The Constitution of the Elements based on the

X-ray Spectra.

The theory of the X-ray spectra involves the determination of the electronic systems next to the nucleus, and may give us valuable information as to the way in which the electrons round the nucleus are grouped together.

The previous investigation has shown that the K-series should be attached to a ring with quant number 1 next to the nucleus and containing 3 electrons. The L-series should be due to two rings with quant numbers 2 and consisting of 7 and 8 electrons. The M-series should probably have rings with a quant number 3 and 9-10 electrons.

If this theory is right, it would mean that if a ring is formed for lower atomic numbers the same ring is kept throughout the whole system of elements. Indeed I think that this is to be considered as a necessary consequence to be derived from the simple laws governing the X-ray spectra, and is independent of any special theory which we propose to explain the frequencies and the type of the spectra. For a change in the number of electrons in the K-ring, say, would necessarily involve a discontinuity in the formula expressing the relation between frequency and atomic number.

Now it might be legitimate as an hypothesis to take this rule as a fundamental property of the atomic structure, and quite general to assume that a system of electrons once formed is kept also for elements of higher atomic numbers. There is no reason why this rule should cease to hold because we pass to lower frequencies.

Now if we would further build on the result of our present theory as to the number of electrons in the K- and L-rings, we should get a quite definite system for the first eighteen elements, and from this start we should be able to see how the electrons are arranged in a series of elements forming one period in the periodic system. If we have proceeded so far, we can get further by the assumption that elements of the same family, such as Li, Na, and K say, must have the same number of electrons in the outer ring. I think this is an assumption which is very well founded, because the chemical properties must be mainly determined by the outer electrons, and the assumption is independent of any other special hypothesis with regard to the grouping of the electrons.

Proceeding in this way, we assume in accordance with Bohr that the strongest electropositive elements have

1 electron in the outer ring. Now the elements from Li to Fl are assumed to maintain an internal system of 2 electrons and add one in the external ring for each step in atomic number. This will make an external ring of 7 electrons. By Ne one electron is added which, however, goes to the central ring, and hence forward we get the K-ring. If so, the K-radiation should begin with Ne or Na; and in fact this result is in agreement with experiments, for Na is the first element for which the K-radiation has been observed. Now the ring of 7 electrons is kept to form the inner L-ring, and a new ring comes into existence for Na. From Ar we have both L-rings with 7 and 8 electrons formed, and the L-radiation might perhaps be expected to begin with potassium; perhaps some of the lines might be traced to Na.

Now we come to the long period from Ar to Kr. At first a ring of 10 electrons is formed, completed by the elements Fe, Co, and Ni with 8, 9, and 10 electrons in the external ring respectively; this should be the first M-ring with quant number 3. At Cu a new ring comes into existence, and we get a monovalent electropositive element. During the next long period from Kr to Xe the same process is repeated.

The next and longest of all periods which go from Xe to Ra Em is peculiar because it contains the rare earths. Now I think that the view here adopted with regard to the constitution of the electronic systems may afford a very simple and natural explanation of this peculiar group of

elements.

When we pass from Xe, a new external ring is formed, with 1 electron for Cs, 2 for Ba, and so on until for Ce we get a ring of 4 electrons. Passing now to the next elements we assume the external ring to be kept, and that the new electrons are forming a new internal ring. From our point. of view such an assumption is a quite legitimate one. It would only mean that the new electronic system had a smaller quant number than the external ring: for a smaller quant number will, according to equation (25), give a smaller radius of the ring. Thus the new electrons which are taken up in the series of rare earths when we pass to higher atomic numbers are, so to speak, soaked into the atom, and the surface systems mainly determining the chemical properties are kept unaltered. How these new

internal electrons are arranged we do not know. In the graphical representation (fig. 2) I have assumed them to form one system inside the surface electrons.

When at last the atom has become saturated as it were,

we pass from the rare earths; new electrons are added as before to the surface system, and we get systems of the same type as those of the two long series.

The whole system here shortly sketched is graphically represented in fig. 2. Along the horizontal axis the elements are arranged in the order of increasing atomic numbers. The principle adopted, that an electronic system once formed is kept throughout the whole series of elements, makes it natural to represent an electron by a horizontal line. These lines are arranged into groups, and each group represents an electronic ring system. The arrangement of electrons for a certain element is got by drawing a vertical line from the place of the element on the horizontal axis. The points of intersection with the horizontal lines give the number of electrons and their arrangement into ring systems.

On the Electron Affinity of the Elements.

When we pass from elements that follow an inert gas, we begin with the strong electropositive elements, and as we pass on they become more electronegative. The transition from electronegative to electropositive elements may either take place by the passage through an inert gas or by passing the groups Fe Co Ni, Ru Rh Pd, and Os Ir Pt. In our system the strong electropositive elements set in with the formation of a new surface ring.

It might now be asked which quantity might rightly be selected to express the chemical electro-affinity.

The idea would naturally suggest itself that the electron affinity is measured by the energy necessary to remove an electron from the external ring. This, however, is identical with the energy necessary to ionize the atom and is proportional to the ionizing potential, which is no measure of the chemical electronegativity *.

Nor can we take the energy which binds an additional electron; for the experiments of J. J. Thomson † on positive rays have shown that the power of an atom to bind electrons does not follow the chemical electronegativity.

I think the explanation of these facts may be found in the following considerations. The electrons forming part of a normal atomic ring system are not to be considered as free electrons, but as linked together in some way, the nature of

* See J. Stark, "Ionisierung der chemischen Elemente durch Elektronenstoss," Jahrb. d. Rad. u. Elektronik, xiii.

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Sir J. J. Thomson, Rays of Positive Electricity,' p. 40 (1913), p. 395 (1916).

which we do not know. Now the forces which are engaged in the chemical binding of elements do not act on a single electron as in the case of an ionizing agency, but much more on the ring as a unity. From this consideration it might be more natural to take the energy necessary to remove an electron when all the other electrons of the ring were removed simultaneously. According to Bohr this energy is equal to the kinetic energy of the electron, and thus elements with the more slowly moving electrons are the more electropositive. Equation (7) gives for this energy

where approximately N'=p and p is the number of electrons in the surface ring; hR is the value of the energy wн for hydrogen.

wH

Let us first consider the variation of σ for elements which have the same number of ring systems and only differ with regard to the number of electrons in the external ring. Suppose, e. g., that we consider the elements from Na to Cl. For such a series the quant number n is constant ando consequently proportional to (p-Sp)2, and we can easily see that σ increases with increasing values of p by forming

Op+1―op={2p+1−(Sp+1−Sp)}{1— (Sp+1—Sp)}. As both factors on the right side are positive, op+1 > Op•

If σ could be taken to represent the electronegativity, the elements in each such group would pass from electropositive to more electronegative as we proceed towards increasing atomic numbers.

Let us next consider elements which are chemically related; such elements have the same value of p. As we pass from low to high atomic numbers, the quant number n will increase and the value of σ will diminish. Thus elements of the same chemical family should be more electropositive as we pass towards increasing atomic numbers, which is indeed a well-known property of the elements.

The Electric Conductivity.

There can probably be no doubt that the electric conductivity in some way or other is related to the energy which binds the electrons of the surface system. Introducing a quantity