Chapter XXXI

Radioactive Decay

The ejection of space or time displacement by an atom which becomes unstable for one of the reasons that have been outlined will be identified as radioactivity or radioactive decay, and the adjective radioactive will be applied to any element or isotope of an element which is in the unstable condition. As has been brought out, there are two distinct kinds of instability. Those elements whose mass exceeds 236, either in rotational mass alone or in rotational mass plus the vibrational mass added by magnetic ionization, are beyond the over-all stability limit and must reduce their respective masses below 236. In a fixed environment this cannot be accomplished by modification of the vibrational mass alone, since the ratio of vibrational to rotational mass is determined by the prevailing magnetic ionization level. The radioactivity resulting from this cause therefore involves the actual ejection of mass and the transformation of the element into an element of lower atomic number. The most common process is the emission of a helium atom, or alpha particle, which gives it the name alpha decay.

The second type of instability is due to a ratio of vibrational to rotational mass which is outside the stable zone. In this case ejection of mass is not necessary; the required adjustment of the ratio can be accomplished by addition or emission of electric rotational displacement, which converts vibrational mass into rotational mass or vice versa and thereby transforms the unstable isotope into another isotope within or closer to the zone of stability. The most common process of this kind is the emission of a beta particle, an electron or positron, and the term beta decay is applied.

In this work the alpha and beta designations will be used in a more general sense. All processes which result from instability due to exceeding the 236 mass limit (that is, all processes which involve the ejection of primary mass) will be classified as alpha radioactivity and all processes which modify only the ratio of vibrational mass to rotational mass will be classed as beta radioactivity. If it is necessary to identify the individual process such terms as ß⁺ decay, etc., will be employed.

On first consideration it might appear that the observed characteristics of radioactivity are incompatible with the origin of this phenomenon as deduced from the Fundamental Postulates and outlined in the foregoing discussion. This derivation clearly requires radioactivity to be an explosive type of action, initiated as soon as an aggregate reaches the limit of stability and continuing as a single event until the atomic transformation is complete. The observed radioactivity, on the other hand, apparently consists of a series of independent events occurring at random within an aggregate and in many instances extending over a very long interval of time. The explanation of this seeming inconsistency is simple, but it will be more convenient to introduce it at a later stage of the discussion, and for the present we will turn to a consideration of the details of the basic radioactive processes.

In analyzing these processes, which are few in number and relatively simple, the essential requirement is to distinguish clearly between the rotational and vibrational mass. For convenience we will adopt a notation in the form 6-1, where the first number represents the rotational mass and the second the vibrational mass. The example cited is the isotope Li⁷. A negative mass will be indicated by parentheses as in the expression 2-(1), which is the isotope H¹. This system is similar to the notation used for the rotational displacements, but there should be no confusion since one is a two-number expression while the other is a three-number expression.

The neutron mass has the same single unit value (one-half unit on the natural scale) which characterizes the vibrational mass and like the latter it is purely magnetic. it is therefore interchangeable with the vibrational mass. The mass symbol for the neutron is 0-1. The relationship between the neutron and the rotational vibration of an atom is the magnetic equivalent of the relation of the uncharged electron to the electric charge of an ion, as discussed in connection with the subject of electrolysis.

The first of the basic transition processes which we will consider is the direct addition or subtraction of pure rotational mass. Since each unit of rotational displacement is equal to two units of atomic mass the effect of this process is to increase or decrease the rotational mass by 2n units. The rotational combination with n = 1 is the H˛ isotope, which is unstable under terrestrial conditions, and the ejected particle is normally the first stable combination, in which n = 2. Emission of this particle, the He⁴ isotope, 4-0, results in a change such as

O¹⁶ → C¹² + He⁴
16-0 → 12-0 + 4-0

In any location where the magnetic ionization level is zero and the H˛ isotope is consequently stable, the emission of H˛ undoubtedly takes precedence since the smaller unit has the greater probability, and in such an environment a forced disintegration of the O¹⁶ isotope proceeds in this manner:

O¹⁶ → N¹⁴ + H²
16-0 → 14-0 + 2-0

Since rotational vibration exists only in conjunction with rotation, units of vibrational mass cannot be added or subtracted directly except by a change of the magnetic ionization level, but the equivalence of the neutron mass and the vibrational mass makes it possible to accomplish this objective by adding or withdrawing neutrons. Thus we may start with the mass 2 hydrogen isotope, the deuteron, and by adding a neutron obtain the mass 3 isotope.

H² + n¹ → H³
2-0 + 0-1 → 2-1

Similarly the ejection of a neutron leaves the mass 1 isotope as the residual product.

H² - n¹ → H¹
2-0 - 0-1 → 2-(1)

Inasmuch as the rotational vibration is a displacement of the same kind and direction as the magnetic rotational displacement itself, the only factor which permits it to exist as an independent vibrational entity rather than becoming merely a component of the total rotation is the lack of motion in the electric dimension. Addition of displacement in the electric dimension therefore has the effect of converting vibrational mass to rotational mass. One unit of electric time displacement is required for each rotational displacement unit, the equivalent of two units of atomic mass. Addition of one unit of electric time displacement thus results in the conversion of two units of atomic mass from the vibrational to the rotational basis. This can take place either by the addition of a positron or by ejection of the inverse particle, the electron, as in the reactions

H³ + e⁺ → He³
2-1 + e⁺ → 4-(1)

H³ - e^- → He³
2-1 - e^- → 4-(1)

Elimination of one unit of electric time displacement by addition of an electron or removal of a positron reverses this process, increasing the vibrational mass by two units and decreasing the rotational mass accordingly.

These are the basic growth and decay processes. The actual course of events in any particular case depends on the situation; it may involve only one such process, it may consist of several successive events of the same kind, or different basic processes may combine to bring about the required result. In natural beta radioactivity a single beta emission is normally sufficient as the unstable isotopes are seldom very far outside the zone of beta stability and alpha stability is not involved. In natural alpha radioactivity, on the other hand, the amount of mass which must be ejected usually amounts to the equivalent of several alpha particles. The loss of this rotational mass by successive alpha emissions necessitates beta emissions to restore the equilibrium between rotational and vibrational mass. As an example we may trace the various steps involved in the radioactive decay of uranium.

Beginning with U²³⁸ which is just over the borderline of stability and has the relatively long half-life of 4.5×10⁹ years, the first event is an alpha emission.

U238 → Th²³⁴ + He⁴
184-54 → 180-54 + 4-0

This puts the vibrational mass outside the zone of stability and two successive beta emissions follow promptly, bringing the atom back to another isotope of uranium.

Th²³⁴ → Pa²³⁴ + e^-
180-54 → 182-52 + e^-

Pa²³⁴ → U²³⁴ + e^-
182-52 → 184-50 + e^-

Two successive alpha emissions now take place, with a considerable length of time between stages, since both U²³⁴ and the intermediate product Th²³⁰ are relatively stable. These events bring us to radium, the best known of all the radioactive elements.

U²³⁴ → Th²³⁰ + He⁴
184-50 → 180-50 + 4-0

Th²³⁰ → Ra²²⁶ + He⁴
180-50 → 176-50 + 4-0

After another somewhat shorter time interval a rapid succession of decay events begins. Half-life periods in this zone range from days down as low as seconds. Three more alpha emissions start this sequence.

Ra²²⁶ → Rn²¹² + He⁴
176-50 → 172-50 + 4-0

Rn²²² → Po²¹⁸ + He⁴
172-50 → 168-50 + 4-0

Po²¹⁸ → Pb²¹⁴ + He⁴
168-50 → 164-50 + 4-0

By this time the vibrational mass of 50 units is well above the zone of stability, the center of which is theoretically 43 units at this point. The next emission is therefore an e^- particle.

Pb²¹⁴ → Bi²¹⁴ + e^-
164-50 → 166-48 + e^-

This isotope is still above the stable zone and another beta emission is in order, but a further alpha emission is also imminent, and the next step may take either direction.

Bi²¹⁴ → Po²¹⁴ + e^-
166-48 → 168-46 + e^-

or Bi²¹⁴ → Tl¹¹⁰ + He⁴
166-48 → 162-48 + 4-0

In either case this emission is followed by one of the alternate kind and the net result of the two successive events is the same regardless of which step is taken first.

Po²¹⁴ → Pb²¹⁰ + He⁴
168-46 → 164-46 + 4-0

or Tl²¹⁰ → Pb²¹⁰ + e^-
162-48 → 164-46 + e^-

After some delay due to a 22 year half-life of Pb²¹⁰, successive emissions of two electrons and one alpha particle occur.

Pb²¹⁰ → Bi²¹⁰ + e^-
164-46 → 166-44 + e^-

Bi²¹⁰ → Po²¹⁰ + e^-
166-44 → 168-42 + e^-

Po²¹⁰ → Pb²⁰⁶ + He⁴
168-42 → 164-42 + 4-0

The lead isotope Pb²⁰⁶ is within the stability limits both with respect to total mass (alpha) and with respect to the vibration-rotation ratio (beta) and the radioactivity therefore ends at this point.

The unstable isotopes which are responsible for natural radioactivity in the local environment originate in two ways: by past or present inflow of matter from regions where the magnetic ionization level is zero, and by atomic transformations initiated by high energy particles such as those in the cosmic rays. In those regions where the formation of matter takes place on a major scale all of the 117 possible elements originate in the proportions established by probability considerations. As long as the magnetic ionization level is zero these elements are all stable and there is no spontaneous alpha radioactivity. If this matter is then transferred to a region of higher magnetic ionization, such as the earth in its present condition, the stability limit in terms of atomic number drops because of the addition of vibrational mass originating from the magnetic vibrational motion, and radioactivity is initiated.

Whether the earth acquired the unit magnetic ionization level at the same time that it assumed its present status as a planet or reached this level at some earlier or later date is not definitely indicated by the information now available. There is some evidence which suggests that this change took place in a considerably earlier era, but in any event the situation with respect to the radioactive elements is essentially the same. They originated in a region of zero magnetic ionization and either remained in that region while the magnetic ionization increased, or in some manner, the nature of which is immaterial for present purposes, were transferred to their present location, where they have become radioactive for the reasons stated.

The other source of natural radioactivity is atomic rearrangement resulting from interaction of the material atoms with particles of other types, principally the cosmic rays and their derivatives. In such reactions stable isotopes of one kind or another are converted into related unstable isotopes and the latter then become sources of radioactivity, mostly of the beta type. The observed reactions of this kind can be duplicated experimentally, together with a great variety of similar transformations which presumably also occur naturally but have been observed only under the more favorable experimental conditions. We may therefore combine our consideration of natural beta radioactivity, the so-called artificial radioactivity, and the other experimentally induced transformations into an examination of atomic transformations in general.

In essence these transformations, regardless of the number and type of particles involved, are no different from the simple addition and decay reactions previously discussed, and the most convenient method of describing these more complex events is to treat them as successive processes in which the reacting particles first join in an addition reaction and then subsequently eject one or more particles from the combination. According to some of the theories currently in vogue this is the way in which the transformation actually takes place. This seems rather improbable, at least as a general rule, but for present purposes it is immaterial whether or not the symbolic representation conforms to physical reality and we will leave this question in abeyance. The formation of the isotope P³⁰ from aluminum, the reaction which led to the discovery of artificial radioactivity, may be represented as

Al²⁷ + He⁴ → P³⁰ + n¹
26-1 + 4-0 → 30-1 → 30-0 + 0-1

Here the rotational motions of two separate particles combine and the total motion is then redistributed in a different pattern. The two phases of the reaction are independent; that is, any combination which adds up 30-1 can produce P³⁰ + n¹, and conversely there are many ways in which the 30-1 resultant of the combination Al²⁷ + He⁴ can be broken down. The final product may therefore be some such combination as Si³⁰ + H¹ rather than P³⁰ + n¹. It is even possible that the decay process may restore the original mass distribution Al²⁷ + He⁴, although energy considerations normally favor a change of some kind.

The usual method of conducting these transformation experiments is to accelerate a small material or sub-material unit to a very high velocity and cause it to impinge on a target. In general the degree of fragmentation of the target atoms depends upon the relative stability of these atoms and the kinetic energy of the incident particles. For example, if we use hydrogen atoms against an aluminum target at a relatively low energy level we will get results similar to those produced in the helium-aluminum reactions previously described. Typical equations are

Al²⁷ + Hą → Mg²⁴ + He⁴
26-1 + 2-(1) → 28-0 → 24-0 + 4-0

Al²⁷ + Hą → Si²⁷ + n¹
26-1 + 2-(1) → 28-0 → 28-(1) + 0-1

Greater energies cause further fragmentation and result in such re-arrangements as

Al²⁷ + Hą → Na²⁴ + 3Hą + n¹
26-1 + 2-(1) → 28-0 → 22-2 + 6-(3) + 0-1

This general principle that the degree of fragmentation is a function of the energy of the incident particles has an important bearing on the relative probabilities of various reactions at very high temperatures and will have further consideration later.

In the extreme situation where the target atom is heavy and inherently unstable the fragments may be relatively large and the process is known as fission. The difference between this fission process and the transformation reactions previously described is merely a matter of degree, and the same relationships apply.

Although it is possible in some instances to transform one stable isotope into another, the more general rule is that if the original reactants are stable the major product is unstable and therefore radioactive. The P³⁰ isotope, for instance, is below the stability zone; that is, it is deficient in vibrational mass. It therefore decays by positron emission to form a stable silicon isotope.

P³⁰ → Si³⁰ + e⁺
30-0 → 28-2 + e⁺

In the fission reactions of the heavy elements the products often have substantial amounts of excess vibrational mass, and in these cases successive emissions result in decay chains in which the unstable atoms move step by step toward stability. One of the relatively long chains of this kind that has been identified is the following:

Xe¹⁴⁰ → Cs¹⁴⁰ → Ba¹⁴⁰ → La¹⁴⁰ → Ce¹⁴⁰
108-32 (19) → 110-30 (19) → 112-28 (20) → 114-26 (21) → 116-24 (22)

The figures in parentheses refer to the vibrational mass corresponding to the center of stability as calculated for each element from equation 137. The original fission product Xe¹⁴⁰ has 13 excess vibrational units and is thus far outside the stability zone. Emission of electrons converts successive 2-unit increments of vibrational mass to rotational mass, and on reaching Ce¹⁴⁰ the excess has been reduced to two units. This is within the stability margin and the radioactivity therefore ceases at this point.

The foregoing description of the atomic transformation processes has been confined to the essential element of the transformation, the redistribution of the primary mass, and the collateral effects have either been ignored or left for later treatment. In the latter category are the mass-energy relationships, which will be considered shortly. The electric charges carried by some of the reaction products are not particularly significant as they are merely an alternate means of absorbing some of the reaction energy which would otherwise go into translatory motion. Even this effect is only a temporary one as the charges are soon converted into kinetic energy. Absorption of energy by neutrinos is likewise a collateral and transient phenomenon which has no direct bearing on the primary process. Unlike the cosmic ray neutrinos, which are actually produced in the decay processes, the neutrinos which carry off part of the excess energy resulting from atomic transformations are pre-existing particles within the material aggregate. When translational energy is liberated at any particular point it can be acquired by any unit which is present; not only time units, atoms or sub-material particles, but also space units, electrons or neutrinos if rotating, photons if not rotating.

The atomic transformations which have been discussed thus far are primarily exchange reactions, in which some of the motion of one of the participants is transferred to the other, or fragmentation reactions, in which one or both of the participants are broken up into smaller units. Another class of transformations of prime importance in the general mechanism of the universe is the addition reaction which was mentioned briefly in the discussion of the basic processes by which the atomic rotational systems are modified.

Direct combination of two multi-unit atoms is not impossible, but it is difficult to accomplish. Because of the inverse gravitational action in the time region there is a strong force of repulsion between the two structures when they approach each other. Furthermore, each atom is a combination of motions in different dimensions and even if the two atoms have sufficient relative velocity to overcome the repulsion and make effective contact they cannot join unless the displacements in the different dimensions reach the proper conditions for combination simultaneously. The product of a reaction involving n units of this kind therefore normally consists of n or more particles, and this type of reaction is not available as an atom building process, except to the extent that the mass of the larger component can be increased without reducing the total number of particles, as in the reaction

C¹³ + He⁴ → O¹⁶ + n¹
12-1 + 4-0 → 16-1 → 16-0 + 0-1

Where the hydrogen atom is employed as the incident particle the situation is much more favorable for combination, since hydrogen has only one net unit of displacement and only one dimension of combination is involved. We therefore encounter many reactions such as

Al²⁷ + H¹ → Si²⁸
26-1 + 2-(1) → 28-0

The 1-1-1 particle which is equivalent to hydrogen is still better adapted to participation in these addition reactions and it is possible that some of the transformations attributed to hydrogen are actually the work of this anonymous and rather elusive particle. The atom builder par excellence, however, is the neutral member of the 1-1 family, the neutron. This particle is essentially nothing more than a unit of magnetic rotational time displacement, and as such it adds readily to any material or sub-material combination. A well-known example is

U²³⁸ + n¹ → U²³⁹
194-54 + 0-1 → 184-55

Neutron absorption is a spontaneous process requiring nothing more than contact with the material atom, and the large kinetic energies commonly used with other bombarding particles are unnecessary. In many instances slow neutrons are actually more effective than fast neutrons, since they spend more time in the vicinity of the target atom. The source of the “raw material” for atom building will be discussed at length in a later section. At that time it will be shown that this building material is preferentially produced in the form of neutrons, and neutrons are therefore available in large numbers in those regions in which they are stable; that is, in regions of zero magnetic ionization. It will also be brought out in the same discussion that the primary units from which the neutrons are produced originate uniformly throughout space, and although the presence of matter has some bearing on the conversion into neutrons the greater part of this activity takes place where most of the primary units are produced; that is, in the vast expanse of inter-galactic and inter-stellar space. It follows that this open space is the primary atom-building region, the location in which most of the light elements are assembled.

A secondary atom-building process is simultaneously operating in the regions where the magnetic ionization is greater than zero. Here the neutron is outside the zone of stability and the equivalent stable particles, the neutrino and the positron, are formed instead. The positrons, although inherently stable, are short-lived as they are so easily absorbed into the rotating systems of the atoms. The neutrinos are normally magnetically charged as produced and they add to the constantly growing neutrino concentration which determines the magnetic temperature. Unlike the neutron, therefore, the neutrino-positron pair makes no immediate contribution to the mass of the system. Sooner or later, however, the continual additions to the neutrino population bring the magnetic temperature up to the next higher ionization level. Magnetic displacement is then transferred from neutrinos to atoms, increasing the rotational mass of the latter, until the equilibrium point as defined by equation 137 is attained. The atom building in these regions is therefore a delayed-action process rather than an immediate event comparable to the absorption of a neutron into the existing atomic system.

The relative abundance of each element in the original product is a question of probability. Conversion of the neutron to hydrogen is a relatively simple matter but anything further requires the making of the proper kind of contacts in a region in which the particle density is so low that contacts of any kind are few and far between. The great majority of the atoms therefore never get beyond the hydrogen stage. As would be expected from probability considerations, helium is in second place. Beyond this point the atomic rotation enters a stage of greater complexity and the individual characteristics of the elements affect the probabilities to some extent, but in relatively young matter we can expect to find a rather small proportion of heavy elements and a general trend toward a decrease in relative abundance as the atomic number increases.

Following this very early diffuse stage of the existence of matter comes a further long period of time spent in various stages of aggregation. Here neutrons are still plentiful as long as the magnetic ionization level remains at zero, and while the production of hydrogen is small compared to that occurring in open space, the building of heavier elements from the lighter ones goes on continuously. The proportion of heavy elements therefore increases with the age of the material aggregate. Although the relative abundance of the different elements is still determined by probability, the abundance curve is more irregular because the distribution of the total rotational displacement between the electric and magnetic rotations at the higher levels introduces some complexities. We have no satisfactory means of determining the relative proportions of the elements in the younger aggregates but we can get a good idea of the situation by examining the terrestrial abundances, which are representative of a somewhat later stage of development, as indicated by the unit magnetic ionization level.

Let us consider the 2B group of elements, for example. The first three of these elements, sodium, magnesium, and aluminum, are formed by successive additions of electric displacement to the 2-2 magnetic rotational base, and all three are among the moderately plentiful elements in the earth’s crust. Silicon, the next element, is likewise produced by a similar addition and the probability of its formation does not differ materially from that of each of the three preceding elements. Another such addition, however, would bring the displacement to 2-2-5, which is unstable, and in order to form the stable equivalent 3-2-(3) the magnetic displacement must be increased by one unit in one dimension. The probability of accomplishing this result is considerably less than that of adding an electric displacement unit and the step from silicon to phosphorus is consequently more difficult than those immediately preceding. The total amount of silicon in existence therefore builds up to the point where the lower probability of the next addition reaction is offset by the larger quantity available to participate in the reaction. As a result silicon is one of the most abundant of the post-helium elements.

The situation with respect to carbon, the equivalent element of the next lower group, is not clear, as the relative proportions in which the light elements are found under terrestrial conditions are not very significant in application to the universe as a whole, and the stars give conflicting testimony. At the midpoint of the next higher group is the iron-cobalt-nickel trio of elements, and iron, the predominant member of this closely related trio, conforms very definitely to the theoretical expectation, being even more abundant than silicon.

When we turn to the corresponding elements of the 3B group, ruthenium, rhodium, and palladium, we find a totally different condition. Instead of being relatively abundant, as would be expected from their position in the atomic series just ahead of another increase in the magnetic displacement, these elements are rare. This does not necessarily mean that the relative probability effect due to the magnetic displacement step is absent, as all of the neighboring elements are likewise rare. In fact, all elements beyond the iron-nickel group exist only in comparatively minute quantities. Estimates indicate that the combined amount of all of these elements in existence is less than one percent of the existing amount of iron.

It does not appear possible to explain this situation in terms of the probability concepts. A fairly substantial decrease in abundance compared to iron would be in order if the age of the local system were such as to put the peak of probability somewhere in the vicinity of iron, but this should still leave the ruthenium group among the relatively common elements. The nearly complete elimination of the heavy elements, including this group which should theoretically be quite plentiful, requires the existence of some much more powerful factor: either (1) an almost insurmountable obstacle to the formation of elements beyond the iron group, or (2) a process which destroys these elements after they are produced.

There is no indication of the existence of any serious obstacle which interferes with the formation of the heavier elements. Laboratory experiments indicate that neutron absorption and other growth processes are just as applicable to the heavy elements as the light ones. The building-up of the very heavy elements is endothermic, but this should not be a serious obstacle, and in any event it does not apply below Group 4A and it therefore has no bearing on the scarcity of the 3B and lower division 3A elements. The peculiar distribution of abundances therefore seems to require the existence of a destructive process which prevents the accumulation of any substantial quantities of the heavy elements even though they are produced in normal amounts. In the next section it will be shown that an independent line of reasoning based on the existence of a limiting value of thermal energy also leads to the same conclusion.