The confluence of two rings of equal number of electrons, which rotate round a nucleus of chargeoutside a ring ofelectrons already bound, must be expected to take place more easily than the confluence of two similar rings rotating round a nucleus of charge;for the stability of the rings for a displacement perpendicular to their plane will (see§2) be smaller in the first than in the latter case. This tendency for stability to decrease for displacements perpendicular to the plane of the ring will be especially marked for the outer rings of electrons of a neutral atom. In the latter case we must expect the confluence of rings to be greatly facilitated, and in certain cases it may even happen that the number of electrons in the outer ring may be greater than in the next, and that the outer ring may show deviations from the assumption of,,,electrons in the rings,e. g. the configurationsandinstead of the configurationsand.We shall here not discuss further the intricate question of the arrangement of the electrons in the outer ring. In the scheme given below the number of electrons in this ring is arbitrarily put equal to the normal valency of the corresponding element;i. e. for electronegative and electropositive elements respectively the number of hydrogen atoms and twice the number of oxygen atoms with which one atom of the element combines.
Such an arrangement of the outer electrons is suggested by considerations of atomic volumes. As is well known, the atomic volume of the elements is a periodic function of the atomic weights. If arranged in the usual way according to the periodic system, the elements inside the same column have approximately the same atomic volume, while this volume changes considerably from one column to another, being greatest for columns corresponding to the smallest valencyand smallest for the greatest valency.An approximate estimate of the radius of the outer ring of a neutral atom can be obtained by assuming that the total force due to the nucleus and the inner electrons is equal to that from a nucleus of charge,whereis the number of electrons in the ring. Puttingin the equation (1) onp. 28, and denoting the value offorby,we get for,;for,;and for,.Accordingly the arrangement chosen for the electrons will involve avariation in the dimensions of the outer ring similar to the variation in the atomic volumes of the corresponding elements. It must, however, be borne in mind that the experimental determinations of atomic volumes in most cases are deduced from consideration of molecules rather than atoms.
From the above we are led to the following possible scheme for the arrangement of the electrons in light atoms:—
Without any fuller discussion it seems not unlikely that this constitution of the atoms will correspond to properties of the elements similar with those observed.
In the first place there will be a marked periodicity with a period of.Further, the binding of the outer electrons in every horizontal series of the above scheme will become weaker with increasing number of electrons per atom, corresponding to the observed increase of the electropositive character for an increase of atomic weight of the elements in every single group of the periodic system. A corresponding agreement holds for the variation of the atomic volumes.
In the case of atoms of higher atomic weight the simple assumptions used do not apply. A few indications, however, are suggested from consideration of the variations in the chemical properties of the elements. At the end of the 3rd period ofelements we meet with the iron-group. This group takes a particular position in the system of the elements, since it is the first time that elements of neighbouring atomic weights show similar chemical properties. This circumstance indicates that the configurations of the electrons in the elements of this group differ only in 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,but,suggests that elements of higher atomic weight contain a recurrent configuration ofelectrons in the innermost rings. The deviation from,,,may be due to a gradual interchange of electrons between the rings, such as is indicated onp. 45. Since a ring ofelectrons will not be stable the electrons may be arranged in two parallel rings (seep. 36). Such a configuration of the inner electrons will act upon the outer electrons in very nearly the same way as a nucleus of charge.It might therefore be possible that with increase ofanother configuration of the same type will be formed outside the first, such as is suggested by the presence of a second period ofelements.
On the same lines, the presence of the group of the rare earths indicates that for still greater values ofanother gradual alteration of the innermost rings will take place. Since, however, for elements of higher atomic weight than those of this group, the laws connecting the variation of the chemical properties with the atomic weight are similar to those between the elements of low atomic weight, we may conclude that the configuration of the innermost electrons will be again repeated. The theory, however, is not sufficiently complete to give a definite answer to such problems.
§5.Characteristic Röntgen Radiation.
According to the theory of emission of radiation given inPart I., the ordinary line-spectrum of an element is emitted during the reformation of an atom when one or more of the electrons in the outer rings are removed. In analogy it may be supposed that the characteristic Röntgen radiation is sent out during the settling down of the system if electrons in inner rings are removed by some agency,e. g. by impact of cathode particles. This view of the origin of the characteristic Röntgen radiation has been proposed by Sir J. J. Thomson[35].
Without any special assumption in regard to the constitution of the radiation, we can from this view determine the minimum velocity of the cathode rays necessary to produce the characteristic Röntgen radiation of a special type by calculating the energy necessary to remove one of the electrons from the different rings. Even if we knew the numbers of electrons in the rings, a rigorous calculation of this minimum energy might still be complicated, and the result largely dependent on the assumptions used; for, as mentioned in Part I.,p. 19, the calculation cannot be performed entirely on the basis of the ordinary mechanics. We can, however, obtain very simply an approximate comparisonwith experiments if we consider the innermost ring and as a first approximation neglect the repulsion from the electrons in comparison with the attraction of the nucleus. Let us consider a simple system consisting of a bound electron rotating in a circular orbit round a positive nucleus of charge From the expressions (1) onp. 28we get for the velocity of the electron, putting,
The total energy to be transferred to the system in order to remove the electron to an infinite distance from the nucleus is equal to the kinetic energy of the bound electron. If, therefore, the electron is removed to a great distance from the nucleus by impact of another rapidly moving electron, the smallest kinetic energy possessed by the latter when at a great distance from the nucleus must necessarily be equal to the kinetic energy of the bound electron before the collision. The velocity of the free electron therefore must be at least equal to.
According to Whiddington’s experiments[36]the velocity of cathode rays just able to produce the characteristic Röntgen radiation of the so-called-type—the hardest type of radiation observed—from an element of atomic weightis for elements from Al to Se approximately equal to.As seen this is equal to the above calculated value for,if we put.
Since we have obtained approximate agreement with experiment by ascribing the characteristic Röntgen radiation of the-type to the innermost ring, it is to be expected that no harder type of characteristic radiation will exist. This is strongly indicated by observations of the penetrating-power ofrays[37].
It is worthy of remark that the theory gives not only nearly the right value for the energy required to remove an electron from the outer ring, but also the energy required to remove an electron from the innermost ring. The approximate agreement between the calculated and experimental values is all the more striking when it is recalled that the energies required in the two cases for an element of atomic weightdiffer by a ratio of.
In connexion with this it should be emphasized that the remarkablehomogeneity of the characteristic Röntgen radiation—indicated by experiments on absorption of the rays, as well as by the interference observed in recent experiments on diffraction of Röntgen rays in crystals—is in agreement with the main assumption used in Part I. (seep. 7) in considering the emission of line-spectra, viz. that the radiation emitted during the passing of the systems between different stationary states is homogeneous.
Putting in (4),we get for the diameter of the innermost ring approximately.Forthis gives,a value which is very small in comparison with ordinary atomic dimensions but still very great compared with the dimensions to be expected for the nucleus. According to Rutherford’s calculation the dimensions of the latter are of the same order of magnitude as.
§6.Radioactive Phenomena.
According to the present theory the cluster of electrons surrounding the nucleus is formed with emission of energy, and the configuration is determined by the condition that the energy emitted is a maximum. The stability involved by these assumptions seems to be in agreement with the general properties of matter. It is, however, in striking opposition to the phenomena of radioactivity, and according to the theory the origin of the latter phenomena may therefore be sought elsewhere than in the electronic distribution round the nucleus.
A necessary consequence of Rutherford’s theory of the structure of atoms is that the-particles have their origin in the nucleus. On the present theory it seems also necessary that the nucleus is the seat of the expulsion of the high-speed-particles. In the first place, the spontaneous expulsion of a-particle from the cluster of electrons surrounding the nucleus would be something quite foreign to the assumed properties of the system. Further, the expulsion of an-particle can hardly be expected to produce a lasting effect on the stability of the cluster of electrons. The effect of the expulsion will be of two different kinds. Partly the particle may collide with the bound electrons during its passing through the atom. This effect will be analogous to that produced by bombardment of atoms of other substances by-rays and cannot be expected to give rise to a subsequent expulsion of-rays. Partly the expulsion of the particle will involve an alteration in theconfiguration of the bound electrons, since the charge remaining on the nucleus is different from the original. In order to consider the latter effect let us regard a single ring of electrons rotating round a nucleus of charge,and let us assume that an-particle is expelled from the nucleus in a direction perpendicular to the plane of the ring. The expulsion of the particle will obviously not produce any alteration in the angular momentum of the electrons; and if the velocity of the-particle is small compared with the velocity of the electrons—as it will be if we consider inner rings of an atom of high atomic weight—the ring during the expulsion will expand continuously, and after the expulsion will take the position claimed by the theory for a stable ring rotating round a nucleus of charge.The consideration of this simple case strongly indicates that the expulsion of an-particle will not have a lasting effect on the stability of the internal rings of electrons in the residual atom.
The question of the origin of-particles may also be considered from another point of view, based on a consideration of the chemical and physical properties of the radioactive substances. As is well known, several of these substances have very similar chemical properties and have hitherto resisted every attempt to separate them by chemical means. There is also some evidence that the substances in question show the same line-spectrum[38]. It has been suggested by several writers that the substances are different only in radioactive properties and atomic weight but identical in all other physical and chemical respects. According to the theory, this would mean that the charge on the nucleus, as well as the configuration of the surrounding electrons, was identical in some of the elements, the only difference being the mass and the internal constitution of the nucleus. From the considerations of§4this assumption is already strongly suggested by the fact that the number of radioactive substances is greater than the number of places at our disposal in the periodic system. If, however, the assumption is right, the fact that two apparently identical elements emit-particles of different velocities, shows that the-rays as well as the-rays have their origin in the nucleus.
This view of the origin of- and-particles explains very simply the way in which the change in the chemical properties of the radioactive substances is connected with the nature of theparticles emitted. The results of experiments are expressed in the two rules[39]:—
1. Whenever an-particle is expelled the group in the periodic system to which the resultant product belongs is two units less than that to which the parent body belongs.
2. Whenever a-particle is expelled, the group of the resultant body isunit greater than that of the parent.
As will be seen this is exactly what is to be expected according to the considerations of§4.
In escaping from the nucleus, the-rays may be expected to collide with the bound electrons in the inner rings. This will give rise to an emission of a characteristic radiation of the same type as the characteristic Röntgen radiation emitted from elements of lower atomic weight by impact of cathode-rays. The assumption that the emission of-rays is due to collisions of-rays with bound electrons is proposed by Rutherford[40]in order to account for the numerous groups of homogeneous-rays expelled from certain radioactive substances.
In the present paper it has been attempted to show that the application of Planck’s theory of radiation to Rutherford’s atom-model through the introduction of the hypothesis of the universal constancy of the angular momentum of the bound electrons, leads to results which seem to be in agreement with experiments.
In a later paper the theory will be applied to systems containing more than one nucleus.
[23]Communicated by Prof. E. Rutherford, F.R.S.
[23]Communicated by Prof. E. Rutherford, F.R.S.
[24]Part I. was published in Phil. Mag. xxvi. p. 1 (1913).
[24]Part I. was published in Phil. Mag. xxvi. p. 1 (1913).
[25]Comp, also Geiger and Marsden, Phil. Mag. xxv. p. 604 (1913).
[25]Comp, also Geiger and Marsden, Phil. Mag. xxv. p. 604 (1913).
[26]Comp. C. G. Barkla, Phil. Mag. xxi. p. 648 (1911).
[26]Comp. C. G. Barkla, Phil. Mag. xxi. p. 648 (1911).
[27]Comp. A. v. d. Broek,Phys. Zeitschr. xiv. p. 32 (1913).Phil. Mag. S. 6. Vol. 26. No. 153.Sept. 1913.
[27]Comp. A. v. d. Broek,Phys. Zeitschr. xiv. p. 32 (1913).Phil. Mag. S. 6. Vol. 26. No. 153.Sept. 1913.
[28]Comp. J. W. Nicholson, Month. Not. Roy. Astr. Soc. 72. p.52(1912).
[28]Comp. J. W. Nicholson, Month. Not. Roy. Astr. Soc. 72. p.52(1912).
[29]This value is that calculated in the first part of the paper. Using the values(see R. A. Millikan, Brit. Assoc. Rep. 1912, p. 410),(see P. Gmelin,Ann. d. Phys. xxviii. p. 1086 (1909) and A. H. Bucherer,Ann. d. Phys. xxxvii. p. 597 (1912)),and(calculated by Planck’s theory from the experiments of E. Warburg, G. Leithäuser, E. Hupka, and C. Müller,Ann. d. Phys. xl. p. 611 (1913)) we getin very close agreement with observations.
[29]This value is that calculated in the first part of the paper. Using the values(see R. A. Millikan, Brit. Assoc. Rep. 1912, p. 410),(see P. Gmelin,Ann. d. Phys. xxviii. p. 1086 (1909) and A. H. Bucherer,Ann. d. Phys. xxxvii. p. 597 (1912)),and(calculated by Planck’s theory from the experiments of E. Warburg, G. Leithäuser, E. Hupka, and C. Müller,Ann. d. Phys. xl. p. 611 (1913)) we getin very close agreement with observations.
[30]J. J. Thomson, Phil. Mag. xxiv. p. 218 (1912).
[30]J. J. Thomson, Phil. Mag. xxiv. p. 218 (1912).
[31]J. Franck u. G. Hertz,Verh. d. Deutsch. Phys. Ges. xv. p. 34 (1913).
[31]J. Franck u. G. Hertz,Verh. d. Deutsch. Phys. Ges. xv. p. 34 (1913).
[32]C. and M. Cuthbertson, Proc. Roy. Soc. A. lxxxiv. p. 13 (1910). (In a previous paper (Phil. Mag. Jan. 1913) the author took the values for the refractive index in helium, given by M. and C. Cuthbertson, as corresponding to atmospheric pressure; these values, however, refer to double atmospheric pressure. Consequently the value there given for the number of electrons in a helium atom calculated from Drude’s theory has to be divided by 2.)
[32]C. and M. Cuthbertson, Proc. Roy. Soc. A. lxxxiv. p. 13 (1910). (In a previous paper (Phil. Mag. Jan. 1913) the author took the values for the refractive index in helium, given by M. and C. Cuthbertson, as corresponding to atmospheric pressure; these values, however, refer to double atmospheric pressure. Consequently the value there given for the number of electrons in a helium atom calculated from Drude’s theory has to be divided by 2.)
[33]See J. Franck,Verh. d. Deutsch. Phys. Ges. xii. p. 613 (1910).
[33]See J. Franck,Verh. d. Deutsch. Phys. Ges. xii. p. 613 (1910).
[34]J. W. Nicholson, Month. Not. Roy. Astr. Soc. lxxiii. p. 382 (1913).
[34]J. W. Nicholson, Month. Not. Roy. Astr. Soc. lxxiii. p. 382 (1913).
[35]Comp. J. J. Thomson, Phil. Mag. xxiii. p. 456 (1912).
[35]Comp. J. J. Thomson, Phil. Mag. xxiii. p. 456 (1912).
[36]R. Whiddington, Proc. Roy. Soc. A. lxxxv. p. 323 (1911).
[36]R. Whiddington, Proc. Roy. Soc. A. lxxxv. p. 323 (1911).
[37]Comp. E. Rutherford, Phil. Mag. xxiv. p. 453 (1912).
[37]Comp. E. Rutherford, Phil. Mag. xxiv. p. 453 (1912).
[38]See A. S. Russell and R. Rossi, Proc. Roy. Soc. A. lxxxvii. p. 478 (1912).
[38]See A. S. Russell and R. Rossi, Proc. Roy. Soc. A. lxxxvii. p. 478 (1912).
[39]See A. S. Russell, Chem. News, cvii. p. 49 (1913); G. V. Hevesy,Phys. Zeitschr. xiv. p. 49 (1913); K. Fajans,Phys. Zeitschr. xiv. pp. 131 & 136 (1913):Verh. d. deutsch. Phys. Ges. xv. p. 240 (1913); F. Soddy, Chem. News, cvii. p. 97 (1913).
[39]See A. S. Russell, Chem. News, cvii. p. 49 (1913); G. V. Hevesy,Phys. Zeitschr. xiv. p. 49 (1913); K. Fajans,Phys. Zeitschr. xiv. pp. 131 & 136 (1913):Verh. d. deutsch. Phys. Ges. xv. p. 240 (1913); F. Soddy, Chem. News, cvii. p. 97 (1913).
[40]E. Rutherford, Phil. Mag. xxiv. pp. 453 & 893 (1912).
[40]E. Rutherford, Phil. Mag. xxiv. pp. 453 & 893 (1912).