112 A SYSTEM OF PHYSICAL CHEMISTRY ring will always be odd or even according as the total number df electrons in the atom is odd or even. This suggests a relation with the fact that the valency of an element of low atomic weight is always odd or even according as the number of the element in the periodic series is odd or even. The fact that several considerations have been introduced into the problem shows that the criterion of stability— constancy of angular momentum and a maximum value for W— is not sufficient to determine completely the constitution of an atomic system. In very simple cases the constitution of the atom is in relatively little doubt. It is possible, however, by making use of all the foregoing considerations to arrive at a moderately satisfactory statement of the constitution of atoms which contain up to twenty-four electrons, that is, up to an atomic weight of forty-eight approximately. Bohr gives the following table for these atomic systems. The large numeral indicates the value of N, the total number of electrons in the neutral atom, whilst the smaller figures in brackets give the composition of the rings starting from the innermost. Thus the symbol 9 (4, 4i i) denotes a neutral atom which contains in all nine electrons, arranged in three concentric rings, the innermost ring containing four electrons, the second likewise four, and the outermost one electron, thereby indicating that the normal valency of this atom is one. The atomic weight of the element in is question approximately 2x9 = 18, i.e. fluorine. It will be observed that Bohr places hydrogen along with the halogens, and not with the alkali metals. Bohr does not give the name of the corresponding element to these configurations but the attempt is here made to do so. Probable Table Showing Structure of Atoms.
RUTHERFORD-BOHR ATOM-MODEL 113 the arrangement of the inner electrons. The fact that the period in the chemical properties of the elements after the iron group is no longer eight but eighteen suggests that elements of higher atomic weight contain a recurrent configuration of eighteen electrons in the innermost rings. The deviation from 2, 4, 8, 16 may be due to a gradual interchange of electrons between the rings as already indicated when speaking of the confluence of rings. Since a single ring of eighteen electrons will not be stable, the electrons may be arranged in two parallel rings. Such a configuration of the inner electrons will act upon the outer electrons in very nearly the same way as a nucleus of (N - 18) x e. It is conceivable that with increase in N another configuration of the same type will be found outside the first, such as is suggested by the presence of a second period of eighteen elements. Systems Containing Several Nuclei. Molecules. According to Bohr a simple molecule such as the molecule of hydrogen consists of two positively charged nuclei, each carrying unit charge with a ring of two electrons rotating between them, the rotation being round the line joining the two nuclei. If the two nuclei are similar in all respects the electron ring rotates at a position midway between the nuclei, the plane of the ring being perpendicular to the line joining the nuclei. If the nuclei be dissimilar the ring will rotate at some position lying nearer the heavier and more complex nucleus. The equilibrium of such a system is conditioned as before by the constancy of the angular momentum of each electron, along with the further condition that W—the energy emitted in binding an electron to the — system is a maximum. Consider a system consisting of two positive nuclei of equal charges, and a ring of electrons rotating round the line joining the nuclei. Let the number of electrons be n, the charge on each be e, and the charge on each nucleus be N^. It can be shown that the system will be in; equilibrium if (i) the nuclei are equidistant from the ring and if (2) the ratio between the diameter of the ring, 2a, and the distance apart of the nuclei, 2b, be given by— .=