fig05Fig. 4.
Fig. 4.
Fig. 4.
These facts are shown infigure 4which gives a survey of the stationary states corresponding to the arc spectra of sodium and potassium. As in figures2and3of the sodium spectrum, we have disregarded the complexity of the spectral terms, and the numbers characterizing the stationary states are simply the quantum numbersand.For the sake of comparison the scale in which the energy of the different states is indicated is chosen four times as small for the spark spectra as for the arc spectra. Consequently the vertical lines indicated with various values ofcorrespond for the arc spectra to the spectral terms of hydrogen, for the spark spectra to the terms of the helium spectrum given by formula (7). Comparing the change in the relative firmness in the binding of theth electron in aandorbit for potassium and calcium we see that we must be prepared already for the next element, scandium, to find that theorbit will correspond to a stronger binding of this electron than aorbit. On the other hand it follows from previous remarks that the binding will be much lighter than for the firstelectrons which agrees that in chemical combinations scandium appears electropositively with three valencies.
If we proceed to the following elements, a still larger number oforbits will occur in the normal state of these atoms, since the number of such electron orbits will depend upon the firmness of their binding compared to the firmness with which an electron is bound in aorbit, in which type of orbit at least the last captured electron in the atom may be assumed to move. We therefore meet conditions which are essentially different from those which we have considered in connection with the previous periods, so that here we have to do withthe successive development of one of the inner groups of electrons in the atom, in this case with groups of electrons in-quanta orbits. Only when the development of this group has been completed may we expect to find once more a corresponding change in the properties of the elements with increasing atomic number such as we find in the preceding periods. The properties of the elements in the latter part of the fourth period show immediately that the group, when completed, will possesselectrons. Thus in krypton, for example, we may expect besides the groups of,and-quanta orbits a markedly symmetrical configuration ofelectrons in-quanta orbits consisting of fourorbits and fourorbits.
The question now arises: In which way will the gradual formation of the group of electrons having-quanta orbits take place? From analogy with the constitution of the groups of electrons with-quanta orbits we might at first sight be inclined to suppose that thecomplete group of-quanta orbits would consist of three subgroups of four electrons each in orbits of the types,andrespectively, so that the total number of electrons would beinstead of.Further consideration shows, however, that such an expectation would not be justified. The stability of the configuration of eight electrons with-quanta orbits occurring in neon must be ascribed not only to the symmetrical configuration of the electronic orbits in the two subgroups ofandorbits respectively, but fully as much to the possibility of bringing the orbits inside these subgroups into harmonic relation with one another. The situation is different, however, for the groups of electrons with-quanta orbits. Three subgroups of four orbits each cannot in this case be expected to come into interaction with one another in a correspondingly simple manner. On the contrary we must assume that the presence of electrons inorbits will diminish the harmony of the orbits within the first two-quanta subgroups, at any rate when a point is reached where theth electron is no longer, as was the case with scandium, bound considerably more lightly than the previously bound electrons in-quanta orbits, but has been drawn so far into the atom that it revolves within essentially the same region of the atom where these electrons move. We shall now assume that this decrease in the harmony will so to say "open" the previously "closed" configuration of electrons in orbits of these types. As regards the final result, the numberindicates that after the group is finally formed there will be three subgroups containing six electrons each. Even if it has not at present been possible to follow in detail the various steps in the formation of the group this result is nevertheless confirmed in an interesting manner by the fact that it is possible to arrange three configurations having six electrons each in a simple manner relative to one another. The configuration of the subgroups does not exhibit a tetrahedral symmetry like the groups of-quanta orbits in carbon, but a symmetry which, so far as the relative orientation of the normals to the planes of the orbits is concerned, may be described as trigonal.
In spite of the great difference in the properties of the elements of this period, compared with those of the preceding period, the completion of the group ofelectrons in-quanta orbits in the fourth period may to a certain extent be said to have the samecharacteristic results as the completion of the group of-quanta orbits in the second period. As we have seen, this determined not only the properties of neon as an inactive gas, but in addition the electronegative properties of the preceding elements and the electropositive properties of the elements which follow. The fact that there is no inactive gas possessing an outer group ofelectrons is very easily accounted for by the much larger dimensions which aorbit has in comparison with aorbit revolving in the same field of force. On this account a complete-quanta group cannot occur as the outermost group in a neutral atom, but only in positively charged ions. The characteristic decrease in valency which we meet in copper, shown by the appearance of the singly charged cuprous ions, indicates the same tendency towards the completion of a symmetrical configuration of electrons that we found in the marked electronegative character of an element like fluorine. Direct evidence that a complete group of-quanta orbits is present in the cuprous ion is given by the spectrum of copper which, in contrast to the extremely complicated spectra of the preceding elements resulting from the unsymmetrical character of the inner system, possesses a simple structure very much like that of the sodium spectrum. This may no doubt be ascribed to a simple symmetrical structure present in the cuprous ion similar to that in the sodium ion, although the great difference in the constitution of the outer group of electrons in these ions is shown both by the considerable difference in the values of the spectral terms and in the separation of the doublets in theterms of the two spectra. The occurrence of the cupric compounds shows, however, that the firmness of binding in the group of-quanta orbits in the copper atom is not as great as the firmness with which the electrons are bound in the group of-quanta orbits in the sodium atom. Zinc, which is always divalent, is the first element in which the groups of the electrons are so firmly bound that they cannot be removed by ordinary chemical processes.
The picture I have given of the formation and structure of the atoms of the elements in the fourth period gives an explanation of the chemical and spectral properties. In addition it is supported by evidence of a different nature to that which we have hithertoused. It is a familiar fact, that the elements in the fourth period differ markedly from the elements in the preceding periods partly in theirmagnetic propertiesand partly in thecharacteristic coloursof their compounds. Paramagnetism and colours do occur in elements belonging to the foregoing periods, but not in simple compounds where the atoms considered enter as ions. Many elements of the fourth period, on the contrary, exhibit paramagnetic properties and characteristic colours even in dissociated aqueous solutions. The importance of this has been emphasized by Ladenburg in his attempt to explain the properties of the elements in the long periods of the periodic system (see p. 73). Langmuir in order to account for the difference between the fourth period and the preceding periods simply assumed that the atom, in addition to the layers of cells containingelectrons each, possesses an outer layer of cells with room forelectrons which is completely filled for the first time in the case of krypton. Ladenburg, on the other hand, assumes that for some reason or other an intermediate layer is developed between the inner electronic configuration in the atom appearing already in argon, and the external group of valency electrons. This layer commences with scandium and is completed exactly at the end of the family of iron metals. In support of this assumption Ladenburg not only mentions the chemical properties of the elements in the fourth period, but also refers to the paramagnetism and colours which occur exactly in the elements, where this intermediate layer should be in development. It is seen that Ladenburg's ideas exhibit certain formal similarities with the interpretation I have given above of the appearance of the fourth period, and it is interesting to note that our view, based on a direct investigation of the conditions for the formation of the atoms, enables us to understand the relation emphasized by Ladenburg.
Our ordinary electrodynamic conceptions are probably insufficient to form a basis for an explanation of atomic magnetism. This is hardly to be wondered at when we remember that they have not proved adequate to account for the phenomena of radiation which are connected with the intimate interaction between the electric and magnetic forces arising from the motion of the electrons. In whatever way these difficulties may be solved it seems simplest to assume that the occurrence ofmagnetism, such as we meet in the elements of the fourth period, results from a lack of symmetry in the internal structure of the atom, thus preventing the magnetic forces arising from the motion of the electrons from forming a system of closed lines of force running wholly within the atom. While it has been assumed that the ions of the elements in the previous periods, whether positively or negatively charged, contain configurations of marked symmetrical character, we must, however, be prepared to encounter a definite lack of symmetry in the electronic configurations in ions of those elements within the fourth period which contain a group of electrons in-quanta orbits in the transition stage between symmetrical configurations ofandelectrons respectively. As pointed out by Kossel, the experimental results exhibit an extreme simplicity, the magnetic moment of the ions depending only on the number of electrons in the ion. Ferric ions, for example, exhibit the same atomic magnetism as manganous ions, while manganic ions exhibit the same atomic magnetism as chromous ions. It is in beautiful agreement with what we have assumed about the structure of the atoms of copper and zinc, that the magnetism disappears with those ions containingelectrons which, as I stated, must be assumed to contain a complete group of-quanta orbits. On the whole a consideration of the magnetic properties of the elements within the fourth period gives us a vivid impression of how a wound in the otherwise symmetrical inner structure is first developed and then healed as we pass from element to element. It is to be hoped that a further investigation of the magnetic properties will give us a clue to the way in which the group of electrons in-quanta orbits is developed step by step.
Also the colours of the ions directly support our view of atomic structure. According to the postulates of the quantum theory absorption as well as emission of radiation is regarded as taking place during transitions between stationary states. The occurrence of colours, that is to say the absorption of light in the visible region of the spectrum, is evidence of transitions involving energy changes of the same order of magnitude as those giving the usual optical spectra of the elements. In contrast to the ions of the elements of the preceding periods where all the electrons are assumed to be very firmly bound, the occurrence of such processes in the fourth period is exactly whatwe should expect. For the development and completion of the electronic groups with-quanta orbits will proceed, so to say, in competition with the binding of electrons in orbits of higher quanta, since the binding of electrons in-quanta orbits occurs when the electrons in these orbits are bound more firmly than electrons inorbits. The development of the group will therefore proceed to the point where we may say there is equilibrium between the two kinds of orbits. This condition may be assumed to be intimately connected not only with the colour of the ions, but also with the tendency of the elements to form ions with different valencies. This is in contrast to the elements of the first periods where the charge of the ions in aqueous solutions is always the same for one and the same element.
Fifth Period. Rubidium—Xenon.The structure of the atoms in the remaining periods may be followed up in complete analogy with what has already been said. Thus we shall assume that theth andth electrons in the elements of the fifth period are bound inorbits. This is supported by the measurements of the arc spectrum of rubidium and the spark spectrum of strontium. The latter spectrum indicates at the same time thatorbits will soon appear, and therefore in this period, which like theth containselements, we must assume that we are witnessing afurther stage in the development of the electronic group of-quanta orbits. The first stage in the formation of this group may be said to have been attained in krypton with the appearance of a symmetrical configuration of eight electrons consisting of two subgroups each of four electrons inandorbits. A second preliminary completion must be regarded as having been reached with the appearance of a symmetrical configuration ofelectrons in the case of silver, consisting of three subgroups with six electrons each in orbits of the types,and.Everything that has been said about the successive formation of the group of electrons with-quanta orbits applies unchanged to this stage in the transformation of the group with-quanta orbits. For in no case have we made use of the absolute values of the quantum numbers nor of assumptions concerning the form of the orbits but only of the number of possible types of orbits which might come into consideration. At thesame time it may be of interest to mention that the properties of these elements compared with those of the foregoing period nevertheless show a difference corresponding exactly to what would be expected from the difference in the types of orbits. For instance, the divergencies from the characteristic valency conditions of the elements in the second and third periods appear later in the fifth period than for elements in the fourth period. While an element like titanium in the fourth period already shows a marked tendency to occur with various valencies, on the other hand an element like zirconium is still quadri-valent like carbon in the second period and silicon in the third. A simple investigation of the kinematic properties of the orbits of the electrons shows in fact that an electron in an eccentricorbit of an element in the fifth period will be considerably more loosely bound than an electron in a circularorbit of the corresponding element in the fourth period, while electrons which are bound in eccentric orbits of the typesandrespectively will correspond to a binding of about the same firmness.
At the end of the fifth period we may assume that xenon, the atomic number of which is,has a structure which in addition to the two-quantum, eight-quanta, eighteen-quanta and eighteen-quanta orbits already mentioned contains a symmetrical configuration of eight electrons in-quanta orbits consisting of two subgroups with four electrons each inandorbits respectively.
Sixth Period. Caesium—Niton.If we now consider the atoms of elements of still higher atomic number, we must first of all assume that theth andth electrons in the atoms of caesium and barium are bound inorbits. This is confirmed by the spectra of these elements. It is clear, however, that we must be prepared shortly to meet entirely new conditions. With increasing nuclear charge we shall have to expect not only that an electron in aorbit will be bound more firmly than in aorbit, but we must also expect that a moment will arrive when during the formation of the atom aorbit will represent a firmer binding of the electron than an orbit ofor-quanta, in much the same way as in the elements of the fourth period a new stage in the development of the-quanta group was started when a point was reached wherefor the first time theth electron was bound in aorbit instead of in aorbit. We shall thus expect in the sixth period to meet with a new stage in the development of the group with-quanta orbits. Once this point has been reached we must be prepared to find with increasing atomic number a number of elements following one another, which as in the family of the iron metals have very nearly the same properties. The similarity will, however, be still more pronounced, since in this case we are concerned with the successive transformation of a configuration of electrons which lies deeper in the interior of the atom. You will have already guessed that what I have in view is a simple explanation of the occurrence of thefamily of rare earthsat the beginning of the sixth period. As in the case of the transformation and completion of the group of-quanta orbits in the fourth period and the partial completion of groups of-quanta orbits in the fifth period, we may immediately deduce from the length of the sixth period the number of electrons, namely,which are finally contained in the-quanta group of orbits. Analogous to what applied to the group of-quanta orbits it is probable that, when the group is completed, it will contain eight electrons in each of the four subgroups. Even though it has not yet been possible to follow the development of the group step by step, we can even here give some theoretical evidence in favour of the occurrence of a symmetrical configuration of exactly this number of electrons. I shall simply mention that it is not possible without coincidence of the planes of the orbits to arrive at an interaction between four subgroups of six electrons each in a configuration of simple trigonal symmetry, which is equally simple as that shown by three subgroups. The difficulties which we meet make it probable that a harmonic interaction can be attained precisely by four groups each containing eight electrons the orbital configurations of which exhibit axial symmetry.
Just as in the case of the family of the iron metals in the fourth period, the proposed explanation of the occurrence of the family of rare earths in the sixth period is supported in an interesting manner by an investigation of the magnetic properties of these elements. In spite of the great chemical similarity the members of this family exhibit very different magnetic properties, so that while some of them exhibit but very little magnetism others exhibit a greater magneticmoment per atom than any other element which has been investigated. It is also possible to give a simple interpretation of the peculiar colours exhibited by the compounds of these elements in much the same way as in the case of the family of iron metals in the fourth period. The idea that the appearance of the group of the rare earths is connected with the development of inner groups in the atom is not in itself new and has for instance been considered by Vegard in connection with his work on X-ray spectra. The new feature of the present considerations lies, however, in the emphasis laid on the peculiar way in which the relative strength of the binding for two orbits of the same principal quantum number but of different shapes varies with the nuclear charge and with the number of electrons previously bound. Due to this fact the presence of a group like that of the rare earths in the sixth period may be considered as a direct consequence of the theory and might actually have been predicted on a quantum theory, adapted to the explanation of the properties of the elements within the preceding periods in the way I have shown.
Besidesthe final development of the group of-quanta orbitswe observe in the sixth period in the family of the platinum metalsthe second stage in the development of the group of-quanta orbits. Also in the radioactive, chemically inactive gas niton, which completes this period, we observe the first preliminary step in the development of a group of electrons with-quanta orbits. In the atom of this element, in addition to the groups of electrons of two-quantum, eight-quanta, eighteen-quanta, thirty-two-quanta and eighteen-quanta orbits respectively, there is also an outer symmetrical configuration of eight electrons in-quanta orbits, which we shall assume to consist of two subgroups with four electrons each inandorbits respectively.
Seventh Period.In the seventh and last period of the periodic system we may expect the appearance of-quanta orbits in the normal state of the atom. Thus in the neutral atom of radium in addition to the electronic structure of niton there will be two electrons inorbits which will penetrate during their revolution not only into the region of the orbits of electrons possessing lower values for the principal quantum number, but evento distances from the nucleus which are less than the radii of the orbits of the innermost-quantum orbits. The properties of the elements in the seventh period are very similar to the properties of the elements in the fifth period. Thus, in contrast to the conditions in the sixth period, there are no elements whose properties resemble one another like those of the rare earths. In exact analogy with what has already been said about the relations between the properties of the elements in the fourth and fifth periods this may be very simply explained by the fact that an eccentricorbit will correspond to a considerably looser binding of an electron in the atom of an element of the seventh period than the binding of an electron in a circularorbit in the corresponding element of the sixth period, while there will be a much smaller difference in the firmness of the binding of these electrons in orbits of the typesandrespectively.
It is well known that the seventh period is not complete, for no atom has been found having an atomic number greater than.This is probably connected with the fact that the last elements in the system are radioactive and that nuclei of atoms with a total charge greater thanwill not be sufficiently stable to exist under conditions where the elements can be observed. It is tempting to sketch a picture of the atoms formed by the capture and binding of electrons around nuclei having higher charges, and thus to obtain some idea of the properties which the corresponding hypothetical elements might be expected to exhibit. I shall not develop this matter further, however, since the general results we should get will be evident to you from the views I have developed to explain the properties of the elements actually observed. A survey of these results is given in the following table, which gives a symbolical representation of the atomic structure of the inactive gases which complete the first six periods in the periodic system. In order to emphasize the progressive change the table includes the probable arrangement of electrons in the next atom which would possess properties like the inactive gases.
The view of atomic constitution underlying this table, which involves configurations of electrons moving with large velocities between each other, so that the electrons in the "outer" groups penetrate into the region of the orbits of the electrons of the "inner" groups, is of course completely different from such statical models of the atom asare proposed by Langmuir. But quite apart from this it will be seen that the arrangement of the electronic groups in the atom, to which we have been lead by tracing the way in which each single electron has been bound, is essentially different from the arrangement of the groups in Langmuir's theory. In order to explain the properties of the elements of the sixth period Langmuir assumes for instance that, in addition to the inner layers of cells containing,,,andelectrons respectively, which are employed to account for the properties of the elements in the earlier periods, the atom also possesses a layer of cells with room forelectrons which is just completed in the case of niton.
fig06
In this connection it may be of interest to mention a recent paper by Bury, to which my attention was first drawn after the deliverance of this address, and which contains an interesting survey of the chemical properties of the elements based on similar conceptions of atomic structure as those applied by Lewis and Langmuir. From purely chemical considerations Bury arrives at conclusions which as regards the arrangement and completion of the groups in the main coincide with those of the present theory, the outlines of which were given in my letters to Nature mentioned in the introduction.
Survey of the periodic table.The results given in this address are also illustrated by means of the representation of the periodic system given inFig. 1. In this figure the frames are meant to indicate such elements in which one of the "inner" groups is in a stage of development. Thus there will be found in the fourth and fifth periods a single frame indicating the final completion of the electronic group with-quanta orbits, and the last stage but one in the development of the group with-quanta orbits respectively. In the sixth period it has been necessary to introduce two frames, of which the inner one indicates the last stage of the evolution of the group with-quanta orbits, giving rise to the rare earths. This occurs at a place in the periodic system where the third stage in the development of an electronic group with-quanta orbits, indicated by the outer frame, has already begun. In this connection it will be seen that the inner frame encloses a smaller number of elements than is usually attributed to the family of the rare earths. At the end of this group an uncertainty exists, due to the fact that no element of atomic numberis known with certainty. However, as indicated inFig. 1, we must conclude from the theory that the group with-quanta orbits is finally completed in lutetium (). This element therefore ought to be the last in the sequence of consecutive elements with similar properties in the first half of the sixth period, and at the placean element must be expected which in its chemical and physical properties is homologous with zirconium and thorium. This, which is already indited on Julius Thomsen's old table, has also been pointed out by Bury. [Quite recently Dauvillier has in an investigation of the X-ray spectrum excited in preparations containing rare earths, observed certain faint lines which he ascribes to an element of atomic number.This element is identified by him as the element celtium, belonging to the family of rare earths, the existence of which had previously been suspected by Urbain. Quite apart from the difficulties which this result, if correct, might entail for atomic theories, it would, since the rare earths according to chemical view possess three valencies, imply a rise in positive valency of two units when passing from the elementto the next element,tantalum. This would mean an exception from the otherwise general rule, that the valency never increases by more than one unit when passing from one element to the next in the periodic table.] In the case of the incomplete seventh period the full drawn frame indicates the third stage in the development of the electronic group with-quantaorbits, which must begin in actinium. The dotted frame indicates the last stage but one in the development of the group with-quanta orbits, which hitherto has not been observed, but which ought to begin shortly after uranium, if it has not already begun in this element.
With reference to the homology of the elements the exceptional position of the elements enclosed by frames inFig. 1is further emphasized by taking care that, in spite of the large similarity many elements exhibit, no connecting lines are drawn between two elements which occupy different positions in the system with respect to framing. In fact, the large chemical similarity between, for instance, aluminium and scandium, both of which are trivalent and pronounced electropositive elements, is directly or indirectly emphasized in the current representations of the periodic table. While this procedure is justified by the analogous structure of the trivalent ions of these elements, our more detailed ideas of atomic structure suggest, however, marked differences in the physical properties of aluminium and scandium, originating in the essentially different character of the way in which the last three electrons in the neutral atom are bound. This fact gives probably a direct explanation of the marked difference existing between the spectra of aluminium and scandium. Even if the spectrum of scandium is not yet sufficiently cleared up, this difference seems to be of a much more fundamental character than for instance the difference between the arc spectra of sodium and copper, which apart from the large difference in the absolute values of the spectral terms possess a completely analogous structure, as previously mentioned in this essay. On the whole we must expect that the spectra of elements in the later periods lying inside a frame will show new features compared with the spectra of the elements in the first three periods. This expectation seems supported by recent work on the spectrum of manganese by Catalan, which appeared just before the printing of this essay.
Before I leave the interpretation of the chemical properties by means of this atomic model I should like to remind you once again of the fundamental principles which we have used. The whole theory has evolved from an investigation of the way in which electrons can be captured by an atom. The formation of an atom was held to consist in the successive binding of electrons, this binding resulting in radiation according to the quantum theory. According to the fundamental postulates ofthe theory this binding takes place in stages by transitions between stationary states accompanied by emission of radiation. For the problem of the stability of the atom the essential problem is at what stage such a process comes to an end. As regards this point the postulates give no direct information, but here the correspondence principle is brought in. Even though it has been possible to penetrate considerably further at many points than the time has permitted me to indicate to you, still it has not yet been possible to follow in detail all stages in the formation of the atoms. We cannot say, for instance, that the above table of the atomic constitution of the inert gases may in every detail be considered as the unambiguous result of applying the correspondence principle. On the other hand it appears that our considerations already place the empirical data in a light which scarcely permits of an essentially different interpretation of the properties of the elements based upon the postulates of the quantum theory. This applies not only to the series spectra and the close relationship of these to the chemical properties of the elements, but also to the X-ray spectra, the consideration of which leads us into an investigation of interatomic processes of an entirely different character. As we have already mentioned, it is necessary to assume that the emission of the latter spectra is connected with processes which may be described as a reorganization of the completely formed atom after a disturbance produced in the interior of the atom by the action of external forces.