T H E O R I G I S OF T H E CHEAIICAL ELEMEXTS BY S. BRADFORD STONE
I. Introduction A recent improvement in the design of the mass spectrograph has enabled Aston to determine the atomic weights of several individual physical atoms t o within one or two parts in ten thousand.’ The new values are accurate enough to be used as criteria for estimating the possibility of hypothetical transformations, or decompositions, of the various atomic species. This can be done by means of the relation between mass and energy given by the special theory of relativity. The energy involved in even a small change of mass is of such greater magnitude than the usual types of energy changes considered in thermodynamics, that the criterion for an atomic transformation reduces to the condition that the mass of the resultants must be less than the mass of the reactants. An illustration of the above reasoning has been given for the radioactive decomposition of thorium.? The difference per gram atom between the weight of the thorium atom, and the combined weights of the decomposed thorium atom and the expelled alpha particle can be estimated from Aston’s curves as 0.0068 grams. If this energy is transferred entirely to the alpha particles, then each particle carries a kinetic energy of 1 . 0 1 X 10-j ergs, a value approximately equal to those involved in radioactive transformations. The application of Einstein’s equation to Aston’s data therefore predicts, to well within the experimental error, the maximum available energy of radioactive decomposition. Another deduction is that, in general, only the healier atoms can undergo spontaneous alpha particle decomposition. For the lighter atoms such changes involw an increase in mass and are therefore forbidden. The explanation of the origin of the cosmic rays given by Millikan and Cameron assumes that atoms are being formed in interstellar space through the union of hydrogen particles. For convenience this hypothesis will be designated as the hydrogen system. One point in connection with this system which has never been stated explicitly, is that it offers a reasonable account of the hithertofore anomalous position of the radioactive elements. Previous theories of the evolution of the elements have failed to explain how an atom which is unstable with respect to atoms of Iower weight can be formed by the union of such lighter atoms. Thermodynamic considerations offer two possible explanations. One is that these elements are created in a thermodynamic environment where they have less tendency to decompose. This limits the possible sites of formation either to interstellar space, with its low temperatures; or to stellar interiors. The second possibility is that these elements are of the nature of intermediate products. This follows directly I F . IT. Aston: Proc. Roy. Sac., 115, A, 487 (1927); J. L. Costa: Ann. Physique, 4, 425 (1925).
R. A. Millikan and G. H. Cameron: Phys. Rev. ( z ) , 32, 537 (1928).
S. BRADFORD STONE
822
from the hydrogen system. The formation of a radioactive atom from hydrogen is accompanied by a decrease in mass. Dissociation into lighter atoms also results in a decrease in mass. Both the formation and the dissociation are thermodynamically possible. The same explanation of the synthesis of the radioactive elements applies to the kinetic hypothesis of atomic formation which will be presented later.
A Possible Test of the Theory of Relativity It has been shown that an improved accuracy in mass spectra measurements would permit a new test of the theory of relativity. I n the change’ from R a A to Ra G there is a decrease in mass due to the liberation of five alpha particles, and of four electrons. There should also be a further decrease equal to the mass equivalent of the liberated energy. Chemical data cannot be used because of the possibility of contamination by isotopes. Mass spectra examination of the radioactive elements is subject to several difficulties. If these can be overcome, then the new measurements are sufficiently accurate to yield direct evidence on this question.
An Equation for the Atomic Weights It has been stated that the mass defect D is proportional to the atomic weight A, if both D and A are calculated*on the basis of hydrogen equal to unity. This equation is of no use for estimating an unknown atomic weight, since it can be shown to be a restatement of the conclusion that the physical atomic weights are whole numbers if oxygen is taken as 16.000. For all but a few of the lighter atoms this is true to within less than one part inonethousand. Starting with the assumption that P =w where P i s the protonic number, and W is the atomic weight on the usual basis. P - W/I.ooid = o.OoidW/L. 1.0078 P - A = 0.0077 h o r D = 0.0077 A Using Strumm’s data the average value of his constant of proportionality is 0.0078, which is identical with the value calculated on the assumption that the atomic weights are whole numbers on an oxygen basis. The equation 1s therefore merely a restatement of this fact.
Objections to a Hydrogen System The assumption that iron is formed by the union of protons (or neutrons) requires that 56 such particles meet in the minute volume of an atomic nucleus, and then release their energy of union in a single quantum jump. Since iron is an abundant element this reaction would have to be of frequent occurrence. Any hesitancy concerning such a n hypothesis becomes still greater for the heavier atoms where it is necessary to postulate the union of more than two hundred particles. Probability considerations do not favor ‘King: Sature, 109, 582
(1922). (1928).
* Strumm: Z. Physik, 50, 555
ORIGIN OF THE CHEMICAL ELEMENTS
523
a hydrogen system. If there is a certain possibility of the union of four protons (neutrons) to form helium, then the possibility of the union of fiftysix such particles to form iron would appear to be an infinitesimal of a very high order, The hydrogen system would seem to require that atomic abundance should decrease very rapidly with increasing atomic weight, and that atoms as heavy as iron should have nearly zero abundance.
11. The Helium, Hydrogen System In view of the objections to a hydrogen system it would be of interest to determine to what extent the same facts can be interpreted on the assumption that the formation of at,oms occurs through the combination of helium and hydrogen nuclei. This hypothesis has the advantage of reducing sharply the number of unit,s concerned. For the more abundant atoms the number of reacting particles is only one fourth of the number necessary on the hydrogen system. A better reason for the adoption of a helium, hydrogen system lies in the fact that such a hypothesis is supported by evidence from several different chemical and physical sources. A complete discussion of this subject can be found in the works of Harkins.‘ The evidence can be summarized as follows: a) The most abundant atoms in the earth’s surface, and in meteorites have nuclei which can be represented as composed solely of alpha particles. For these atoms the number of protons in the nucleus is divisible by four, and the number of nuclear electrons is one half that of the number of protons; that is the ratio of nuclear electrons to protons is the same as that of the alpha particle. Such atoms compose 76.j7C of the atoms in the crust of the of those in meteorites. earth, and 91.77~ b) Alpha particles are expelled in radioactive decomposition. c) Hydrogen atoms are released in alpha particle impacts on atoiiiic nuclei. Atoms whose atomic weights are multiples of four are most stable towards a hydrogen decomposition. d) The alpha particle can attach itself directly to an atomic nucleus.? A neF type of evidence may result from the development of the wave mechanics. When this theory is applied to band spectral data, it is found that helium shows no nuclear spin. The same is true of 0l6,which agrees with the hypothesis that the oxygen nucleus is composed of four alpha particles. Both hydrogen, nitrogen, and fluorine have nuclear spins, in agreement with the supposition that the nitrogen and fluorine nuclei contain protons.8 Basic Assumptions of the Kinetic Hypothesis I t is intended to show that certain assumptions concerning the mechanism of atomic formation lead to a helium, hydrogen system of the various atomic species, and that such a system is ablet o set a upper limit to the atomic weight. I) W. D. Harkins: Chem. Rev., 4, 393 (1928)an excellent summary of Harkins’ theory.
* Blackett: Proc. Roy. SOC., 107A
349 (1925).
IT.Heisenberg: Z. Physik, 38,4;1 (1926); 41, 26 (1927); H.G.Gale and G. 9. Monk: rlstrophys. J., 69,77 (1929).
824
S. BRADFORD STONE
to account for thc known facts regarding atomic abundance. to interpret the cosmic radiation. The following assumpt,ions will be set forth explicitly as being fundamental to the new system. a) In those portions of space where atomic format,ion takes place, hydrogen is by far the most abundant element. b) Helium is formed directly from hydrogen and ranks second in abundance. These two statements apply only to the site of atomic synthesis. I n stars, nebulae, or planets the abundance of helium and hydrogen is less because of their consumption in the formation of the other elements. Assumptions a) and b) are supported by spectroscopic evidence which indicates the abundance,-possibly even in excessive amounts, of both hydrogen and helium in all stars.' For all reactions leading to the formation of atoms, the following assumptions will be made: c) The most important factor in the abundance of any reaction is the kinetic factor. Reactions involving a large number of particles will in general be less probable than those involving a smaller number. d) Any reaction can occur if there is a decrease in mass. Reactions in which the mass increases can not take place. e) Reactions between similar nuclei are more probable than those between different nuclei. Of these postulates c) and d) are a priori reasonable, while e) is purely an assumption, and can only be justified if it leads to correct results. It will be shown later that this assumption (e) follows directly from a certain hypothesis concerning the nature of atomic synthesis. The above assumptions do not limit the possible reactions to the union of hydrogen and helium nuclei. Changes such as 2)
3)
2
Si28
Fe56
are accompanied by a decrease in mass and are theoretically possible. Although such reactions are not prohibited, they would, because of the relative scarcity of the reacting atoms be expected to be of less frequent occurrence. It has been postulated that hydrogen is by far the most abundant element; and also that the kinetic factor or the number of reacting units determines the abundance of a reaction. Transformations involving only hydrogen nuclei should therefore be of more frequent occurrence than reactions involving the same number of helium nuclei. The formation of Fej6 from helirim requires the union of sixteen helium particles. I n view of the greater abundance of hydrogen, the reaction 16H
=
0
sh ,uld be of more frequent occurrence, and a certain portion of the known oxygen atons should have been formed in this manner. For the same reason the synthesis j6 H = Fej6 would be expected to create a number of iron atoms greater than the initial C. H. Payne: "Stellar Atmospheres", 188.
ORIGIS OF T H E CHEMICAL ELEMEXTS
825
riuriiber of U2" (61 reacting units). Since both uranium, and its decomposition products have only a vanishingly low abundance; the number of iron atoms thus formed would be expected to be small.
The Kinetic Hypothesis We have been led to the following view of the nature of atom formation. All reactions associated with a decrease of mass can take place. The most important are the union of hydrogen nuclei alone, or of helium nuclei alone. The union of n hydrogen nuclei is more probable than the union of the same number of helium particles. Keactions involving a mixture of helium and hydrogen units can take place in more than one manner, i.e., Na23 can be formed by j He 3 H = Ka23 4 He 7 H = KaZ3
+ +
or by similar changes. Syntheses involving heavier nuclei are not common because of the lower abundance of the reactants. The new system is therefore to be regarded as a kinetic hypothesis in which all possible types of collisions and reactions can occur. The abundance of any atomic species will depend partly on the nature of the reactions leading to its formation, Le., the number and type of reacting units; and partly on specific conditions connected with the reaction itself, and with the stability of the reaction products. It will be convenient to give to this system the name kinetic hypothesis, which also serves to distinguish it from the helium, hydrogen system of Harkins. The following nomenclature will be used. A reaction in which only H (He) units are concerned will be called :I. hydrogen (helium) reaction. When a mixture of helium and hydrogen units are concerned, the reaction will be called a mixed reaction. The requirement of alternative processes for the formation of any one atom raises the interesting speculative possibility of differences between individual atoms. I n terms of the wave mechanics it might be expected that an atom formed from hydrogen alone would have a nuclear spin, while the same atom formed by a helium reaction would have zero spin. Another possibility is that alternative methods of formation might produce atoms of slightly different weights. This would mean that the individual mass spectra lines have a fine structure This possibility might be tested by examining single lines under the greatest attainable dispersion. Calculation of Mass Decrease Berore proceeding, an example will be given of the calculation of the decrease in mass attending the formation of an atom by a mixed reaction. From Aston's measurements we have C P = 34.9830 H = 1.00778 He = 4.00216
826
S. BRADFORD
STOSE
If C P is composed of 8 He and 3 H nuclei then its calculated weight is 8 X 4.00216 -I-3 X 1.007;8 = 35.0407 The decrease in mass due to the mixed reaction is equal to 34.9830 - 35.0407 = For convenience this d l be multiplied by
-0.Oj77
1 0 4 and
designated as A m ,
The Upper Limit of Atomic Weight I n Fig. I the value of A m has been plotted against P, the number of protons in the nucleus. The data is divided into four groups for which P can be represented by the equations.
P=4K+N
(N
= 0,1,2,3)
I u
9 K t l
A 4Kt2
K , 4Ktl - - _ _44_ - _ 4KK ttZ3
100
Protonic Number
f‘
FIG.I
It will be seen that the absolute value of A m goes through a maximum with increase of P, and for each group falls to zero a t a value of P greater than 238. The kinetic hypothesis therefore sets a practical upper limit to the complexity of atomic nuclei. For the heaviest known atom U*38 the value of A m is - 520, so that the theory provides for the formation of all known atoms. The probable errors in hston’s data for the heavier atoms range from 0.02 to 0.04 units of atomic weight. Only by making the most unfavorable assumptions
ORIGIN OF T H E CHEMICAL ELEMESTS
827
concerning the possible errors can the maximum be reduced below 238. The possibility of hydrogen reactions for the formation of the heavier atoms does not lead to any modification of these ideas. Such reactions are theoretically possible since they are accompanied by large decreases in mass. However if is an infrequent event, then the union the union of 61 particles to form UZ3* of more than 238 hydrogen nuclei to form an atom heavier than uranium should be of an infinitely lower order of frequency. The kinetic hypothesis does not set an absolute limit to the atomic weight, but it does establish a practical upper limit; in that no atom of weight greater than about 340 can be formed by a helium reaction, while the possibility of the union more than 238 hydrogen particles is infinitely small.
The Abundance of the Various Atomic Species Before applying the kinetic hypothesis to the question of atomic abundance, an attempt will be made to show that accepted facts and theories indicate that the composition of the earth’s crust can be regarded as representative of that of all known matter, and that a t least any general conclusion based on this data can be regarded as essentially correct. Knowledge of atomic abundance comes from only three sources: spectral data for stars and nebulae, and chemical analyses of the earth’s crust, and of meteorites. The enormous extent of the various nebulae indicate a relatively high extent for their constituent elements, of which the most abundant are H, He, 0, K, and C (weak). The hypothetical element nebulium has been shown to be due to N and 0. It will be noticed that all these atoms are of low atomic weight. Stellar spectra are divided into several classes. The approximate uniformity within any given class shows a t least a corresponding uniformity of surface composition. This may correspond to a similarity of internal composition since any pronounced internal differences would, because of effects due to radiation pressure, be expected to produce observable differences in some stars. The differences between the various classes of stellar spectra are interpreted as due primarily to changes in surface temperatures, and not to any variation in chemical constitution.’ The uniformity of composition may extend further than the surface of the stars, for Eddington has pointed out that the theorem of H. van Zeipel indicates the existence of both surface and internal convection currents flowing along the stellar meridians. These currents should be effective in producing a somewhat uniform composition of the entire star.* The six most abundant elements in the stars as estimated by the method of Fowler and Milne3 are Si, Ka, Mg, AI, Ca, and Fe respectively. The same metals in the order Si, Al, Na, Fe, Ca, and rvlg make up the six most abundant metals in the crust of the earth. The metals are chosen for comparison bel C. H. Payne. “Stellar Atmospheres”; J. 11. Jeans. “Astronomy and Cosmogony”, (1928). A. S. Eddington. hI. S . R. A . S., 88, 73 (Ipj); H. van Zeipel: 84, 665; Rosseland: 89,49 (1928). C. H. P a p e : “Stellar Atmospheres.”
22
828
S.
BRADFORD STONE
cause of their better spectral lines. A list of the fourteen most abundant elements in the stars shows thirteen of the fourteen most abundant in the earth. The only discrepancy is in the case of zinc which is more abundant in the stars than in the eart’h. Every element listed by Payne as possibly missing in stellar spectra has an abundance in the earth of less than 0.01 atomic percent. Stellar spectra do not show any elements which are unknown to the earth. Knowledge of the composition of the earth is limited to the first few miles of the crust. Because of the difference in density between the outer crust and the earth as a whole (2.7 and j.j), it is often assumed that the heavier metals constitute a large portion of the earth’s interior. There is no good evidence that bears on this question. The estimated temperature and pressure a t the center of the earth are 16,6oo0C and 2,800,000atmospheres, and lie far outside the range of experimental knowledge.’ The heaviest elements however appear to be less abundant in the earth’s interior. The average fraction of radium igneous rocks, a type which constitutes 9j% of the lithosphere, is 1.7 X 10-l~.This is twenty-eight times the amount necessary to account for the measured temperature gradient of the earth.2 Data on the composition of meteorites when averaged to take account of the relative number of stone and iron meteorites show much the same results as found for the earth’s crust.3 The only differences consist in larger amounts of Ni, Fe, and Co in t,he meteorites. The elements Ni, and C1 have been found to show the same isotopic composition in the meteorites as in the terrestrial element^.^ These various types of evidence all support the statement that the earth’s outer crust has in general much the same chemical nature as the meteorites, and the outer layers of the stars; and in addition indicate the possibility that the resemblances may extend below the surfaces of the stars, and that the composition of the earth may be representative of that of all known matter. Any general conclusions concerning the earth’s crust should therefore furnish valuable material for speculations concerning the formation of the elements. The most important of such relationships is that of the concentration of matter into the lighter elements as shown in Table 1.j
TABLE I Atomic number I8 9- 16 17-24
Atomic percent age in the earth’s crust
25-32
67.11 27.88 3.30 1.74
33-92
0.03
.4tomic number
Atomic percentage in the earth’s crust
1-16
95.93 5.04
I
- 16
33 - 9 2
0.03
Lunn: “Tidal and other Problems”, 201 (1909). F. W.Clarke: “Data of Geochemistry”, Bull. 491,L-. S. Geol. Survey, p. 301. 8 W.D.Harkins: Phil. Mag., 42, 305 (1921). 4 W.D.Harkins and S. B. Stone: J. Am. Chem. SOC.,48,938,(1926). 6 W.D. Harkins: Chem. Rev., 4,393 (1928). 1 9
ORIGIN OF THE CHEMICAL ELEMENTS
829
It will be seen that there is an excessive concentration of matter in the lighter atoms. This is t o be expected from the kinetic hypothesis, since the most common atomic syntheses would be those involving small numbers of reacting units. The elements show a striking preference for species whose protonic number can be represented by 4 K , where K is an integer. (See Table 11).
TABLE I1 Atomic Abundance Atom 0'6
Sizs Si29
4K 57.44 16.48
4K
I
4Ii
2
4K
3
1.75
~ 1 2 7
5.55
NaZ3 Fe% Fej6 Ca4O CaM Mg24 Mg'Z Mg'6 K39
2 .27
0.13 I 4 5 1.55 0.13
I .22
0.19 0.18
1.16 0.06
K4I
Ti4* C Totals
0.27
0.15
-
-
-
-
78.79
2
.oo
0.31
8.98
If hydrogen with its abundance of 9.48 is excluded, the above totals would be 87.04, 2 . 2 2 , 0.34, and 9.92, a total of 99.5270. The overwhelming concentration of matter in the 4 K type atoms finds an obvious explanation in terms of the kinetic hypothesis. Of the 4 K type atoms, OI6, Siz8,Ca4O, MgZ4, and C1* have a ratio of nuclear electrons to protons equal to 0.500,the same value as that of the alpha particle. These atoms make up 76.48% of the total atoms of the earth's crust, or excluding hydrogen, 84.894,. Such facts again find an obvious explanation in the kinetic hypothesis. The more important general relationships concerning the abundance of the various chemical elements therefore indicate that the alpha particle plays an important role in the act of atomic synthesis, and that kinetic factors hinder the formation of the heavier atoms. Missing Atomic Species The atoms of protonic numbers five and eight are unknown. Harkins' rules for nuclear stability show that the species Z5 should be either rare or else unknown. The missing species Z8 can only be assigned the formulae GP,
830
S. BRADFORD STOSE
which places it in the same class as all the abundant light elements. It is therefore interesting to note that this atom cannot be formed by the union of two helium particles. This is best shown by consideration of the original data of Aston. Table I11 gives the mass defect for several of the nearby atomic species TABLE 111 Atom
He Lie Li7
Mass defect, or the deviation from a whole number (multiplied by 104) 21.6
Possible error in value of mass defect
I20
1 4 *I8
I20
*I8
€3’0
I35
*I5
B”
IIO
*I7
For the hypothetical species the mass defect would appear to lie close to 1 2 j . The reaction 2 He = G1* therefore calls for a value of A m equal to 1 2j 2 X 21.6 or 82. and the reaction is a thermodynamic impossibility. 111. Penetrating Radiation The existence of penetrating radiation of higher frequency than the hardest gamma rays was first discovered’ in 1903. These rays enter the earth’s atmosphere with equal or very nearly equal intensity in all directions. The intensity shows little variation with time, and depends primarily on the amount of absorbing material through which the rays have passed. The site of origin2 appears to be the depths of intersteller space. Of the many measiirements on the radiation those of Nillikan, Cameron, and Bowers are not only the most extensive but also appear to possess a higher accuracy. These measurements will therefore be used as the basis of all further discussion The rays have been resolved into three bands for which the mass absorption coefficients are 0.35, 0.08,and 0.04 meters of water. By the use of Dirac’s equation (based on the new quantum mechanics) it is possible to calculate the wave length corresponding to any given absorption coefficient. The quantum relation, E = hL, can then be used to determine the change in energy which produced the r a d i a t i ~ n . ~The most plausible hypothesis for the formation of the rays ascribes them to the formation of heavier atoms from hydrogen. The change in frequency accompanying an atomic synthesis is assumed to appear as light energy according to the fundamental quantum relation. The necessary transformations are the syntheses of He, 0, Si, and Fe by the union of the requisite number of protons. The different bands are not due solely to these changes but include other reactions which release approximately the same amounts of energy. (See Table IV) l1IcLennan and Burron: Phys. Rev., ( 2 ) 16, 184; Rutherford and Cook: 183 (1903). hlillikan and Cameron: Phvs. Rev., ( 2 ) 31, 169 (1928). For evidence of slight directional effects see Kohlhorster: “Sitzungsber. preuss. Akad., 34, 169 (1913); Buttner: Z. Geophysik, 21, 87, 291 (1926); Corin: 2. Physik, 50, 808 (1928). P. Dirac: Proc. Roy. Poc., 111A, 423 (1916).
ORIGIN O F THE CHEMICAL ELEMENTS
83 1
The creation of heavier atoms from hydrogen is supposed to be favored by the conditions of low temperature and low pressure existing in interstellar space. It is supposed that the union of large numbers of particles may take place through the clustering of several hydrogen particles into larger aggregates which release the energy of union in a single quantum jump. The above hypothesis of the origin of the rays accounts satisfactorily for the shape of the ionization-depth-curve. The interpretation of the cosmic rays on the hydrogen system is given in Table I V
TABLE IV Summary of the hIillikan, Cameron hypothesis of the Cosmic Radiation. Reaction
4He
=
Am
He -290
4He = 0 7He = Si 2Si = Fe = Fe 4N
-
0.30
0.35
Abundant and determines the character of the band. A possible reaction. A possible reaction. Not shown by balloon tests. Kot shown by balloon tests.
0.08
Abundant and determines the nature of the band. Abundant and determines the nature of the band. Would merely broaden band on long wave side. If present would appear as a small addition to the carbon band.
86
-290
-168 -j60
0
-124j
0.074
I ~ H= N
-1080
0.086
16H
12H
=
=
C
14He = Fe
28H
56H
=
Remarks
absorption coefficient calculated observed
-933
-750
Si
-2320
0.041
0.04
X1, Si, and Mg formed by hydrogen reactions would appear in this band. Ca, and K formed in the same manner would broaden the band on the short wave side.
Fe
-4800
0.019
-
Kot detected by experiments, but assumptions of the existence of this band improves the fit of the calculated ionization - d e p t h curve.
Some Fundamental Objections to the Hydrogen System It is claimed that the penetrating radiation consists of high-speed corpuscles.: This conclusion, if accepted, does not necessarily dispose of the
’ K. Bothe and W. Kohlhorster:
Sature, 123, 638 (1929).
832
S . BRADFORD STOKE
Millikan-Cameron hypothesis, for this hypothesis deals with the energy changes involved in the creation of the rays, and not with the manner in which the released energy makes its appearance. A more important and fundamental objection lies in the use of the Dirac scattering formula. Data on the scattering of gamma rays are in better agreement with the equation of Klein and Nishina.' This equation requires that a given absorption coefficient, (p),be associated with a larger change in energy than is calculated by the Dirac formula. As an example a value of p equal to 0.04 meters of water is due to an energy change of 920 X IO^ electron-volts, or very nearly the energy released in the annihilation of a proton. For the Dirac formula the same value of p corresponds to only z 14X 106electron-volts. The Millikan-Cameron hypothesis would be eliminated if the new equation is accepted. The validity of the Klein-Nishina equation in the gamma ray region does not mean that it necessarily applies t o the much harder cosmic rays. With radiation of such high frequency the nucleus may take part in the scattering. There are indications of such an effect even in the X-ray region.* If the nuclear electrons are effective in scattering then the KleinNishina equation would for the cosmic rays approach towards that of Dirac. The Dirac equation will therefore be used, because its use permits an interpretation of the cosmic rays consistent with the evidence from other sources.
Other Objections to a Hydrogen System It will be noted that the iron band was not experimentally detected. It is reasonable however to assume its existence. Such an assumption results in a better fit between the calculated and observed ionization-depth curve. The helium band is softer than the calculated value. The calculated absorption coefficient is 0.30, while the observed is 0.35. On the hydrogen system there are no apparent reactions to furnish the soft radiations necessary to account for this difference. The formation of oxygen by a helium reaction was suggested as a possibility. A minor objection is that through a mathematical error the relative number of quanta in the 0, Si, and Fe bands are not in the ration of 55::26::7, (the ratio of the relative abundance of these atoms) but are in the ratio of 55::37.4::16.4 (see following section).
The Cosmic Rays and the Kinetic Hypothesis The explanation of the cosmic rays given by the kinetic hypothesis is based directly on the fundamental postulates of this system, and avoids the objections raised against the hydrogen system. Because of the assumed excessive abundance of hydrogen, the new interpretation is in its essentials the same as that of Millikan and Cameron. The Helium Band On the kinetic hypothesis this band is due to the formation of several of the lighter and more abundant elements. The reactions are tabulated in Table V. 0. Klein and Y. Nishina: Nature, 122, 398 (1928); Gray: Proc.Roy. Soc., 122A,647 (1929).
B. Davis and H. Purks: Phys. Rev.,
(2)
34, I (1929).
ORIGIN O F THE CHEMICAL ELEMESTS
833
TABLE V Reaction
Am
4H =He 3 He
+
2
4He = o
H
= S
Reaction
+
Am
- 290
6 He n He = Mg n = 0, I , 2
-(zoo
- 141
7 H e + n H = Si n=o,r
-(285t03Ij)
-
to
290)
86
The abundance of helium radiation determines the character of the band, and leads to essentially the same explanation as given by the hydrogen system. The chief difference consists in the greater prominence assigned to the reaction 4He = 0 This reaction is necessarily a common transformation, and the softer radiation thus produced is largely responsible for the difference between the observed and calculated absorption coefficients. The effect of the nitrogen rays is that of softening the harder helium rays. Rays due to MgZ6would slightly soften the band, while the other isotopes of h1g and Si give radiation nearly identical with that of the helium rays.
The Oxygen Band Mixed reactions yielding the necessary decrease in mass are the formation of atoms lying between Zn and Pb. ( A m = -900 to - 1200). There is no evidence to indicate more than a low abundance for these elements. The sum total of their radiations would be outweighted by the formation of Fej6 with A m equal to - 7 jo, and the composite band would be softer than that observed. The number of particles involved in the above mentioned mixed reactions range from sixteen to twenty two. The assumption that hydrogen is by far the most common element leads to the expectation that the union of fourteen to sixteen hydrogen nuclei will be far more common than the union of sixteen to twenty two helium nuclei. The new interpretation therefore ascribes this band chiefly t o the reactions 16H=O 14H = K In addition mixed reactions such as 3 He 11 H = Na23 will make a portion of the band.
+
The Silicon Band These rays are explained in nearly the same manner as on the hydrogen system. The most important reaction is 2 8 H = Si A m = -2190 The formation of A,and M g by hydrogen reactions yield radiation of nearly the same hardness. The kinetic hypothesis also ascribes a portion of the band to mixed reactions such as 9He ZOH= Fej6 A m = -2190
+
834
S. BRADFORD STONE
The Iron Band This band for which A m is - d o 0 (hydrogen system) was not experimentally detected. On the hydrogen system it seems reasonable to assume its existence, and such an assumption results in a better fit between the calculated and observed ionization-depth curve. On the new system no rays harder than A m equal to about - 1800 can be produced by a helium reaction. The formation of RaZz6by a mixed reaction requires the combination of at least fifty-six particles. Because of the unfavorable kinetics, radium is an exceedingly rare element. Its atoms constitute less than a 10-l~part of the total atoms in the earth’s crust, and are probably less abundant in the centrosphere. The kinetic hypothesis requires that the reaction 56 H = FeS6
should also occur, and that iron formed as above should be more abundant than radium. But even the assumption that the union of fifty six hydrogen units is many times more probable than the union of the same number of helium particles does not indicate the formation of enough iron atoms to produce more than a weak radiation. On the new interpretation this band is not of sufficient strength to be detected. The proposed interpretation of the cosmic rays is summarized in Table VI. The kinetic hypothesis should be capable of producing a satisfactory ionization-depth curve. I n the hydrogen system the iron band niakes an important contribution to the total ionization. At 1 2 meters it produces 107~ of the ionization, while at i o meters this portion has increased to 53%. Since the kinetic hypothesis eliminates the iron band it must demonstrate that the ionization can be calculated using only the He, 0, and Si bands.
Analysis of the Penetrating Radiation A theoretical ionization-depth curve would be founded on the following considerations. a) A complete spectrum of the cosmic rays, together with the initial intensity of each ray.
b) The absorption in the atmosphere surrounding a spherical earth. Both the density and composition of the absorbing medium are point functions of the distance above sea level. The ionization at any point is caused by rays coming from all possible directions, and traversing widely varying distances through the atmosphere. c) The effect of secondary, tertiary, and softer radiations due to Compton scattering. These rays make all possible directions with reference to the primary beam. d)
Softer radiation caused by the Compton electrons.
83 5
O R I G I S O F T H E CHEMICAL ELEMENTS
TABLE VI Interpretation of the Comic Rays on the Kinetic Hypothesis. Coefficient
Remarks
Am
Absorption calculated
4H = He
-290
greater than
3He = zH = K
-141
0.30
4He = 0
- 86
6He = MgZ4
- 200
Causes a slight softening
7He = Siz8
-285
Not distinguishable from helium radiation.
16H = 0
-1245
0.086
N
-1080
0.074
IZH = C
-750
14He = Fe@
-750
Same as for carbon.
-(900
These rays make up a portion of the band.
Reaction
14H =
formation of metals between Zn and As by mixed reactions 3He
0 . 35
+ zoH = Fe56
56H = Fe56
-2320
Softens the band and increases the absorption coefficient.
0.08
Determines character of band. Determines character of band. Would broaden band on long wave side.
to
1200)
The band contains mixed reactions of this type. 0.041
-2190
-4800
Determines nature of band. Softens the band and increases the absorption coefficient.
+ I I H = NaZ3 -1180
28H = Si28
9He
observed
o ,019
0,04
This reaction with formation of Al, and Mg by hydrogen reactions determine the nature of the band. Ca, and K formed in same manner may broaden band on short wave side. The band includes mixed reactions of this type.
not Too weak to be detected. observed
83 6
S . BRADFORD STONE
e) Experimental limitations on the mathematical analysis; as in the case of underwater measurements in lakes of finite area surrounded by mountains, the effect of electroscope design, etc. Experimental facts permit a simplification of the analysis. The radiation' can be regarded as entering the atmosphere with equal intensity in all directions. For penetrating rays approximately half of the original energy of the quantum will appear as kinetic energy of the electron, and the scattered quantum will have a frequency hv/z. Both the scattered quantum and the electron will move in nearly the same direction as the original beam. An analysis based on these approximations has been carried out by Gray.2 It was found that the total ionization produced by a homogeneous band of absorption coefficient comes close to an exponential law.
I = Ioe+ The total ionization includes that due to the primary beam, together with all the ions produced by the various degraded quanta. This equation is valid for both the scattering equations of Compton and Dirac. Construction of an Ionization-Depth Curve Using an exponential equation with values of IOfor the He, 0, and Si bands of 151.2, 10.79, and 1.79 respectively the ionization was calculated at different depths. The calculated values are shown in Table VII. TABLE VI1 Cosmic Ray Ionization as calculated by the Kinetic Hypothesis Observed ionization
Ionization caused by the Height in equi%alent Si band meters of He band 0 band water Total calculated 70
0.00
60
0.00
0.040 0.088
50
0.00
0.20
40 30
0.00
20
0.44 0.98 2.18 3.24 4.13 4.85
0.02
I2
0.38 1.68 4.13
10
7.54
9 7
10.15 18.53 33'73 61.53 83.00
I5
5 3 2 1
2
5.25
6.16 7'23 8.49 9.19
0.115
0.171 0.26 0.38 0.57 0.85 .04 1.17 I
I .27
.32 I .42 1.55 I .68 I
1.74
0.16 0.24 0.44 0.85 1.79 3.95 6.24 8.60
0,155 0.26 0.46 0.82
1.57 3.41 5.96 9.43 13.66 16.72 26.I
7'
difference (obs. - cal.) cal. Kinetic Hydrogen hypothesis system
Ioo
3% 8
-5 4
-50
-34 -15
I2
0.0
I5 4
3 3
-10
-3
12.20
-I 2
0
16 .os 30.7 61 .o
-4
'5
42.5 51.7
127.5
30 44
92.9
192.0
52
R. .4. Millikan and G . H. Cameron: Phys. Rev., Gray: Proc. Roy. Soc., 1 2 2 4 647 (1929).
-55%
(2) 28,
860 (1926).
.o
7 23 31 35 34
ORIGIN O F THE CHEMICAL ELEMENTS
83 7
Between nine and forty meters both systems show equally good agreement with the observed values. Below forty meters the new system is closer to the observed ionization. At heights above seven meters all calculated values are lower than the observed. On the kinetic hypothesis this is a necessary consequence of the presence of softer radiation, due chiefly to the formation of the relatively abundant oxygen from helium. Millikan seems inclined to the opinion that the differences are due to experimental errors in the measurements at higher altitudes. These errors are estimated as high as possibly 30%, although he also states that the formation of oxygen by a helium reaction may account for the high ionizations. The kinetic hypothesis on the other hand definitely states that this reaction takes place, that it is a common transformation, and that high values are therefore to be expected in the upper portions of the atmosphere. Part of the excess ionization is however caused by the approximation used in the mathematical treatment. The assumption that the scattered quanta travel in the same direction as the original beam reduces to a certain extent the calculated ionization in the higher regions of the atmosphere. A comparison of the relative number of quanta in each band gives values that accord well with the kinetic hypothesis. The calculations are as follows. The primary ionization according to either the Gray or the Gold formula can be represented by the equation I = IoF(&h). The total number of ions formed per second in a volume of unit cro'oss section, and of infinite length is
I* = I o l mF(ph)dh = IO/P Jm
I* = constant
F(rh)d(rh)
x
Io/p
It is obvious that the values of I* or of ID/pwill to a very high approximation be proportional to the relative number of quanta formed in each band, or expressed in another manner, proportional to the abundance of the atoms in TABLE VI11 Relative Number of Atoms formed in each Band Value of IOon
Band Hydrogen' system
He
0 Si Fe
372 22.2
7.65 I .65
Value of Io/r on
Kinetic hypothesis 151.2
Hydrogen system 1240
Relative number of atoms in each band
Kinetic hypothesis Hydrogen system
504
Kinetic hypotbesis
100
IO0
10.79
277.5
134
22.4
26.8
I .89
189.5 82.5
47
15.2
-
-
6.65
Calculated from the Gold tables, me M W a n and Cameron: Phys. Rev., 533 (192'3).
9.4
(2) 32,
838
S.
BRADFORD STOSE
the different bands. This follows from the fact that in the absorption of the primary band one ion is formed for each quantum originally present. The upper limit of integration, infinity, means no more than a few hundred meters. The curvature of the earth can therefore be neglected, The calculated number of quanta in the various bands are given in Table VIII. The calculations of hydrogen system are supposedly based on the assumption that the number of atoms in the 0, Si, and Fe bands are in the ratio of 55::26::1.8, or proportional to the relative abundance of these three types of atoms. If the calculations had been correct the numbers in the next to the last column, under the heading hydrogen system, would have b e m 100,2 2 . 4 , 10.6, and 2.86. The calculated ionization-depth curve of the hydrogen system is therefore based on a larger abundance of silicon as compared to oxygen, and a larger abundance of iron relative to oxygen, than is found for the earth’s surface. It will be observed that the new system gives a relative abundance of atoms in the silicon and oxygen bands that is about the same as the known abundance of these elements. This is not however a necessary consequence of the kinetic hypothesis.
The Effect of the Softer Radiations The difference between the observed and calculated absorption coefficients of the helium band was ascribed to the presence of softer rays. An estimate of the effect of the soft oxygen radiation can now be made. I t is reasonable to assume that about 50% of the total helium formed will appear as oxygen, or that for every I O O helium atoms there are formed a t the same time, say 48/4 or 12 oxygen atoms. Using as before the Dirac and Gray equations, the value of I0/p for the soft oxygen rays is 60.5. This radiation produces a t nine and two meters ionizations of 0.03 and 9.70 ions. With an exponential equation, the absorption coefficient between nine and two meters (the same points as used by Millikan and Cameron) increases to 0.315. The explanation givnn by the kinetic hypothesis is therefore capable of explaining a large portion of the difference between the observed and calculated absorption coefficient. Because of the assumed abundance of hydrogen, the new explanation of the cosmic rays is in essentials the same as that of the hydrogen system. The differences which do exist are important. They can be summarized as follo\\-s: a) The helium band is now ascribed partly to the formation of certain of the lighter and more abundant elements. Because of this the absorption coefficient is greater than the calculated value. b) The oxygen band is due in some part to the formation of elements lying betvieen Zn and As. Another part of the band is ascribed to mixed reactions. c) d portion of the silicon band is due to mixed reactions. d) The iron band is present in either very lon-, or else zero intensity.
ORIGIN OF THE CHEMICAL ELEMENTS
839
Two of these differences are capable of experimental tests, namely; the conclusion that a large amount of soft oxygen radiation exists in the upper reaches of the atmosphere, and the conclusion that radiation more penetrating than the silicon band has very low or else zero intensity.
IV. An Hypothesis of the Mechanism of Atomic Formation It is proposed to demonstrate that by means of a single hypothesis concerning the mechanism of atomic formation it is possible to explain several of the most important facts concerning the chemical elements. It will be assumed that the union of electrically charged nuclei results because of magnetic-like forces acting a t right angles to the direction of motion of the particles. Classical electrical theory states that such a force exists between two moving charged particles, and that it is proportional to the product of the speeds of the particles, and inversely proportional to the distance apart. There may be additional attractive forces arising from nuclear spins or from polarization effects. Present interpretations of the wave mechanics also permit the possibility of the union of the particles even when the attractive forces are not sufficient t o overcome the potential barrier created by the classical electrostatic repulsive forces. The problem of interest in connection with this hypothesis is not however that of the union of two nuclei, but rather that of the union of several charged nuclei when under the influence of such forces. It will be assumed that between several moving charged nuclei there exist magnetic like forces acting at right angles to the direction of motion, and that such forces increase with increase in the velocity of the moving nuclei, and a t high velocities are capable of causing the union of a large number of nuclei. Atomic formation would on this hypothesis be possible only in a region of long mean free path, or of very low density. The only possible site for the process of atomic creation and for the origin of the cosmic rays would therefore be the depths of interstellar space. This agrees with the accepted conclusions regarding the origin of these rays. On such a magnetic hypothesis the most favorable conditions for the collision of two or more nuclei consists in their having the same velocity and same initial direction. Now the distribution of kinetic energy among a system of particles must be such that in general only atoms of the same mass will have equal velocities. The most common reactions would then be the combination of particles having the same mass, which justifies one of the basic postulates of the kinetic hypothesis, namely; the assumption that the most probable type of reaction would involve nuclei of one kind only. The kinetics of this hypothesis require a rapid decline in the probability of the formation of the heavier atoms. This agrees with the known facts of atomic abundance. For collisions involving larger numbers of particles there should be a greater chance of the accidental inclusion of a foreign nucleus, so that in the formation of the heavier elements mixed reactions become relatively more probable. This conclusion is supported by the fact that there are no abundant atoms of this type having an atomic weight less than twenty-
840
S. BRADFORD STONE
three. The same reasoning indicates that the heavier atoms will have much less tendency to concentrate in the 4K type. This can be illustrated by considering those elements which contain both a 4K,and a 4K N type of isotope. The only lighter atoms containing the two types are Ne, Mg, Si, A, and Fe. In every case the most abundant isotope has an atomic weight divisible by four. Of the remaining heavier elements listed in Aston’s latest tables’ m containing both kinds of isotopes, the most abundant isotope in six cases out of thirteen falls into the 4K N type. The magnetic hypothesis therefore gives an explanation for the failure of the heavier elements to display the same regularities as observed for the lighter atoms. The previous discussion did not take into account the electronic constitution of the nucleus. The accepted theories of atomic structure call for the presence of nuclear electrons equal in number to at least one half that of the number of protons. The charged nuclei which are formed according to the magnetic hypothesis will act as centers of attraction for any electrons which are present. Depending upon conditions a given nucleus will capture electrons as either planetary or nuclear electrons. For the heavier nuclei with their larger charges there should be a greater probability of the capture of nuclear electrons. Isobars should therefore be more abundant for the heavier elements. The same statement obviously applies to isotopes. Both conclusions are supported by Aston’s experimental facts. The lightest known isobaric atoms are Ca4O and A’O, while at least seven such pairs are found in atoms heavier than zinc. No element lighter than Mg has more than two isotopes. No atom lighter than Zn has more than three isotopes. At least six of the elements above Zn have from five to nine isotopes. It is of interest to note that this last argument can be dissociated entirely from the magnetic hypothesis. In which case the same reasoning indicates that the known facts of isotopic constitution can be qualitatively explained on the assumption that electrons are captured by preexisting atomic nuclei.
+
+
Conclusions Calculations based on the early theory of relativity, and on new atomic weight determinations show that the calculated mass decreases in radioactive transformations are of the proper magnitudes to account for the energy changes. Aston’s new method is sufficiently accurate to permit another test of the theory of relativity. An equation relating mass defect to atomic weight has been found to be a restatement of the condition that the atomic weights are approximately integers on an oxygen basis. The assumption that atomic formation occurs through the union of helium and hydrogen nuclei indicates :a) An upper limit of about 340 for the atomic weight. b) The concentration of matter into the lighter elements. c) The concentration of matter into the 4K type of atom. 1
Aston: Phil. Mag.,
(2)
49, 1 1 9 (1925).
ORIGIX O F THE CHEMICAL E L E M E h T S
841
dj An explanation of the evolution of the radio-active elements which accords with thermodynamic principles. e) The possibility of slight variations in any one given type of atom. This suggests the existence of a fine structure in individual mass spectra lines. An explanation of the cosmic rays is developed in terms of a kinetic hypothesis. While essentially the same as that of Millikan and Cameron it, differs in requiring the necessary presence of a large amount of soft radiation in the helium band, and the absence of an iron band. An experimental examination of these differences should be possible. X satisfactory ionizationdepth curve was constructed for the new interpretation. h magnetic hypothesis of the mechanism of atomic creation was proposed. This hypothesis explains the following: a) The origin of the cosmic rays in interstellar space. b) The concentration of the lighter atoms into the 4K type. c) The reason for the divergence of the heavier atoms from Harkins' rules. d) The known facts concerning the distribution of isotopes and isobars.
