Chapter 24

i022Fig. 22—X-ray absorption spectra.series

Fig. 22—X-ray absorption spectra.series

i023Fig. 23—X-ray absorption spectra,series

Fig. 23—X-ray absorption spectra,series

i024Fig. 24—Hydrogen spectrum from the star Vega

Fig. 24—Hydrogen spectrum from the star Vega

i025Fig. 25

Fig. 25

According to modern theory an absorption edge appears where the incident energy—which is proportional to the incident frequency—has become just large enough to lift the particular electron which absorbs it entirely out of the atom. If this removed electron should then fall back to its old place in the atom, it would emit in so doing precisely the frequency which was absorbed in the process of removal.

Since these enormously high X-ray frequencies must arise from electrons which fall into extraordinarily powerful fields of force, such as might be expected to exist in the inner regions of the atom close to the nucleus, Moseley’s discovery strongly suggests that the charge on this nucleus is produced in the case of each atom by adding some particular invariable charge to the nucleus of the atom next below it in Moseley’s table. This suggestion gains added weight when it is found that with one or two trifling exceptions, to be considered later,Moseley’s series of increasing X-ray frequencies is exactly the series of increasing atomic weights. It also receives powerful support from the following discovery.

Mendeleéff’s periodic table shows that the progression of chemical properties among the elements coincides in general with the progression of atomic weights. Now it was pointed out ten years ago that whenever a radioactive substance loses a doubly charged-particle it moves two places to the left in the periodic table, while whenever it loses a singly charged-particle it moves one place to the right,[149]thus showing that the chemical character of a substancedepends upon the number of free positive charges in its nucleus.

One of the most interesting and striking characteristics of Moseley’s table is that all the known elements between sodium (atomic number 11, atomic weight 23) and lead (atomic number 82, atomic weight, 207.2) have been fitted into it and there are left but three vacancies within this range. Below sodium there are just 10 known elements, and very recent study[150]of their spectra in the extreme ultra-violet has fixed the place of each in the Moseley progression, though in this region the progression of atomic weights and of chemical properties is also altogether definite and unambiguous. It seems highly probable, then, from Moseley’s work that we have already found all except three of the complete series of different types of atoms from hydrogen to lead, i.e., from 1 to 82, of which the physical world is built. From 82 to 92 comes the group of radioactive elements which are continually transmuting themselves into one another, and above 92 (uranium) it is not likely that any elements exist.

That hydrogen is indeed the base of the Moseley series is rendered well-nigh certain by the following simple computation. If we write Moseley’s discovery that the square roots of the highest frequencies,,,etc., emitted by different atoms are proportional to the nuclear charges,,,etc., in the following form:and substitute forthe observed wave-length of the highest frequency line emitted by tungsten—a wave-length which has been accurately measured and found to be;and, further, if we substitute for,74, the atomic number of tungsten, and for,1, if the Moseley law were exact we should obtain, by solving for the wave-length of the highest frequency line which can be emitted by the element whose nucleus contains but one single positive electron. The result of this substitution is(millionths millimeters). Now the wave-length corresponding to the highest observed frequency in the ultra-violet series of hydrogen lines recently discovered by Lyman isand there is every reason to believe from the form of this series that its convergence wave-length—this corresponds to the highest frequency of which the hydrogen atom is theoretically capable—is.The agreement is only approximate, but it is as close as could be expected in view of the lack of exact equality in the Moseley steps.It is well-nigh certain, then, that this Lyman ultra-violet series of hydrogen lines is nothing but theX-ray series of hydrogen. Similarly, it is equally certain that theX-rays series of hydrogen is the ordinary Balmer series in the visible region, the head of which is atIn other words, hydrogen’s ordinary radiations are its X-rays and nothing more.

There is also anseries for hydrogen discovered by Paschen in the ultra-red, which in itself would make it probable that there are series for all the elements of longer wave-length than theseries, and that the complicated optical series observed with metallic arcs are parts of these longer wave-length series. As a matter of fact, anseries has been found for a considerable group of the elements of high atomic number.

Thus the Moseley experiments have gone a long way toward solving the mystery of spectral lines. They reveal to us clearly and certainly the whole series of elements from hydrogen to uranium, all producing spectra of remarkable similarity, at least so far as theandradiations are concerned, but scattered regularly through the whole frequency region, from the ultra-violet, where thelines for hydrogen are found, all the way up to frequenciesor 8,464 times as high. There is scarcely a portion of this whole field which is not already open to exploration. How brilliantly, then, have these recent studies justified the predictions of the spectroscopists that the key to atomic structure lay in the study of spectral lines!

Moseley’s work is, in brief, evidence from a wholly new quarter that all these elements constitute a family, each member of which is related to every other member in a perfectly definite and simple way. It looks as if the dream of Thales of Miletus had actually come true and that we have found a primordial element out of which all substances are made, or better two of them. For the succession of steps from one to ninety-two, each corresponding to the addition of an extra free positive charge upon the nucleus, suggests at once that the unit positive charge is itself a primordial element, and this conclusion is strengthened by recently discovered atomic-weight relations. It is well known that Prout thought a hundred years ago that the atomic weights of all elements were exact multiples of the weight of hydrogen, and hence tried to make hydrogen itself the primordial element. Butfractional atomic weights like that of chlorine (35.5) were found, and were responsible for the later abandonment of the theory. Within the past five years, however, it has been shown that, within the limits of observational error, practically all of those elements which had fractional atomic-weights are mixtures of substances, so calledisotopes, each of which has an atomic weight that is an exact multiple of the unit of the atomic-weight table, so that Prout’s hypothesis is now very much alive again.

So far as experiments have now gone, the positive electron, the charge of which is of the same numerical value as that of the negative,and which is in fact the nucleus of the hydrogen atom, always has a mass which is about two thousand times that of the negative. In other words, the present evidence is excellent that, to within one part in two thousand, the mass of every atom is simply the mass of the positive electrons contained within its nucleus. Now the atomic weight of helium is four, while its atomic number, the free positive charge upon its nucleus, is only two. The helium atom must therefore containinside its nucleustwo negative electrons which neutralize two of these positives and serve to hold together the four positives which would otherwise fly apart under their mutual repulsions. Into that tiny nucleus of helium, then, that infinitesimal speck not as big as a pin point, even when we multiply all dimensions ten billion fold so that the diameter of the helium atom, the orbit of its two outer negatives, has become a yard, into that still almost invisible nucleus there must be packed four positive and two negative electrons.

By the same method it becomes possible to count the exact number of both positive and negative electrons which are packed into the nucleus of every other atom. In uranium, for example, since its atomic weight is 238, we know that there must be 238 positive electrons in its nucleus. But since its atomic number, or the measured number of free unit charges upon its nucleus, is but 92, it is obvious that (238 - 92 = 146) of the 238 positive electrons in the nucleus must be neutralized by 146 negative electronswhich are also within that nucleus; and so, in general, the atomic weight minus the atomic number gives at once the number of negative electrons which are contained within the nucleus of any atom. That these negative electrons are actually there within the nucleus is independently demonstrated by the facts of radioactivity, for in the radioactive process we find negative electrons, so called-rays, actually being ejected from the nucleus. They can come from nowhere else, for the chemical properties of the radioactive atom are found to change with every such ejection of a-ray, and change in chemical character always means change in the free charge contained in the nucleus.

We have thus been able to look with the eyes of the mind, not only inside an atom, a body which becomes but a meter in diameter when looked at through an instrument of ten billion fold magnification, but also inside its nucleus, which, even with that magnification, is still a mere pin point, and to count within it just how many positive and how many negative electrons are there imprisoned, numbers reaching 238 and 146, respectively, in the case of the uranium atom. And let it be remembered, the dimensions of these atomic nuclei are aboutone-billionth of those of the smallest object which has ever been seen or can ever be seen and measured in a microscope. From these figures it will be obvious that, for practical purposes, we may neglect the dimensions of electrons altogether and consider them as mere point charges.

But what a fascinating picture of the ultimate structure of matter has been presented by this voyage to the land of the infinitely small! Only two ultimate entities have we been able to see there, namely, positive and negative electrons; alike in the magnitude of their charge but differing fundamentally in mass; the positive being eighteen hundred and forty-five times heavier than the negative; both being so vanishingly small that hundreds of them can somehow get inside a volume which is still a pin point after all dimensions have been swelled ten billion times: the ninety-two different elements of the world determined simply by the difference between the number of positives and negatives which have been somehow packed into the nucleus; all these elements transmutable, ideally at least, into one another by a simple change in this difference. Has nature a way of making these transmutations in her laboratories? She is doing it under our eyes in the radioactive process—a process which we have very recently found is not at all confined to the so-called radioactive elements but is possessed in very much more minute degree by many, if not all, of the elements. Does the process go on in both directions, heavier atoms being continually formed as well as continually disintegrating into lighter ones? Not on the earth so far as we can see. Perhaps in God’s laboratories, the stars. Some day we shall be finding out.

Can we on the earth artificially control the process? To a very slight degree we know already how to disintegrate artificially, but not as yet how to build up. As early as 1912, in the Ryerson Laboratory at Chicago, Dr. Winchester and I thought we had good evidence that we were knocking hydrogen out of aluminum and other metals by very powerful electrical dischargesin vacuo. There may be some doubt about the character of this evidence now. But, certainly, Rutherford has been doing just this for three years past by bombarding the nuclei of atoms with-rays. How much farther can we go in this artificial transmutation of the elements? This is one of the supremely interesting problems of modern physics to which there is as yet no answer.

VI. THE BOHR ATOM

Thus far nothing has been said as to whether the electrons within the atom are at rest or in motion, or, if they are in motion, as to the character of these motions. In the hydrogen atom, however, which contains, according to the foregoing evidence, but one positive and one negative electron, there is no known way of preventing the latter from falling into the positive nucleus unless centrifugal forces are called upon to balance attractions, as they do in the case of the earth and moon. Accordingly it seems to be necessary to assume that the negative electron is rotating in an orbit about the positive. But such a motion would normally be accompanied by a continuous radiation of energy of continuously increasing frequency as the electron, by virtue of its loss of energy, approached closer and closer to the nucleus. Yet experiment reveals no such behavior, for, so far as weknow, hydrogen does not radiate at all unless it is ionized, or has its negative electron knocked, or lifted, from its normal orbit to one of higher potential energy, and, when it does radiate, it gives rise, not to a continuous spectrum, as the foregoing picture would demand, but rather to a line spectrum in which the frequencies corresponding to the various lines are related to one another in the very significant way shown in the photograph ofFig. 24and represented by the so-called Balmer-Ritz equation,[151]which has the formIn this formularepresents frequency,a constant, and,for all the lines in the visible region, has the value 2, whiletakes for the successive lines the values 3, 4, 5, 6, etc. In the hydrogen series in the infra-red discovered by Paschen[152]andtakes the successive values 4, 5, 6, etc. It is since the development of the Bohr theory that Lyman[153]discovered his hydrogen series in the ultra-violet in whichand,etc. Since 1 is the smallest whole number, this series should correspond, as indicated heretofore, to the highest frequencies of which hydrogen is capable, the upper limit toward which these frequencies tend being reached whenand,that is, when.

i026Fig. 26—The original Bohr model of the hydrogen atom.

Fig. 26—The original Bohr model of the hydrogen atom.

Guided by all of these facts except the last, Niels Bohr, a young mathematical physicist of Copenhagen, in 1913 devised[154]an atomic model which has had some very remarkable successes. This model was originally designed to cover only the simplest possible case of one single electron revolving around a positive nucleus. In order to account for the large number of lines which the spectrum of such a system reveals (seeFig. 24), Bohr’s first assumption was that the electron may rotate about the nucleus in a whole series of different orbits, as shown inFig. 26, and that each of these orbits is governed by the well-known Newtonian law, which when mathematically stated takes the form:in whichis the change of the electron,that of the nucleus,the radius of the orbit,the orbital frequency, andthe mass of the electron. This is merely the assumption that the electron rotates in a circular orbit which is governed by the laws which are known, from the work on the scattering of thealpha particles, to hold inside as well as outside the atom. The radical element in it is that it permits the negative electron to maintain this orbit or to persist in this so-called “stationary state” without radiating energy even though this appears to conflict with ordinary electromagnetic theory. But, on the other hand, the facts of magnetism[155]and of optics, in addition to the successes of the Bohr theory which are to be detailed, appear at present to lend experimental justification to such an assumption.

Bohr’s second assumption is that radiation takes place only when an electron jumps from one to another of these orbits. Ifrepresents the energy of the electron in one orbit andthat in any other orbit, then it is clear from considerations of energy alone that when the electron passes from the one orbit to the other the amount of energy radiated must be;further, this radiated energy obviously must have some frequency,and, in view of the experimental work presented in the next chapter, Bohr placed it proportional to,and wrote:being the so-called Planck constant to be discussed later. It is to be emphasized that this assumption gives no physical picture of the way in which the radiation takes place. It merely states the energy relations which must be satisfied when it occurs. The red hydrogen lineis, according to Bohr, due to a jump from orbit 3 to orbit 2 (Fig. 26), the blue lineto a jump from 4to 2,to a jump from 5 to 2, etc.; while the Lyman ultra-violet lines correspond to a series of similar jumps into the inmost orbit 1 (seeFig. 26).

Bohr’s third assumption is that the various possible circular orbits are determined by assigning to each orbit a kinetic energysuch thatin whichis a whole number,the orbital frequency, andis again Planck’s constant. This value ofis assigned so as to make the series of frequencies agree with that actually observed, namely, that represented by the Balmer series of hydrogen.

It is to be noticed that, if circular electronic orbits exist at all, no one of these assumptions is arbitrary. Each of them is merely the statement of the existingexperimentalsituation. It is not surprising, therefore, that they predict the sequence of frequencies found in the hydrogen series. They have been purposely made to do so. But they have not been made with any reference whatever to the exact numerical values of these frequencies.

The evidence for the soundness of the conception of non-radiating electronic orbits is to be looked for, then, first, in the success of the constants involved, and, second, in the physical significance, if any, which attaches to the third assumption. If these constants come out right within the limits of experimental error, then the theory of non-radiating electronic orbits has been given the most crucial imaginable of tests, especially if these constants are accurately determinable.

What are the facts? The constant of the Balmer series in hydrogen, that is, the value ofin equation (34), is known with the great precision attained in all wave-length determinations and is equal to.From the Bohr theory it is given by the simplest algebra (Appendix G) asAs already indicated, in 1917 I redetermined[156]with an estimated accuracy of one part in 1,000 and obtained for it the value.As will be shown in the next chapter, I have also determinedphoto-electrically[157]with an error, in the case of sodium, of no more than one-half of 1 per cent, the value for sodium, upon which I got the most reliable data, being.The value found by Duane’s X-ray method,[158]which is thought to yield a result correct to one part in 700, is exceedingly close to mine, namely,.Substituting this in (38), we get with the aid of Bucherer’s value of(), which is probably correct to 0.1 per cent,,which agrees within a fourth of 1 per cent with the observed value. This agreement constitutes most extraordinary justification of the theory of non-radiating electronic orbits. It demonstrates that the behavior of the negative electron in the hydrogen atom is at least correctly described by theequationof a circular non-radiating orbit. If this equation can be obtained from some other physical condition than that of an actualorbit, it is obviously incumbent upon those who so hold to show what that condition is. Until this is done, it is justifiable to suppose that the equation of an orbit means an actual orbit.

Again, the radii of the stable orbits for hydrogen are easily found from Bohr’s assumptions to take the mathematical form (Appendix G)In other words, sinceis a whole number, the radii of these orbits bear the ratios 1, 4, 9, 16, 25. If normal hydrogen is assumed to be that in which the electron is in the inmost possible orbit, namely, that for which,the diameter of the normal hydrogenatom, comes out.The best determination for the diameter of the hydrogenmoleculeyieldsin extraordinarily close agreement with the prediction from Bohr’s theory.

Further, the fact that normal hydrogen does not absorb at all the Balmer series lines which it emits is beautifully explained by the foregoing theory, since, according to it, normal hydrogen has no electrons in the orbits corresponding to the lines of the Balmer series. Again, the fact thathydrogen emits its characteristic radiations only when it is ionized or excitedfavors the theory that the process of emission is a process of settling down to a normal condition through a series of possible intermediate states, and is therefore in line with the view that a change in orbit is necessary to the act of radiation.

Another triumph of the theory is that the third assumption, devised to fit a purely empirical situation, viz., the observed relations between the frequencies of the Balmer series, is found to have a very simple and illuminating physical meaning and one which has to do withorbitalmotion. It is that all the possible values of theangular momentumof the electron rotating about the positive nucleus are exact multiples of a particular value of this angular momentum. Angular momentum then has the property ofatomicity. Such relationships do not in general drop out ofempiricalformulae. When they do, we usually see in them real interpretations of the formulae—not merely coincidences.

Again, the success of a theory is often tested as much by its adaptability to the explanation of deviations from the behavior predicted by its most elementary form as by the exactness of the fit between calculated and observed results. The theory of electronic orbits has had remarkable successes of this sort. Thus it predicts the Moseley law (33). But this law, discovered afterward, was found inexact, and it should be inexact when there is more than one electron in the atom, as is the case save foratoms and for such He atoms as have lost one negative charge, and that because of the way in which the electrons influence one another’s fields. By taking account of these influences, the inexactnesses in Moseley’s law have been very satisfactorily explained.

Another very beautiful quantitative argument for the correctness of Bohr’s orbital conception comes from the prediction of a slight difference between the positions in the spectrum of two sets of lines, one due to ionized helium and the other to hydrogen. These two sets oflines, since they are both due to a single electron rotating about a simple nucleus, ought to be exactly coincident, i.e., they ought to be one and the same set of lines,if it were not for the fact that the helium nucleus is four times as heavy as the hydrogen nucleus.

To see the difference that this causes it is only necessary to reflect that, when an electron revolves about a hydrogen nucleus, the real thing that happens is that the two bodies revolve about their common center of gravity. But since the nucleus is two thousand times heavier than the electron, this center is exceedingly close to the hydrogen nucleus.

When, now, the hydrogen nucleus is replaced by that of helium, which is four times as heavy, the common center of gravity is still closer to the nucleus, so that the helium-nucleus describes a much smaller circle than did that of hydrogen. This situation is responsible for a slight but accurately predictable difference in the energies of the two orbits, which should cause the spectral lines produced by electron-jumps to these two different orbits to be slightly displaced from one another.

This predicted slight displacement between the hydrogen and helium lines is not only found experimentally, but the most refined and exact of recent measurements has shown thatthe observed displacement agrees with the predicted value to within a small fraction of 1 per cent.

This not only constitutes excellent evidence for the orbit theory, but it seems to be irreconcilable with a ring-electron theory once favored by some authors, since it requires the mass of the electron to be concentrated at a point.

The next amazing success of the orbit theory came when Sommerfeld[159]showed that the “quantum” principle underlying the Bohr theory ought to demand two different hydrogen orbits corresponding to the second quantum state—second orbit from the nucleus—one a circle and one an ellipse. And by applying the relativity theory to the change in mass of the electron with its change in speed as it moves through the different portions (perihelion and aphelion) of its orbit, he showed that the circular and elliptical orbits should have slightly different energies, and consequently that both the hydrogen and the helium lines corresponding to the second quantum state should be close doublets.

Now not only is this found to be the fact, but the measured separation of these two doublet lines agrees precisely with the predicted value, so that this again constitutes extraordinary evidence for the validity of the orbit-conceptions underlying the computation.

InFig. 27the two orbits which are here in question are those which are labeledand;the large numeral denoting the total quantum number, and the subscript the auxiliary, orazimuthal, quantum number which determines the ellipticity of the orbit. The figure is introduced to show the types of stationary orbits which the extended Bohr theory permits. For total quantum number 1 there is but one possible orbit, a circle. For total quantum numbers 2, 3, 4, etc., there are 2, 3, 4, etc., possible orbits, respectively. The ratio of the auxiliary to the total quantum number gives the ratio of the minor and major axes of the ellipse. The fourth quantum state, for example,has four orbits,,,,,all of which have the same major axis, but minor axes which increase in the ratios 1, 2, 3, 4 up to equality, in the circle (), with the major axis. It is this multiplicity of orbits which predicts with beautiful accuracy the “fine-structure” of all of the lines due to atomic hydrogen and to helium.

i027Fig. 27—Bohr-Sommerfeld model of the hydrogen atom with stationary orbits corresponding to principal quantum numbers and auxiliary or azimuthal quantum numbers.

Fig. 27—Bohr-Sommerfeld model of the hydrogen atom with stationary orbits corresponding to principal quantum numbers and auxiliary or azimuthal quantum numbers.

The next quantitative success of the Bohr theory came when Epstein,[160]of the California Institute, applied his amazing grasp of orbit theory to the exceedingly difficult problem of computing the perturbations in electron orbits, and hence the change in energy of each, due to exciting hydrogen and helium atoms to radiate in an electrostatic field. He thus predicted the whole complex character of what we call the “Stark effect,” showing just how many new lineswere to be expected and where each one should fall, and thenthe spectroscope yielded, in practically every detail, precisely the result which the Epstein theory demanded.

Another quantitative success of the orbit theory is one which Mr. I. S. Bowen and the author,[161]at the California Institute, have just brought to light. Through creating what we call “hot sparks” in extreme vacuum we have succeeded in stripping in succession, 1, 2, 3, 4, 5, and 6 of the valence, or outer, electrons from the atoms studied. In going from lithium, through beryllium, boron and carbon to nitrogen, we have thus been able to work with stripped atoms of all these substances.

Now these stripped atoms constitute structures which are all exactly alike save that the fields in which the single electron is radiating as it returns toward the nucleus increase in the ratios 1, 2, 3, 4, 5, as we go from stripped lithium to stripped nitrogen.We have applied the relativity-doublet formula, which, as indicated above, Sommerfeld had developed for the simple nucleus-electron system found in hydrogen and ionized helium, and have found that it not only predicts everywhere the observed doublet-separation of the doublet-lines produced by all these stripped atoms, but that it enables us to compute how many electrons are in the inmost, orshell, screening the nucleus from the radiating electron. This number comes out just 2, as we know from radioactive and other data that it should. (See inset photograph,Fig. 37, followingFig. 36, oppositep. 260.)

Further, when we examine the spectra due to the stripped atoms of the group of elements from sodium to sulphur, one electron having beenknocked off from sodium, two from magnesium, three from aluminum, four from silicon, five from phosphorus, and six from sulphur, we ought to find that the number of screening electrons in the two inmost shells combined is,and it does come out 10, precisely as predicted, and all this through the simple application of the principle of change of mass with speed in elliptical electronic orbits of the type shown inFig. 27.

The physicist has thus piled Ossa upon Pelion in his quantitative proof of the existence of electronic orbits within atoms. About theshapesof these orbits he has some little information (Fig. 27) but about theirorientationshe is as yet pretty largely in the dark. The diagrams[162]on the accompanying pages, Figs.28,29, and31, represent hypothetical conceptions, due primarily to Bohr, of the electronic orbits in a group of atoms. Since, however, these orbits are some sort of space configurations, the accompanying plane diagrams are merely schematic. They may be studied in connection withFig. 27,Table XV, and Bohr’s diagram[163]of the periodic system of the elements shown inFig. 30. These contain the most essential additions which Bohr made in 1922 and 1923 to the simple theory developed in 1913.

The most characteristic feature of these additions is the conception of the penetration, in the case of the less simple atoms, of electrons in highly elliptical orbits into the region inside the shells of lower quantum number.

i028Fig. 28—Hypothetical atomic structures

Fig. 28—Hypothetical atomic structures

This gives, so Bohr believes, these penetrating electron-orbits in some cases a smaller mean potential energy, and therefore a higher stability, than some of the orbits corresponding to the smaller quantum numbers.

A glance at the group of elements beginning with argon, the last element in shell 3, in bothTable XVandFig. 30, will make clear the meaning of this statement. The fourth column ofTable XVshows that Bohr assigns to argon four very elliptical orbits of shapeand four of shape.Glancing down the same column to copper, or lower, one sees that there are eighteen possible third-shell orbits, namely, six of shapesix of shape,and six of shape,i.e., there are in the third shell in argon ten unfilled orbits. But when a new electron is added, as we pass from argon to potassium, it goes, according to Bohr, into theorbit, thus giving potassium univalent properties like lithium and sodium (seeFig. 28). Similarly, calcium is shown inTable XVas taking its two extra electrons into itsorbits. But as now the nuclear charge gets stronger and stronger with increasing atomic number, the empty third-shell orbits gain in stability over the fourth-shell ones, and a stage of reconstruction sets in with scandium (Fig. 30) and continues down to copper, all the added electrons now goinginsideto fill the ten empty orbits in the third shell, with the result that the chemical properties, which depend on the outer or valence electrons, do not change much while this is going on. With copper (seeTable XV) the eighteen third-shell orbits are completely filled and one electron is in theorbit (see alsoFig. 29), and from there down to krypton the chemical properties progress normally much as they do from Mg to Ar.

Back to Index Next