(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 [Pg 93] 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 [Pg 94] 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.