VIII.RINGS OF ELECTRONS
WHEN we come to atoms that have more than one electron, we can no longer work out the mathematics in the same complete way as we can in the case of hydrogen and positively electrified helium. We shall see in the next chapter, however, that X-ray spectra (which are a very modern discovery) tell us a great deal about the inner rings of electrons in complex atoms, while optical spectra continue to tell us a good deal about the outer ring. As we travel up the periodic table, the first element in each period, which is an alkali, has only one electron in the outermost ring; accordingly we might expect this one electron to move more or less as the hydrogen electron does, since the positive charge on the nucleus exceeds the negative charges on the inner electrons by just the amount of the charge on an electron or a hydrogen nucleus, and the inner electrons may be expected to be never very near the outer electron, as distances go within an atom. This would leadus to look out for a spectrum, in the case of an alkali, more or less similar to that of hydrogen; and in fact, this is found to be the case. Some inferences can be drawn from the fact that in all series spectra Rydberg’s constant makes its appearance. There can be no doubt that the quantum theory applies, and that the orbit of an electron (as in the case of elliptical orbits in hydrogen) is in general determined by two quantum numbers, both of them whole numbers which are usually small.
There is, however, considerable uncertainty about the arrangement of the electrons when there are more than one.
Already with helium, which has only two electrons, complications arise. There are two complete systems in the helium spectrum, each such as one might expect to constitute the whole spectrum of an element. This leads Bohr to the conclusion that there are two possibilities for the stable state of the second electron, in one of which it moves in an orbit similar to that of the first, while in the other it moves in an orbit considerably larger than that of the first. These two states would not be related as are the different possible orbits in the hydrogen atom; that is to say, an electron left to itself would never jump from the larger to the smaller orbit. They are both final states, afterall jumps have been made. The atom cannot pass from one to the other directly, but only by a roundabout process. When both electrons move in similar minimum orbits, they cannot be in the same plane. Originally it was assumed, merely in order to try simple hypothesis first, that the electrons in an atom all moved in the same plane. This hypothesis has had to be abandoned, and it is now believed that even the electrons constituting one ring are in different planes. In fact it is suggested that, in an inert gas, the eight electrons constituting the outer ring are arranged more or less like the eight corners of a cube. But according to Bohr even this hypothesis is still too simple.
It will be remembered that, when we were dealing with elliptic orbits in the hydrogen atom, we found that the two quantum membersandwere not individually so important as their sum,.We call this the “total quantum number.” Although we cannot calculate in detail the paths of electrons in other atoms, we can see that there will still be a “total quantum number,” the sum of two partial quantum numbers, which will determine the most important features of the orbit. Rings of electrons will be sets having the same total quantum number. If their two partial quantum numbers severally are the same,their orbits will have the same shape; if not, the orbits of some will be much more eccentric than those of others. It may happen that the orbit of an electron belonging to an outer ring is so eccentric that at moments it penetrates within an inner ring, just as a comet which is usually very distant from the sun may for a short time be nearer than any of the planets. When an electron penetrates in this way into regions thoroughly settled by other electrons, all of which are repelled by it, the effect must be very disturbing. Comets produce no great disturbance in the solar system, because their mass is very small; but electrons are all equal, not only as to their mass, which is less important, but as to their electric charge, which is what governs their motions. It seems as if an atom must be somewhat uncomfortable, and have anything but a harmonious family life, if it is subject to such irruptions several billions of times in every second. However, apparently it gets used to them, and learns to adjust itself.
The phenomena of the optical spectrum are produced by disturbances in the outer ring of electrons, i.e. when one of the outer electrons has been moving in an orbit which is larger than the normal orbit of an electron in the outer ring, and suddenly jumps to this normal orbit or to some intermediate one. But X-rays arise from disturbances inthe inner rings of electrons. If an electron is torn away from the inner regions of an atom, it will soon be replaced by some electron which was formerly in the outer ring; there is a vacant place near the nucleus, and any electron that can will seize the chance to occupy it. The amount of energy radiated out in waves when this occurs is very great, and therefore the frequency of the waves is very great. X-rays only differ from ordinary light-waves by their great frequency, so that the emission of X-rays is just what might be expected under such circumstances. This is why X-rays give us so much information about the inner rings.
Bohr[8]has given a table setting out his theory of the way the electrons are arranged in the various inert gases, each of which has its outer ring as full as it will hold until there are other electrons outside it. The helium atom, in its commoner form, he supposes to contain two electrons moving in circles, each with the same total quantum number, namely 1, as the minimum circle in hydrogen. There is, however, as we saw, another form of helium, in which one of the electrons moves in an eccentric orbit. In the next inert gas, neon, there are 10 electrons, two in the inner ring and eight inthe outer. The two in the inner ring, according to his table, remain as in helium, but of the outer eight four are moving in circles and four in ellipses. This and the other figures in his table apply, of course, to the atom in its most compressed state, the state to which it tends when it is let alone, the state corresponding to the minimum circle in hydrogen. Argon, which comes next with 18 electrons, has its two inner rings as in neon, but has eight electrons in a third ring. Partly from spectroscopic considerations, partly on grounds of stability, Bohr maintains that these eight outer electrons none of them move in circles, but are divided into two groups of four, the first group moving in orbits of very great eccentricity, the second in less eccentric orbits. The first group of four will, at moments penetrate inside the first ring. It is assumed that the two inner rings are definitely completed as soon as we reach neon, but that the later rings are not completed so quickly. For reasons which we explained inChapter III, the periods containing a great many elements in the periodic table are best explained by assuming that the change from one element to the next is not always in the outermost ring, but is sometimes in the next ring, or even (in the case of the rare earths) in the next but one. According to these principles, krypton, which is theelement, and so has 18 more electrons than argon, is not to have the whole 18 in its outer ring. Only 8 are to be in the outer ring; the remaining 10 are added to the third ring, which is to have eighteen electrons, six in orbits like one previous group of four, six in orbits like the other previous group of four, and six in circles. The eight outer electrons are again divided into two groups of four, one group exceedingly eccentric (more so than any in argon), and the other group somewhat less so. Passing to xenon, theelement in the periodic table, the first three rings are as in krypton, the fourth ring has 18 electrons instead of 8, six in each of the groups that previously had four, and six in orbits that are not circles, but have only a small eccentricity. As we saw in connection with hydrogen in theprevious chapter, as the total quantum number increases, the number of possible orbits increases. When the total quantum number is one, there is only one possibility (a circle); when 2, there are two; when 3, there are three, and so on. This does not mean that there can be only one orbit whose total quantum number is one; it only means that any orbit whose total quantum number is one must be a circle of a certain size. There may be (except in hydrogen there are) two electrons moving in circles ofthis size, but in different planes. Similarly in the other cases. As we travel up the series of total quantum numbers, more and more eccentric orbits become possible; circles always remain possible, but the number of possible types of ellipses increases by one at each step. When the total quantum number is three (third ring), the ratio of the breadth to the height may be 3 or 2 or 1. (The ratio 1 corresponds to a circle.) When it is four (fourth ring), the ratio may be 4 or 3 or 2 or 1; and so on. When the breadth is very much greater than the height, the orbit is very eccentric. Bohr holds that in each ring the more eccentric orbits are filled first, and the less eccentric later; he bases this view on considerations of stability, because we always have to account for the fact that the system of electrons does not break down more often than it does.
In accordance with this principle, the outer (fifth) ring in xenon is to have eight electrons divided into two groups of four, the first group having the most eccentric orbits possible at this stage (length five times the breadth), the second group having the next most eccentric orbits (length five times half the breadth). For convenience, we are speaking as if the orbits of the electrons were still ellipsesand circles, but of course this is only very roughly true when we have to deal with a crowd of electrons which all have to dodge each other. It is only true to the same degree that a person walking along Oxford Street in the afternoon walks in a straight line; a straight line gives the general direction of his movement, but he is always deviating from it to get out of people’s way. Similarly the electrons, when they come close together, repel each other violently, and shove each other out of the smooth circular or elliptical course. But for general descriptive purposes it is convenient to ignore this. What we can hope to find out about the electrons is the quantum-numbers of their orbits, because these determine the spectral lines. But we cannot hope with our present mathematical knowledge to calculate exactly the orbit of an electron with two given quantum numbers, although we can see in a general way what sort of orbit it must be. This is to be borne in mind when, for brevity, we speak of ellipses and circles in connection with atoms that have a great many electrons.
Between xenon and niton comes the period of 32 elements, so that in constructing a model of the niton atom in its normal state we have to find room for 32 new electrons. This is done as follows: the first three rings remain unchanged; the fourth is augmented tocontain 32 electrons, 8) in each group that previously held 6, and 8 in circular orbits; the fifth ring is increased from 8 electrons to 18, of which there are 6 in each group that previously held 4, and 6 in a new group of slightly eccentric orbits; the sixth ring contains 8 electrons, four moving in very eccentric orbits (length six times breadth), the other four in less eccentric orbits (length three times breadth). It would of course be possible to go on constructing models of atoms with larger numbers of electrons, but after niton only six more elements are known, and they are breaking down through radio-activity. It seems therefore that the series stops where it does because heavier atoms would not be stable. However, since new elements are discovered from time to time, we cannot be sure that no element heavier than uranium will ever be discovered. It would therefore be rash to get to work to prove that such elements are impossible.
It must not be supposed that the above models of complicated atoms have the same degree of certainty as the theory of the hydrogen atom. They are as yet in part speculative. But it is in the highest degree probable that the models give a more or less correct general picture of the way the electrons behave when the atoms in question are intheir most stable state. The emission of light and X-rays occurs when one electron makes a transition towards the most stable configuration, which is the one intended to be described by the models we have been considering. Absorption, on the contrary, takes place when there is a transition away from the most stable configuration under the influence of outside forces.
[8]0p. cit. p. 113
[8]0p. cit. p. 113