Chapter VII
The Inner Regions
§ 1. X-Ray Spectra
IN speaking of X-rays we have referred to their wave-lengths and to their spectra, but we have not yet given any indication as to how these wave-lengths are measured. The most satisfactory method of determining the wave-lengths of ordinary light is by means of a “diffraction grating.” This apparatus consists, essentially, of a sheet of glass on which a large number of very fine lines have been ruled very close together. The lines should be parallel and equidistant. Now the distance between two adjacent lines should be of the same order of magnitude as the wave-lengths to be measured. The lengths of visible light waves are comprised between 4 × 10-5 cm. and 7 × 10-5 cm., i. e., they lie between 4 and 7 hundred-thousandths of a centimetre. X-rays, as we have said, have wave-lengths about 10,000 times smaller than this. It is difficult enough to rule lines close enough together for the distances to be comparable with the lengths of light-waves; it is utterly impossible to rule them ten thousand times closer still. The distance between adjacent lines would have to be of the order of 10-8 cm., i. e., of the same order of magnitude as the molecular distances in a solid body. Manifestly such an apparatus is impossible to construct. But it so happens that nature has provided such an apparatus.
Certain mineralogists and mathematicians were long ago concerned to elucidate the regular shape and structure of crystals in terms of regular arrangements of their molecules or atoms. These molecules or atoms were supposed to be arranged in definite patterns, so that a crystal consisted of layers, arranged one behind the other, containing these regular assemblages. The distance between the molecules or atoms, so arranged, would be of the order of 10-8 cm. A crystal of salt, for instance, would have as the distance between its molecules 5·6 × 10-8 cm. The brilliant idea occurred to a German scientist named Laue that such an arrangement really constituted a sort of diffraction grating and one, moreover, of just the right dimensions to serve for the measurement of X-ray wave-lengths. The realisation of this idea was highly successful, and the employment of crystals has not only served to measure X-ray spectra, but has also taught us a great deal about the structure of the crystals themselves. It is now possible, employing this method, to obtain photographs of X-ray spectra.
As a result of these researches we now know that the wave-lengths of X-rays vary within fairly wide limits, according to the conditions of their emission. The longest waves are about 12 × 10-8 cm. in length, while the shortest are about 3 × 10-8 cm. The shorter the wave the greater its penetrative power or “hardness.” Now we have already said that each of the chemical elements, on being bombarded by cathode rays, emits a group of X-rays which is characteristic of it. The hardness of these X-rays varies with the substance that emits them, and in such a way that the greater the atomic number of the substance the harder are the emitted rays. We are concerned here with a wholly atomic phenomenon, for if a substance be chosen as the anti-cathode which is a compound of two or more elements, it is found that the resultant X-ray emission, when the anti-cathode is bombarded, is really a combination of the X-ray groups which would be emitted separately by the elements that have gone to make up the compound. These important facts were discovered by Barkla, who also discovered that there were two series of X-rays in the characteristic X-ray emission from an element. He called these two series the K-group and the L-group. He observed that the lighter elements (up to silver) gave the K-group of X-rays, and that heavy metals (such as gold and platinum) gave the L-group. Of these two groups, the K-group is the more penetrating. The harder or more penetrating the X-rays, the greater the impact of the cathode rays necessary to produce them, and Barkla saw that the K-group, in the case of the heavy metals, would be so hard that the experimental methods known to him would not suffice to produce them. Similarly, the L-group for the lighter elements would be too little penetrating, too soft, to be observable by the then known means. Barkla had determined the hardness of the rays he obtained by measuring their absorption by thin sheets of aluminium. And he had established a relation, as we have said, between hardness and atomic weight.
These results were made much more precise when the analysis of X-ray spectra by crystals replaced the absorption method of measurement, and when the wave-lengths so determined were related, not to the atomic weight, but to the atomic number. Besides the K- and L-groups, a third group, called the M-group, has been discovered. The M-group of rays is still softer than the L-group. The K-group, so far as our means of observation carry us, begins with sodium, whose atomic number is 11. With this light element the K-group, the hardest of the three groups, is distinctly weak. As the atomic number advances the K-groups emitted by the corresponding elements grow harder and harder, reaching their extreme degree of hardness with wolfram, whose atomic number is 74. For one and the same element, emitting both the K-group and the L-group, the L-group is much the softer. The L-group has been observed with copper, whose atomic number is 29, and here it is even weaker than the K-group of sodium. From copper onwards the L-group gets harder and harder, and it has been observed right up to the last of the elements, uranium. The still weaker M-group has only been observed so far with the heaviest elements, and even then special precautions have to be taken to observe it at all. These three groups of rays together make up the X-ray spectrum.
§ 2. The K-Group
Moseley, probably the most gifted of the young English men of science killed in the war, was the first to make a considerable advance on Barkla’s work. His first photographs (1913) were devoted to the K-group, and extended from calcium, with atomic number 20, to copper, with atomic number 29. These elements were used, successively, to form the anti-cathode of a cathode tube, and were therefore bombarded directly by electrons. To obtain the X-ray spectra he used, of course, the method of crystal analysis, but not in its most modern form. He established the following results.
As the atomic number increases the corresponding lines in the spectrum move regularly in the direction of smaller wave-lengths, that is, the hardness of the lines increases with the atomic number. This result, in a less definite form, was, as we have seen, already reached by Barkla.
Each element gives two K-lines. The stronger, more obvious, line corresponds to the longer wave-length. This line in the K-spectrum of an element is called the line. The weaker line is the harder line, i. e., it corresponds to the shorter wave-length. This line is called the line.
The X-ray spectrum of an element is purely a property of the atoms of that element. Brass, for instance, which is an alloy of copper and zinc, gives four K-lines, of which two are the K-lines of copper, while the other pair are the K-lines of zinc. Thus the K-spectrum of a complex substance is obtained by merely adding together the K-spectra of its elementary constituents.
The fourth result is of particular interest. It will be remembered that, for a few places in the periodic table, we inverted the order of the elements as given by their atomic weights. There are two or three places where a heavier element is put before a lighter one. The whole complex of the chemical and physical properties of such pairs of elements is allowed to determine their position in the periodic table, even when this is not in agreement with the atomic weight. Nickel and cobalt form such a pair. Cobalt is heavier than nickel, with an atomic weight of 58·97 as against an atomic weight of 58·68. Nevertheless, cobalt is written before nickel. This order, justified by general considerations, was completely confirmed by the X-ray spectra of these elements. The K-group for nickel has harder lines than the K-group for cobalt, and the increase in hardness corresponds to an advance of one step in the periodic table. Here we have a clear proof that the X-ray spectra follow the order of the atomic numbers, not the order of the atomic weights. To settle this point was the original object of Moseley’s research.
The fifth result which emerges from these researches is also of great interest. We have spoken of gaps in the periodic table and we have left spaces for elements which have not yet been discovered, but to which we have ascribed appropriate atomic numbers. In Moseley’s original research there was a gap between calcium and titanium. This gap was immediately revealed by the X-ray spectra. The advance in hardness from one element to another is quite uniform, and in passing from calcium to titanium a sudden jump was found, corresponding to the omission of one element. This missing element is known. It is the rare substance named Scandium, with atomic number 21. Its absence from Moseley’s series was at once revealed by the X-ray spectra. The regularity of the growth in hardness of the X-ray spectra enables us, without ambiguity, to say precisely how many elements (up to uranium) are yet undiscovered, and exactly whereabouts they occur in the periodic table. Thus, corresponding to atomic number 43, there is a missing element. It has received the name Ekamanganese. Other gaps in the system occur at atomic numbers 61, 75, 85, and 87. The study of the X-ray spectra of the elements, therefore, enables us to say definitely that five elements are missing.
Moseley’s results have been followed up, and his experiments repeated with better apparatus. The main discoveries that have been made by these later researches on the K-group are that there is a third line belonging to the group, and that the K α-line really consists of two lines very close together—what is called a doublet. The third line of the K-group is even weaker and harder than the K β-line. It is called the K γ-line. The same law holds for this third line as for the other two. Like them, it increases in hardness for elements of increasing atomic number.
The beautiful simplicity and precision of the results make this research on the K-group one of the most interesting in all the modern work on the atom.
Of the L- and M-groups we need only say at present that they contain a large number of lines of which many are doublets. The general law of their variation in hardness with the atomic number is the same as for the K-group.
§ 3. The Electrons near the Nucleus
We shall now proceed to show how these experimental facts are explained by the theory of atomic structure that we have outlined. In doing so we shall present the problem in a rather simplified form, but one which serves, in its main lines, as the basis for the detailed examination which Bohr, and one or two others, are attempting. We recall again the fact that the atom is regarded as a kind of planetary system, of which the nucleus is the central body and the electrons the revolving planets. We have already discussed the way in which we may suppose these electrons to be arranged. They exist in groups; each member of any one group moves in the type of orbit characteristic of that group. We shall find that it simplifies our ideas and does not essentially disturb the main lines of the theory if we imagine these groups of electrons to be situated on circles all centring about the nucleus. The circles get larger and larger, of course, as we proceed outwards from the nucleus. The circle closest to the nucleus we shall call the K-circle and the others, as we go outwards from the nucleus, the L-, M-, N-, etc., circles.
Let us now consider how we may suppose a radiation belonging to the K-group to be caused. We may suppose the first step to consist in the removal of an electron from the K-ring to the periphery of the atom, or else outside the atom altogether. If this removal be effected by a cathode-stream bombardment, we may imagine that it is the result of the direct impact of one of the bombarding electrons on the electron of the K-ring. A certain minimum amount of energy is necessary for this impact to be powerful enough to remove the electron. The electrons of the K-ring, the innermost ring, are powerfully attracted by the nucleus, and the bombarding electron must be moving sufficiently fast for its impact to overcome this attraction. There is therefore a certain minimum velocity below which the cathode-stream bombardment cannot detach an electron from the K-ring. The higher the atomic number the greater the charge on the nucleus, and the more firmly, therefore, the electrons in the K-ring are held. For elements of high atomic numbers, therefore, only the most intense bombardment would suffice to detach an electron from the K-ring.
When the electron is detached, the K-ring is left incomplete, and an electron from another ring will rush to take the vacant place. Now we must remember that each ring corresponds to a different level of energy, in accordance with Bohr’s quantum theory of the atom. In passing from one ring to another an electron passes from one energy level to another. A certain amount of energy is liberated by the process, and this energy manifests itself as a radiation. It will be what we have called a “monochromatic” radiation, that is, it will be of one definite wave-length. It will furnish a line in the K-spectrum. Now it may happen that the electron which rushes to take the vacant place comes from the ring next to the K-ring, or from the ring next but one, or from the ring next but two, and so on. It is not at all likely to come from a very far-off ring, so we may say that it will come from the L-ring, or the M-ring, or the N-ring. But the farther off the ring from which it comes the greater is the energy liberated, and the higher the frequency of the resultant radiation or, what comes to the same thing, the greater the hardness of the resultant radiation. So that an electron which falls from the N-ring to the K-ring will give a harder radiation, i. e., one of smaller wave-length, than an electron which falls from an M-ring to a K-ring, and harder still, of course, than an electron which falls from an L-ring to a K-ring. At the same time, it is more likely that the missing K-ring electron will be replaced from the ring next to it, the L-ring, than from the other more distant rings. And, as between the M-and the N-rings, an electron is more likely to come from the M-ring than from the N-ring. So that we should expect the least hard line in the K-spectrum, the one due to the passage of an electron from the L-ring to the K-ring, to be also the strongest line, since the proportion of atoms where this particular change is occurring is the largest proportion. And, by the same reasoning, we should expect the hardest line, the one due to the passage of an electron from the N-ring to the K-ring, to be also the weakest line. The other line, the one due to the passage from the M-ring to the K-ring, would be intermediate, of course, both in strength and hardness. Thus our theory explains the observed fact that the hardest line is the weakest and that the softest line is the strongest, while the other line is, of course, intermediate in both respects.
A similar explanation holds good for the L- and M-groups of the X-ray spectrum. The bombardment will sometimes detach an electron from the L-ring. It is to be noticed that the energy necessary to do this is less than in the case of the K-ring, and that for two reasons. In the first place, the electrons in the L-ring are farther removed from the nucleus than the electrons in the K-ring, and in the second place they are subject to a certain repulsive effect from the electrons of the K-ring. All electrons repel one another. An electron belonging to any ring is repelled by the other members of that ring, as well as by the members of other rings. As we get farther away from the nucleus this effect becomes more marked, and it acts, to a first approximation, as if the charge on the nucleus had been reduced, and therefore exerted a less firm binding effect on the electron. It requires less energy, therefore, in the case of any given element, to detach an electron from the L-ring than from the K-ring. The electron having been detached the vacant place may be occupied by an electron from any of the farther outlying rings. And, here again, an electron is more likely to come from the next farther ring than from a more distant ring. At the same time, the passage of the electron from the nearer ring will radiate less energy than the passage from a more distant ring. So that in this case also the weaker line should be the harder. This agrees with the experimental results.
The same general remarks apply to the detachment and replacement of an electron from the M-ring, with the difference that the detachment is still easier than in the case of the L-ring. The M-ring is farther from the nucleus and also the repulsive effect of the inner electrons is more noticeable.
§ 4. Doublets
The simplicity of the K-spectrum is due to the fact that we are here concerned only with the innermost electrons of the atom and, in this region, the charge on the nucleus exerts a very firm control. The stability of the electrons close to the nucleus is very considerable. As we get farther away from the nucleus, however, the conditions become more complicated and the resulting spectra, indicating what changes are going on, also become more complicated. When we reach the outer electrons, those concerned in producing the visible spectrum, the changes going on are of the greatest complexity. This growth in complexity is apparent directly we pass from the K-spectrum to the L-spectrum. The L-spectrum contains more lines than the K-spectrum, and their explanation is less simple. An interesting feature of the L-spectrum is the large number of doublets it contains. It is found that close pairs of lines may be distinguished in the L-spectrum and that the distance between these pairs is constant. It is this fact, that the doublets are of the same size, as it were, that calls for explanation. The explanation offered by the theory is that the L-ring is not really a single ring, but consists of two or more rings, each ring corresponding to a slightly different energy level. Let us suppose that the L-ring really consists of two rings. Then an electron from the M-ring may fall on to one or the other of these two rings. We shall denote these two L-rings by L1 and L2.
If an electron falls from the M-ring on to the L1-ring, it will radiate an amount of energy slightly different from that radiated by an electron falling from the M-ring on to the L2-ring. The wave-lengths corresponding to these radiations will therefore be slightly different and the corresponding lines in the spectrum, indicating these wave-lengths, will therefore consist of a pair of lines close together—a doublet. Now let us consider what happens when the electrons fall from the N-ring. The electron which falls from the N-ring, whether it falls on the L1- or the L2-ring, will radiate more energy than the electron from the M-ring. But the difference in the energy radiated, depending on whether it falls on to the L1- or the L2-ring, is obviously the same as the corresponding difference in the case of an electron falling from the M-ring. It is the difference in the two paths which is concerned, and this difference is simply the distance between the L1- and the L2-rings. In the case of electrons falling from the N-ring, therefore, although the actual amounts of energy radiated are greater, and therefore the corresponding wavelengths are shorter, yet the resulting pair of lines are at the same distance apart as in the case of the M-ring. Similar reasoning applies to any pair of electrons which start from the same outer ring and fall, one on the L1-ring, and the other on the L2-ring. In each case, a doublet is produced, and all these doublets have their component lines separated by the same interval.
This theory gives a satisfactory explanation of the observed equality of the L-doublets, but we can go on to deduce a result from it which can be used as a test. We have seen that the K α-line in the K-spectrum is produced by the passage of an electron from the L-ring to the K-ring. But there are two L-rings. The passage of an electron from each of these to the K-ring should produce a line in the K-spectrum. These two lines should be very close together; they should form a doublet. Now we have seen that the K α-line actually is a doublet. But we can go further. The difference in path, according to whether the electron falls on the K-ring from the L1- or the L2-ring, is the same as the difference in the paths of two electrons, coming from the same outer ring, but falling one on the L1-ring and the other on the L2-ring. So that the interval between the components of the K-doublet should be the same as the interval between the components of the L-doublets. This result is confirmed by actual measurement. The “interval” or “distance” between the components of a doublet is really a difference, of course, in the hardness of the corresponding waves.
We have said sufficient to make the main lines of the theory clear. We need only add that the further explanation of the L-spectrum and also of the M-spectrum requires us to assume that the M-ring also is not a single ring, but consists of two or more.