The Periodic System.
Instead of inquiring how the chemical processes may take place, we shall now study the general correlation between the chemical properties and the atomic numbers of the elements, a correlation which has found its empirical expression in the natural or periodic system of the elements ([cf. p. 23]). The explanation of the puzzles of this system must be said to be one of the finest results which Bohr has obtained, and it constitutes a striking evidence in favour of the quantum theory of atoms.
There is nothing new in the idea of connecting the arrangement of the elements in the periodic system with an arrangement of particles in the atom in regular groups, the character of which varies, so to say, periodically with increasing number of particles. In the atom model of Lord Kelvin and J. J. Thomson ([cf. p. 86]), with the positive electricity distributed over the volume of the whole atom, Thomson tried to explain certain leading characteristics of the periodic system by imagining the electrons as arranged in several circular rings about the centre of the atom. He pointed out that the stability of the electronic configurations of this type varied in a remarkable periodic way with the number of electrons in the atom. By considerations of this nature Thomson was able to enunciate a series of analogies to the behaviour of the elements in the periodic system as regards the tendency of the neutral atoms to lose one or more electrons (electropositive elements) or to take up one or more electrons (electronegative elements). But, setting aside possible objections to his considerations and calculations, the connection with the system was very loose and general, and his theory lost its fundamental support when his atomic model had to give way to Rutherford’s. With Bohr’s theory the demand for a stable system of electrons was placed in an entirely new light.
In his treatise of 1913, Bohr tried to give an explanation of the structure of the atom, by thinking of the electrons as moving in a larger or smaller number of circular rings about the nucleus. His theory did not exclude the possibility of orbits of electrons having different directions in space instead of lying in one plane or being parallel. The tendency of the considerations was to attain a definite, unique determination of the structure of the atom, as is demanded by the pronounced stability of the chemical and physical properties of the elements. The results were, however, rather unsatisfactory, and it became more and more clear that the bases of the quantum theory were not sufficiently developed to lead in an unambiguous way to a definite picture of the atom. Nowadays the simple conception of the electrons moving in circular rings in the field of the nucleus is definitely abandoned, and replaced by a picture of atomic constitution of which we shall speak presently.
In the following years the general conception of the group distribution of the electrons in the atom formed the basis of many theoretical investigations, which in various respects have led to a closer understanding of chemical and physical facts. The German physicist, Kossel, showed that the characteristic X-ray spectra of the elements, which are due to a process of reconstruction of the atom subsequent to the removal of one or more of the innermost electrons ([cf. p. 161]), give a most striking support to the assumption that the electrons are distributed in different groups in which they are bound with different strength to the atom.
The connection between the electron groups and the chemical valence properties of the atoms, to which Thomson had first drawn attention and which also played an important part in Bohr’s early considerations, was further developed in a significant way by Kossel, as well as by Lewis and by Langmuir in America. These chemical theories had, however, little or no connection with the quantum theory of atomic processes; even the special features of the Rutherford atom, which are of essential importance in the theory of the hydrogen spectrum and of other spectra, played only a subordinate part.
In 1920 Bohr showed how, by the development of the quantum theory which had taken place in the meantime, and the main features of which consisted in the introduction of more than one quantum number for the determination of the stationary states and in the establishment of the correspondence principle, the problem of the structure of the atom had appeared in a new light. In fact, he outlined a general picture of atomic constitution, based on the quantum theory, which in a remarkable way accounted for the properties of the elements. In order to decide doubtful questions, he has often had to call to his aid the observed properties of elements, and it must be readily admitted that the finishing touches of the theory are still lacking. But from his general starting-point he has been able to outline the architecture of even the most complex atomic structures and to explain, not only the known regularities, but also the apparent irregularities of the periodic system of the elements.
The method Bohr used in his attempt to solve the problem was to study how a neutral normal atom may gradually be formed by the successive capturing and binding of the individual electrons in the field of force about the nucleus of the atom. He began by assuming that he had a solitary nucleus with a positive charge of a given magnitude. To this nucleus free electrons are now added, one after the other, until the nucleus has taken on the number sufficient to neutralize the nuclear charge. Each individual electron undergoes a “binding” process, i.e. it can move in different possible stationary orbits about the nucleus and the electrons already bound. With the emission of radiation it can go from stationary states with greater energy to others with less energy, ending its journey by remaining in the orbit which corresponds to the least possible energy. We may designate this state of least energy as the normal state of the system, which, however, is only a positive atomic ion, so long as all the electrons needed for neutralization are not yet captured.
From the exposition in the [preceding chapter] it will be seen that the ordinary series spectra (arc spectra) may be considered as corresponding to the last stage in this formation process, since the emission of each line in such a spectrum is due to a transition between two stationary states in each of which N-1 electrons are bound in their normal state, i.e. as tight as possible, by the nucleus, while the Nth electron moves in an orbit mainly outside the region of the other electrons. In the same way the spark spectra give witness of the last stage but one of the formation process of the atom, since here N-2 electrons are bound in their normal state while an N-1th electron moves in an orbit large compared with the dimensions of the orbits of the inner electrons. From these remarks it will be clear that the study of the series spectra is of great importance for the closer investigation of the process of formation of the atom outlined above. Furthermore, the general ideas of the correspondence principle, which directly connects the possibility of transition from one stationary state to another with the motion of the electron, has been very useful in throwing light on the individual capturing processes and on the stability of the electronic configurations formed by these. In what follows we cannot, however, reproduce Bohr’s arguments at length; we must satisfy ourselves with some hints here and there, and for the rest restrict ourselves to giving some of the principal results.
Before going farther we shall recall what has previously been said about the quantum numbers. In the undisturbed hydrogen atom, the stationary orbits can be numbered with the principal quantum numbers 1, 2, 3 ... n. But to each principal quantum number there corresponds not one but several states, each with its auxiliary quantum number 1, 2, 3 ... k, k at the most being equal to the principal quantum number. In a similar way, the stationary orbits of the electrons in an atom containing several electrons can be indicated by two quantum numbers, the 3₂ orbit, for instance, being that with principal quantum number 3 and auxiliary quantum number 2. But while in the hydrogen atom the principal quantum number n, in the stationary orbits which are slowly rotating ellipses, is very simply connected with the length of the major axis of the ellipse, and k: n is the ratio between the minor and major axes, still in other atoms with complex systems of electrons the significance of the principal quantum number is not so simple and the orbit of an electron consists of a sequence of loops of more complicated form ([cf. Fig. 29]). We must satisfy ourselves with the statement that a definition of their significance can be given, but only by mathematical-physical considerations which we cannot enter into here. It may, however, be stated that, if we restrict ourselves to a definite atom, the rule will hold that, among a series of orbits with the same auxiliary quantum number but different principal quantum numbers, that orbit in which the electron attains a greater distance from the nucleus has the higher number. Another rule which holds is, that an orbit with a small auxiliary quantum number in comparison with its principal quantum number (as 4₁ for instance, [cf. Fig. 29]), will consist of very oblong loops with a very great difference between the greatest and least distances of the electron from the nucleus, while the orbit will be a circle when the two quantum numbers are the same as for 1₁, 2₂, 3₃. Although each orbit has two quantum numbers, we often speak simply of the 1-, 2-, 3- ... n-quantum orbits, meaning here the orbits with the principal quantum numbers 1, 2, 3 ... n.
The one electron of hydrogen will, upon being captured, first be at “rest” when it reaches the 1₁-path, and we might perhaps be led to expect that in the atoms with greater nuclear charges the electrons in the normal state also would be in the one quantum orbit 1₁, because to this corresponds the least energy in hydrogen. This assumption formed actually the basis of Bohr’s work of 1913 on the structure of the heavier atoms. It cannot be maintained, however. Considerations of theoretical and empirical nature lead to the assumption that the electrons which already are gathered about the nucleus can make room only to a certain extent for new ones, moving in orbits of the same principal quantum number. Those electrons which are captured later are kept at an appropriate distance; they are, for instance, prevented from passing from a 3-quantum orbit to a 2-quantum one, if the number of electrons moving in 2-quantum orbits has reached a certain maximum value. When it is said that the captured electrons end in the stationary state which corresponds to the least energy, it must, therefore, mean, not the 1-quantum orbit, but the innermost possible under the existing circumstances. The final result will be that the electrons are distributed in groups, which are characterized each by their quantum numbers in such a way that passing from the nucleus to the surface of the atom, the successive groups correspond to successive integer values of the quantum number, the innermost group being characterized by the quantum number one. Moreover, each group is subdivided into sub-groups corresponding to the different values which the auxiliary quantum number may take.
That the electrons first collected keep the latecomers at an appropriate distance must be understood with reservations; a new electron moving in an elongated orbit can very well come into the territory already occupied; in fact, it may come closer to the nucleus than some of the innermost groups of electrons. In case an outer electron thus dives into the inner groups, it makes a very short visit, travelling about the nucleus like a comet which at one time on its elongated orbit comes in among the planets and perhaps draws closer to the sun than the innermost planet, but during the greater part of its travelling time moves in distant regions beyond the boundaries of the planetary system. It is a very important characteristic of the Bohr theory of atomic architecture that the outer electrons thus penetrate far into the interior of the atom and thus chain the whole system together.
Such a “comet electron” has, however, a motion of a very different nature from that of a comet in the solar system. Let us suppose that the nuclear charge is 55 (Caesium), that there already are fifty-four electrons gathered tightly about the nucleus, and that No. 55 in an orbit consisting of oblong loops moves far away from the nucleus, but at certain times comes in close to it. Then, for the greater part of its orbit, this electron will be subject to approximately the same attraction as the attraction towards one single charge, as a hydrogen nucleus; but when No. 55 comes within the fifty-four electrons it will for a very short time be influenced by the entire nuclear charge 55. Together with the nearness of the nucleus, this will cause No. 55 to acquire a remarkably high velocity and to move in an orbit quite different from the elliptical one it followed outside. Moreover, the great velocity of the electron during its short visit to the nucleus is in a considerable degree determinative of its principal quantum number; this will be higher than would be expected from the dimensions of the outer part of the orbit if we supposed the motion to take place about a hydrogen nucleus (cf. Figs. 27 and 29).
After these general remarks we shall try in a few lines to sketch the Bohr theory of the structure of the atomic systems from the simplest to the most complicated. We shall not examine the entire periodic system with its ninety-two elements, but here and there we shall bring to light a trait which will illustrate the problem—partly in connection with the schematic representations in the atomic diagrams at the end of the book.
Description of the Atomic Diagrams.
The curves drawn represent parts of the orbital loops of the electrons in the neutral atoms of different elements. Although the attempt has been made to give a true picture of these orbits as regards their dimensions, the drawings must still be considered as largely symbolic. Thus in reality the orbits do not lie in the same plane, but are oriented in different ways in space. It would have been impracticable to show the different planes of the orbits in the figure. Moreover, there is still a good deal of uncertainty as to the relative positions of these planes. On this account the orbits belonging to the same sub-group, i.e., designated by the same quantum numbers, are placed in a symmetric scheme in the sketch. For groups of circular orbits the rule has been followed to draw only one of them as a circle, while the others in the simpler atoms are drawn in projection as ellipses within the circle, and in the more complicated atoms are omitted entirely. The two circular orbits of the helium atom are both drawn in projection as ellipses. Further, for the sake of clearness, no attempt has been made to draw the inner loops of the non-circular orbits of electrons which dive into the interior of the atom. In lithium only, the inner loop of the orbit of the 2₁ electron has been shown by dotted lines.
In order to distinguish the groups of orbits with different principal quantum numbers two colours have been used, red and black, the red indicating the orbits with uneven quantum numbers, as 1, 3, 5, the black those with even quantum numbers, as 2, 4, 6. Wherever possible the nucleus is indicated by a black dot; but in the sketches of atoms with higher atomic numbers the 1-quantum orbits are merged into one little cross and the nucleus has been omitted. It should be noticed that the radium atom is drawn on a scale twice as great as that for the other atoms.
We shall begin with the capture of the first electron. If the nucleus is a hydrogen nucleus the hydrogen atom is completed when the electron has come into the 1₁ orbit, a circle with diameter of about 10⁻⁸ cm. (cf. the diagram). If the nucleus had had a greater nuclear charge the No. 1 electron would have behaved in the same way, but the radius of its orbit would have been less in the same ratio as the nuclear charge was greater. For a lead nucleus, with charge (atomic number) 82, the radius of the 1₁ orbit is ¹/₈₂ that of the hydrogen 1₁ orbit. Since atoms with high atomic numbers thus collect the electrons more tightly about them it is understandable that, in spite of their greater number of electrons, they can be of the same order of magnitude as the simpler atoms.
Let us now examine the helium atom. The first electron, which its nucleus (charge 2) catches, moves as shown in a circle 1₁, but with a smaller radius than in the case of the hydrogen atom. Electron No. 2 can be caught in different ways, and the closer study of the conditions prevailing here, which are still comparatively simple since there are only two electrons, has been of greatest importance in the further development of the whole theory. We cannot go into it here, but must content ourselves with saying that the stable final result of the binding of the second electron consists in the two electrons moving in circular 1-quantum orbits of the same size with their planes making an angle with each other (cf. the diagram). This state has a very stable character, and the helium atom is therefore very disinclined to interplay with other atoms, with other helium atoms as well as with those of other elements. Helium is therefore monatomic and a chemically inactive gas.
In all atomic nuclei with higher charges than the helium nucleus the first two orbits are also bound into two 1-quantum circular orbits at an angle with each other; this group cannot take up any new electron having the same principal quantum number. It takes on an independent existence and forms the innermost electron group in all atoms of atomic number higher than 2.
Electron No. 3 will accordingly not be bound in the same group with 1 and 2. It must be satisfied with a 2-quantum orbit, 2₁, which consists of oblong loops, and, when nearest the nucleus, comes into the territory of the 1-quantum orbits. It is but loosely bound compared to the first two electrons, and the lithium atom, which has only three electrons, can therefore easily let No. 3 loose so that the atom becomes a positive ion. Lithium is therefore a strongly electropositive monovalent metal. The element beryllium (No. 4) will probably have two electrons in the orbits 2₁; it will therefore be divalent. But during the short visit of these electrons to the nucleus they are subject to a greater nuclear charge than in lithium. The 2₁ electrons are therefore, in beryllium, more firmly bound than in lithium, and the electropositive character of beryllium is therefore less marked.
We have something essentially new in the boron atom (atomic No. 5) where the two electrons No. 3 and No. 4 are taken into 2₁ orbits, but where No. 5 will very probably be bound in a circular 2₂ orbit. How the conditions will be in the normal state of the following atoms preceding neon is not known with certainty. We only know that the electrons coming after the first two will be captured in 2-quantum orbits, the dimensions of which get smaller, according as the atomic number increases.
The neon atom (compare the diagram) has a particularly stable structure, both “closed” and symmetric, which besides two 1₁-orbits contains four electrons in 2₁ orbits and four electrons in 2₂ orbits. As regards the four electrons in 2₁ orbits, they do not have symmetrical positions at every moment or move simultaneously either towards or away from the nucleus; on the contrary, it must be assumed that the electrons come closest to the nucleus at different moments at equal intervals of time.
The name of inert or inactive gases is given to the entire series of helium (2), neon (10), argon (18), krypton (36), xenon (54) and niton (86), the O-column in the periodic system given in the [table on p. 23]. All these elements are monatomic and quite unwilling to enter into chemical compounds with other elements (although there is about 1 per cent. of argon in the air about us this element has, on this account, escaped the observation of chemists until about 1895, when it was discovered by the English chemist, Ramsay). This complete chemical inactivity is explained by the fact that the atoms of all these elements have a nicely finished “architecture” with all the electrons firmly bound in symmetrical configurations. They may be said to form the mile posts of the periodic system, and to be the ideals towards which the other atoms aspire. The [table shows] how the electrons in the atoms of these gases are divided among the types of orbits corresponding to the different quantum numbers.
Table showing the Distribution of the Electrons
of different Orbital Types in the Neutral Atoms
of the Inactive Gases.
| Atomic Number | Quantum Numbers. | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1₁ | 2₁ | 2₂ | 3₁ | 3₂ | 3₃ | 4₁ | 4₂ | 4₃ | 4₄ | ||
| Helium | 2 | 2 | 2 | ||||||||
| Neon | 10 | 2 | 4 | 4 | |||||||
| Argon | 18 | 2 | 4 | 4 | 4 | 4 | - | ||||
| Krypton | 36 | 2 | 4 | 4 | 6 | 6 | 6 | 4 | 4 | - | - |
| Xenon | 54 | 2 | 4 | 4 | 6 | 6 | 6 | 6 | 6 | 6 | - |
| Niton | 86 | 2 | 4 | 4 | 6 | 6 | 6 | 8 | 8 | 8 | 8 |
| ? | 118 | 2 | 4 | 4 | 6 | 6 | 6 | 8 | 8 | 8 | 8 |
| Atomic Number | Quantum Numbers. | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 5₁ | 5₂ | 5₃ | 5₄ | 5₅ | 6₁ | 6₂ | 6₃ | 6₄ | 6₅ | 6₆ | 7₁ | 7₂ | 7₃ | ||
| Helium | 2 | ||||||||||||||
| Neon | 10 | ||||||||||||||
| Argon | 18 | ||||||||||||||
| Krypton | 36 | ||||||||||||||
| Xenon | 54 | 4 | 4 | - | - | - | |||||||||
| Niton | 86 | 6 | 6 | 6 | - | - | 4 | 4 | - | - | - | - | |||
| ? | 118 | 8 | 8 | 8 | 8 | - | 6 | 6 | 6 | - | - | - | 4 | 4 | - |
The elements fluorine, oxygen and nitrogen can attain the ideal neon-architecture by binding respectively one, two and three additional electrons. Naturally they do not become neon atoms, but merely negative atomic ions with single, double or triple charge; and their tendency in this direction appears in their character of monovalent, divalent and trivalent electronegative elements respectively. If we return to carbon it can probably not become a tetravalent negative ion by binding four free electrons; but in the typical carbon compound, methane (CH₄), the neon ideal is realized in another manner. In fact, it is reasonable to assume that the four electrons of the hydrogen atoms together with the six of the carbon atom give approximately a neon-architecture. The four hydrogen nuclei naturally cannot be combined with the carbon nucleus; the mutual repulsions keep them at a distance. They will probably assume very symmetrical positions within the electron system which holds them together. The nitrogen atom may in a similar way find completion in a neutral molecule with neon-architecture, if it unites with three hydrogen atoms to form ammonia NH₃; but the three hydrogen nuclei, although having symmetrical positions, will not lie in the same plane as the nitrogen nucleus. The electric centre of gravity for the positive nuclei will therefore not coincide with the centre of gravity for the negative electron system. The molecule obtains thus what might be called a positive and a negative pole, and this dipolar character appears in the electrical action of ammonia (its dielectric constant). Something similar holds true for the water molecule, where, in a neon-architecture of electrons, in addition to the oxygen nucleus in the centre there are two hydrogen nuclei which are not co-linear with the oxygen nucleus.
If we go on from neon in the periodic system we come to sodium (11). When the sodium nucleus captures electron No. 11, this cannot find room in the neon-architecture formed by the first ten electrons. Since the eleventh electron thus cannot find a place in either a 2₁ or a 2₂ orbit, it is bound in a 3₁ orbit ([cf. Fig. 29] and diagram at the end). The atom then has a character like that of the lithium atom, and we can therefore understand the chemical relationship between the two elements, which are both monovalent electropositive metals.
We shall not dwell longer upon the individual elements of the atomic series. If we pass from neon through sodium (11), magnesium (12), aluminium (13), etc., to argon (18), we get what is essentially a repetition of the situation in the series from lithium to neon. We first get two orbits of the 3₁ type in magnesium, a 3₂ orbit is for the first time added in aluminium, and for the atomic number 18, eight 3-quantum orbits, together with the eight orbits of the inner 2-quantum group and the two of the innermost 1-quantum group, give the symmetric architecture of argon ([cf. table on p. 196], and [diagram at the end]).
The architecture of the argon atom is in a certain sense less complete than that of the neon atom. In argon there are indeed four orbits of the 3₁ type and four of the 3₂ type, but the third kind of 3-quantum orbit, the circular 3₃ one, is missing. Nor does it appear in the next element, potassium (19). The electron No. 19 prefers, instead of the 3₃ orbit, the 4₁ orbit, which consists of oblong loops and which gives a firmer binding because it dives in among the electrons bound earlier, while the circle 3₃ would lie outside them all. We thus obtain an atom of type similar to the lithium and sodium atoms. But the slighted 3₃ path lies, so to speak, on the watch to steal a place for itself in the neutral atom, and this has grave results for the subsequent development. Even in calcium (20), after the first eighteen electrons are bound in the argon architecture, both the nineteenth and the twentieth go into a 4₁ orbit, and the behaviour of calcium is like that of magnesium. But since the increasing nuclear charge means for the electron No. 19 a decrease in the dimensions and an increase in the binding of the orbits corresponding to the quantum number 3₃, a point will finally be attained where the 3₃ orbit of the nineteenth electron lies within the boundaries of what may be called the argon system, i.e., the architecture corresponding to the first eighteen electrons, and corresponds to a stronger binding than a 4₁ orbit would do. In scandium (21) the 3₃-type orbit occurs for the first time in the neutral atom and will not only come into competition with the 4₁ type, but will also cause a disturbance in the 3-quantum groups, which in the following elements must undergo reconstruction. As long as this lasts the situation is very complicated and uncertain. When the reorganization is almost completed, we come to the blotting out of chemical differences, particularly known from the triad, iron, cobalt and nickel. Moreover, there comes a fluctuation in the valency of the elements. Iron can, as has been said, be divalent, trivalent or hexavalent. This oscillation in valency begins in titanium.
We should perhaps expect that the reconstruction would be completed long before nickel (28) is reached, because even with twenty-two electrons we could get four orbits of each of the 3-quantum types (3₁, 3₂ and 3₃); but from the chemical facts we are led to assume that in a completed group of 3-quantum orbits there can be room for six electrons in each sub-group. At first sight we should, then, expect the end of the reconstruction with nickel, which has indeed eighteen electrons more than neon where the group of 2-quantum orbits was completed. We might expect that nickel would be an inert element in the series with helium, neon, and argon. On the contrary, nickel merely imitates cobalt. This is explained by the fact that the group of eighteen 3-quantum orbits, although it has a symmetric architecture, is weakly constructed if the nuclear charge is not sufficiently large. The binding of this group is too weak for it to exist as the outer group in a neutral atom. In nickel the electrons, in a less symmetrical manner, will probably arrange themselves with seventeen 3-quantum orbits and one 4-quantum orbit.
The group of eighteen 3-quantum orbits becomes stable, however, when the nuclear charge is equal to or larger than 29, in which case it can become the outer group in a positive ion. In this we find the explanation of the properties of the atom of copper. The neutral copper atom has its twenty-ninth electron bound in a 4₁ orbit consisting of oblong loops (cf. diagram at the end); this electron can easily be freed and leaves a positive monovalent copper ion with a symmetrical architecture. Even under these circumstances, although possessing a certain stability, the ion is not very firmly constructed. Thus the fact that copper can be both monovalent and divalent, must be explained by the assumption that for a nuclear charge 29, the 3-quantum group still easily loses an electron.
When we come to zinc (30) the group of eighteen is more firmly bound; zinc is a pronounced divalent metal which in its properties reminds us of calcium and magnesium. From zinc (30) to krypton (36) we have a series of elements which in a certain way repeat the series from magnesium (12) to argon (18).
In [Fig. 34] is shown Bohr’s arrangement of the periodic system in which the systematic correlation of the properties of the element appears somewhat clearer than in the usual plan ([cf. p. 23]). It shows great similarity with an arrangement proposed nearly thirty years ago by the Danish chemist, Julius Thomsen. The elements from scandium to nickel, where, in the neutral atom, the electron group of 3-quantum orbits is in a state of reconstruction, are placed in a frame; the neutral oblique lines connect elements which are “homologous,” i.e., similar in chemical and physical (spectral) respect.
Fig. 34.—The periodic system of the elements. The elements where an inner group of orbits is in a stage of reconstruction are framed. The oblique lines connect elements which in physical and chemical respects have similar properties.
In krypton (36) we again have a stable architecture with an outer group of eight electrons, four in 4₁ orbits and four in 4₂ orbits. Owing to the appearance of 4₃ orbits in the normal state of the atoms of elements with atomic number higher than 38, there follows in the fifth period of the natural system a reconstruction and provisional completion of the 4-quantum orbits to a group of eighteen electrons, which shows a great simplicity with the completion of the 3-quantum group in the fourth period. In [Fig. 34] the elements where the 4-quantum group is in a state of reconstruction are framed. The 4-quantum group with eighteen electrons is of more stable construction than the group of eighteen 3-quantum orbits in the elements with an atomic number lower by eighteen. This is due to the fact that all the orbits in the first-mentioned group are oblong and therefore moored, so to say, in the inner groups, while in the complete group of 3-quantum orbits there are six circular orbits. This is the reason why silver, in contrast to copper, is monovalent.
The next inactive gas is xenon (54), which outside of the 4-quantum group has a group of eight electrons in 5-quantum orbits, four in 5₁ orbits and four in 5₂ orbits. We notice that in xenon the group of 4-quantum orbits still lacks the 4₄ orbits. On the theory we must, therefore, expect to meet a new process of completion and reconstruction when proceeding in the system of the elements. The theoretical argument is similar to that which applies in the case of the completion of the 3-quantum group which takes place in the fourth period of the natural system. In fact, in the formation of the normal atoms of the elements next after xenon, caesium, 55, and barium, 56, the fifty-four electrons first captured will form a xenon configuration, while the fifty-fifth electron will be bound in a 6₁ orbit, consisting of very oblong loops, which represents a much stronger binding than a circular 4₄ orbit. Calculation shows, however, that with increasing nuclear charge there must soon appear an element for which a 4₄ orbit will represent a stronger binding than any other orbit. This is actually the case in cerium (58), and starting from this element we meet a series of elements where, in the normal neutral atom, the 4-quantum group is in a state of reconstruction. This reconstruction must occur far within the atom, since the group of eighteen 4-quantum orbits in xenon is already covered by an outer group of eight 5-quantum orbits. The result is a whole series of elements with very slight outward differences between their neutral atoms, and therefore with very similar properties. This is the rare earths group, which in such a strange way seemed to break down the order of the natural system ([cf. p. 21]), but which thus finds its natural explanation in the quantum theory of the structure of the atom.
The elements in which the 4-quantum group is in a state of reconstruction are, in [Fig. 34], enclosed in the inner frame in the sixth period. Moreover, in the outer frame all elements are enclosed where the group of 5-quantum orbits is in a state of reconstruction, which started, even before cerium in lanthanum (57), where the fifty-fifth electron in the normal state is bound in a 5₃ orbit. The element cassiopeium, with atomic number 71, which is the last of the rare earths, stands just outside the inner frame, because in the normal neutral atom of this element the 4-quantum group is just completed; this group, instead of eighteen electrons with six electrons in each sub-group, consists now of thirty-two electrons with eight electrons in each sub-group. The theory was able to predict that the element with atomic number 72, which until a short time ago had never been found, and the properties of which had been the subject of some discussion, must in its chemical properties differ considerably from the trivalent rare earths and show a resemblance to the tetravalent elements zirconium (40), and thorium (90). This expectation has recently been confirmed by the work of Hevesy and Coster in Copenhagen, who have observed, by means of X-ray investigations, that most zircon minerals contain considerable quantities (1 to 10 per cent.) of an element of atomic number 72, which has chemical properties resembling very much those of zirconium, and which on this account had hitherto not been detected by chemical investigation. A preliminary investigation of the atomic weight of this new element, for which its discoverers have proposed the name hafnium (Hafnia = Copenhagen), gave values lying between 178-180, in accordance with what might be expected from the atomic weight of the elements (71) and (73). ([Cf. p. 23].)
The further completion of the groups of 5- and 6-quantum orbits, which in the rare earths had temporarily come to a standstill, is resumed in hafnium and goes on in a way very similar to that in which the 4- and 5-quantum groups in the fifth, and the 3- and 4-quantum groups in the fourth period underwent completion. Thus the reconstruction of the 5-quantum group which began in lanthanum, and which receives a characteristic expression in the triad of the platinum metals, has come to a provisional conclusion in gold (79), gold being the first element outside the two frames which, in [Fig. 34], appear in the sixth period. The neutral gold atom possesses, in its normal state—besides two 1-quantum orbits, eight 2-quantum orbits, eighteen 3-quantum orbits, thirty-two 4-quantum orbits and eighteen 5-quantum orbits—one loosely bound electron in a 6₁ orbit.
In niton (86), finally, we meet again an inactive gas, the structure of the atom of which is indicated in the [table on p. 196].
In this element the difference between nuclear and electron properties appears very conspicuously, since the structure of the electron system is particularly stable, while that of the nucleus is unstable. Niton, in fact, is a radioactive element which is known in three isotopic forms; one of these is the disintegration product of radium, the so-called radium emanation; it then has a very brief life. In the course of four days over half of the nuclei in a given quantity of radium emanation will explode.
In the diagram at the end of the book, as an example of an atom with very complicated structure, there is given a schematic representation of the atom of the famous element radium, on a scale twice as large as the one used in the other atoms. It follows clearly enough, from what has been said in [Chap. IV]., that the structure of the electron system has nothing to do with the radioactivity. All the remarkable radiation activities are due to the nucleus itself. There has not even been room in the figure to draw the nucleus; the 1-quantum orbits consist only of a small cross, and in the other groups we have contented ourselves with summary indications. The electron system, with its eighty-eight electrons, is, however, in itself very interesting, with its symmetry in the number of electrons in the different groups. In the different quantum groups from 1 to 7 there are found respectively two, eight, eighteen, thirty-two, eighteen, eight and two electrons. The last group is naturally of a very different nature from the first; they are “valence electrons,” which easily get loose and leave behind a positive radium ion with stable niton architecture. Radium then belongs to the family of the divalent metals, magnesium, calcium, strontium and barium.
Four places from radium is uranium (92) and the end of the journey, if we restrict ourselves to the elements which are known to exist. One could very well continue the building-up process still further and discuss what structure would have to be assumed for the atoms of the elements with higher atomic numbers. That they cannot exist is not the fault of the electron system but of the nuclei, which would become too complicated and too large to be stable. In the [table on p. 196] there is shown the probable structure of the atom of the inert gas following niton; it must be assumed to have one hundred and eighteen electrons distributed in groups of two, eight, eighteen, thirty-two, thirty-two, eighteen and eight among the quantum groups from 1 to 7.
As has been said, in all this symmetrical structure of the atoms of the elements, Bohr has in many cases had to rely upon general considerations of the information that observation gives about the properties of the individual elements. It must, however, not be forgotten that the backbone of the theory is and remains the general laws of the quantum theory, applied to the nucleus atom in the same way as they originally were applied to the hydrogen atom, leading thereby to the interpretation of the hydrogen spectrum.
We have, further, a most striking evidence as to the correctness of Bohr’s ideas in the fact that not only do the pictures of the atoms which he has drawn agree with the known chemical facts about the elements, but they are also able to explain in the most satisfactory manner possible the most essential features of the characteristic X-ray spectra of the different elements, a field we shall not enter upon here.
In all that has been said above we have been considering the Bohr theory simply as a means of gaining a deeper understanding of the laws which determine activities in the atomic world. Perhaps we shall now be asked if we can “utilize” the theory, or, in other words, if it can be put to practical use.
To this natural and not unwarranted question we may first give the very general answer, that progress in our knowledge of the laws of nature always contributes sooner or later, directly or indirectly, to increase our mastery over nature. But the connection between science and practical application may be more or less conspicuous, the path from science to practical application more or less smooth. It must be admitted that the Bohr theory, in its present state of development, hardly leads to results of direct practical application. But since it shows the way to a more thorough understanding of the details in a great number of physical and chemical processes, where the peculiar properties of the different elements play parts of decided importance, then in reality it offers a wealth of possibilities for making predictions about the course of the processes—predictions which undoubtedly in the course of time will be of practical use in many ways. In this connection the discovery of the element hafnium, discussed on [p. 204], may be mentioned. It must be for the future to show what the Bohr theory can do for technical practice.
Below is given an explanation of the different symbols which occur at various places in the book; also the values of important physical constants.
1 m. = 1 metre; 1 cm. = 1 centimetre = 0·394 inches.
1 μ = 1 micron = 1/1000 of a millimetre = 0·0001 cm. = 10⁻⁴ cm.
1 μμ = 1/1,000,000 of a millimetre = 10⁻⁷ cm.
1 cm.³ = 1 cubic centimetre.
1 g. = 1 gram; 1 kg. = 1 kilogram = 2·2 pounds.
1 kgm. = 1 kilogrammetre (the work or the energy required to lift 1 kg. 1 m.).
1 erg = 1·02 × 10⁻⁸ kgm. = 7·48 × 10⁻⁸ foot-pounds.
λ represents wave-length.
ν represents frequency (number of oscillations in 1 second).
ω represents frequency of rotation (number of rotations in 1 second).
n represents an integer (particularly the Bohr quantum numbers).
The velocity of light is c = 3 × 10¹⁰ cm. per second = 9·9 × 10⁸ feet per second.
The wave-length of yellow sodium light is 0·589 μ = 589 μμ = 2·32 × 10⁻⁵ inches.
The frequency of yellow sodium light is 526 × 10¹² vibrations per second.
The number of molecules per cm.³ at 0° C. and atmospheric pressure is about 27 × 10¹⁸.
The number of hydrogen atoms in 1 g. is about 6·10²³.
The mass of a hydrogen atom is 1·65 × 10⁻²⁴ g.
The elementary quantum of electricity is 4·77 × 10⁻¹⁰ “electrostatic units.”
The negative electric charge of an electron is 1 elementary quantum (1 negative charge).
The positive electric charge of a hydrogen nucleus is 1 elementary quantum (1 positive charge).
The mass of an electron is ¹/₁₈₃₅ that of the hydrogen atom.
The diameter of an electron is estimated to be about 3 × 10⁻¹³ cm.
The diameter of the atomic nucleus is of the order of magnitude 10⁻¹³ to 10⁻¹² cm.
The diameter of a hydrogen atom in the normal state (the diameter of the first stationary orbit in Bohr’s model) is 1·056 × 10⁻⁸ cm.
The Balmer constant K = 3·29 × 10¹⁵.
The Planck constant h = 6·54 × 10⁻²⁷.
An energy quantum is E = hν.
The Balmer-Ritz formula for the frequencies of the lines in the hydrogen spectrum is
| ν = K |  | 1 | - | 1 |  |
| n″ ² | n′ ² |
DIAGRAMS OF SPECTRA
AFTER BUNSEN AND KIRCHHOFF
MAIN LINES OF
THE ATOMIC STRUCTURE
OF SOME ELEMENTS
STRUCTURE OF THE RADIUM ATOM
Transcriber’s Notes:
The cover image was created by the transcriber, and is in the public domain.
The illustrations have been moved so that they do not break up paragraphs and so that they are next to the text they illustrate.
Typographical and punctuation errors have been silently corrected.
[Page 41]: “1,000,000 feet or 300,000 kilometres per second” changed to “1,000,000,000 feet or 300,000 kilometres per second”