element 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 the [previous 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 of this 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 ellipses and 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 to contain 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 in their 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
IX.
X-RAYS
EVERYBODY knows something about X-rays, because of their use in medicine. Everybody knows that they can take a photograph of the skeleton of a living person, and show the exact position of a bullet lodged in the brain. But not everybody knows why this is so. The reason is that the capacity of ordinary matter for stopping the rays varies approximately as the fourth power of the atomic number of the elements concerned. Thus carbon, whose atomic number is 6, is 1296 times as effective as hydrogen in stopping X-rays; oxygen, whose atomic number is 8, is 4096 times as effective as hydrogen; nitrogen, whose atomic number is 7, is 2401 times as effective as hydrogen; calcium, whose atomic number is 20, is 160,000 as effective as hydrogen. The human body consists mainly of carbon, oxygen, nitrogen and hydrogen, but the bones consist mainly of calcium. Consequently X-rays which go through the rest of the body easily are stopped by the bones with the result that we get a photograph of the skeleton. Lead, of which the atomic number is 82, is about 45 million times as effective as hydrogen and about 280 times as effective as calcium; so it no wonder that bullets come out clearly in X-ray photographs.
In this chapter we shall be concerned with the physical nature of X-rays, not with their application to medicine.
When swiftly moving electrons strike ordinary matter, which happens in the case of so-called “cathode-rays” and “
