circular orbit of the electron around the nucleus (Figure 4). In the particle aspect, this is a clear picture. According to this view, the electron has a spin moment about the nucleus. To-day we know that actually it has none. Therefore, to-day we say rather—still within the framework of the particle aspect—that the electron shuttles on a straight line about the nucleus. Thus, we imagine the atoms as shown in Figure 7 (a).
But on the other hand, we can conceive of the state of electronic matter in a hydrogen atom also as a wave process (Figure 7 (b)). If we should take thousands of snapshots of the atom in its ground state and then develop them superimposed on each other, we would get a density distribution, or probability distribution, such as is shown in Figure 7 (b). It is computed from Schrödinger’s wave mechanics.
But there exist also ‘overtones’—excited states—through which an atom can pass as a result of the impact of a foreign electron. In such an excited state, the atom becomes capable of radiation, of emitting a light photon (quantum of energy of light). This happens because the atom passes from its excited state back to its ground state, or into another excited state of smaller energy. Figure 7 (a) and (b) show such excited states, marked by the symbols 2p and 2s. In the wave aspect of matter, the excited state closest to the ground state is represented by a stationary wave with a nodal plane perpendicular to the plane of our drawing. But this density distribution is, again, just a model, a mere aid to our visual perception, and acquires a concrete significance solely by virtue of thousands of snapshots. If we want to depict the same stationary states under the particle aspect of matter, we obtain the picture of a circular orbit, as in Bohr’s original theory. But this orbit can assume many different spatial positions, and the superposition of all these possible states results in a probability or density distribution, in which the same nodal plane appears which is present in the wave aspect.
Figures 7—Hydrogen atom in the ground state and in states of excitation.
For excited states of higher energy (2s), a high degree of density is obtained in the centre, with a sparsely occupied ring on the outside. In such cases, there is always a certain probability that the electron may suddenly be encountered outside, in the vicinity of the ring.
We shall not go into any further details here. My sole purpose has been to give you an approximate idea of the different concepts employed in physics these days in order to illustrate the structure of the atom, in some degree at least. The reason why no such visual representation can ever manage to cover simultaneously every characteristic of atomic structure, has been discussed already.
III. THE PERIODIC SYSTEM OF ELEMENTS
We come now, finally, to the question of the relationship between the chemical properties of the elements and the structure of the extranuclear parts of their atoms, the number of planetary electrons, and thus, ultimately, the nuclear charges of these atoms. We are indebted to Bohr’s theory for our understanding of this interrelationship, and we can obtain the most satisfactory general idea of it by arranging the elements according to the magnitude of their respective nuclear charges, in other words, according to their atomic numbers, which are always identical with the number of elementary quanta of positive electricity on their respective nuclei. (Table II, at the end of this book.) Thus, we start with hydrogen (1), continue with helium (2), and proceed in this manner until we reach curium (96). It has been known to chemists for about a hundred years that the chemical properties of the elements repeat themselves when they are arranged in the order of their atomic numbers. If we break off the series at the end of each such period and start a new line; we get the well known periodic system of elements of Newlands, Mendelejeff and Mayer (Table III, at the end of this book). Acc
ording to Bohr, this periodicity of the elements can be explained on the ground of atomic theory as follows:
According to a principle formulated by Pauli, one orbit cannot be occupied by more than one electron. There is room for one electron only in any one orbit (or in any one stationary vibration with a specific quantum number). This principle may be cited here without proof. So, if an atom has several electrons, the electrons after the first one will be located in ever farther outlying orbits. In considering such problems, it is always advisable to refrain from imagining a completed atom and to proceed, instead, outward from the bare nucleus, and to imagine that one electron is added after another, outwards from the centre, until finally the number of electrons characteristic of the element is completed.
If we continue with the successive addition of individual electrons according to this structural principle, we find that after the incorporation of a specific number of electrons, these electrons constitute, in an important sense, a complete system, the addition of further electrons begins, as it were, a new structure at a considerably greater distance from the nucleus. The extranuclear electron structure of the atom is said to be built up of a number of individual shells. Those chemical elements in which the extranuclear atomic structure is, itself, completed by the completion of such a shell, hold a special significance. They are the inert gases. The first one of these, helium, may be imagined, under the particle aspect of matter, as a nucleus with two electrons revolving about it, at approximately equal distances (Figure 8 (a)). Thus the first shell is completed by two electrons already. The next element, lithium, has one electron more, and this third electron moves in a much wider orbit, as a lone electron in a new shell (Figure 8 (b)). It is evident that this atom can yield up an electron very easily, and consequently, occurs very frequently as a positive ion. This is the explanation of the electro-positive character of lithium, the most important characteristic of the chemical behaviour of this element.