CHAPTER 25
Radioactivity
The ejection of positive or negative displacement by an atom that becomes unstable for one of the reasons discussed in the preceding pages will be identified as radioactivity, or radioactive decay, and the adjective radioactive will be applied to any element or isotope that is in the unstable condition. As brought out in Chapter 24, there are two distinct kinds of instability. Those elements whose atomic mass exceeds 236, either in rotational mass alone, or in rotational mass plus the vibrational mass added by magnetic ionization, are beyond the overall stability limit, and must reduce their respective masses below 236. In a fixed environment this cannot ordinarily be accomplished by modification of the vibrational mass alone, since the normal 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 a lower atomic number. The most common process is the ejection of one or more helium atoms, or alpha particles, and is known as alpha decay.
The second type of instability is due to a ratio of vibrational to rotational mass which is outside the zone of stability. In this case ejection of mass is not necessary; the required adjustment of the ratio can be accomplished by a process that 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, together with a neutrino, 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 that result from instability due to exceeding the 236 mass limit (that is, all processes that involve the ejection of primary mass) will be classified as alpha radioactivity, and all processes that modify only the ratio of vibrational mass to rotational mass will be classed as beta radioactivity. If it is necessary to identify the individual processes, such terms as b+ decay, etc., will be employed. The nature of the processes will be specified in terms of the beta particle, and coincident emission of the appropriate neutrino should be understood.
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 mass of the isotope Li7. A negative mass (space displacement) will be indicated by parentheses, as in the expression 4-(1), which is the mass of the isotope He3. This system is similar to the notation used for the rotational displacement in the different scalar dimensions, but there should be no confusion since one is a two-number system while the other employs three numbers.
Radioactive processes generally involve some adjustments of the secondary mass, but these are minor items that have not yet been studied in the context of the Reciprocal System of theory. They will not be considered in the present discussion, which will refer only to the primary mass, the principal component of the total.
The composition of the motions of a stable isotope can be changed only by external means such as violent contact, absorption of a particle, or magnetic ionization, and the frequency of such changes is related to the nature of the environment, rather than to anything inherent in the structure of the isotope itself. An unstable isotope, on the other hand, is capable of moving toward stability on its own initiative by ejecting the appropriate motion or combination of motions, Consequently, each such process has a specific time pattern, subject to the probability relations.
The basic process of alpha radioactivity is the direct removal of rotational mass. Since each unit of rotational displacement is equal to two units of mass on the atomic weight scale, the effect of each step in this process is to decrease the rotational mass by 2n units. The rotational combination with n = 1 is the H2 isotope, which is unstable because its total rotation is above the limit for either a single rotating system, or an intermediate type of structure similar to that of the H1 isotope, but is less than one double (atomic number) unit in each of the two rotating systems of the atomic structure. This H2 isotope therefore tends either to lose displacement and revert to the H1 status, or to add displacement and become a helium atom. The particle ejected in alpha radioactivity is the smallest stable double rotating system, in which n = 2. Emission of this particle, the He4 isotope, with mass components 4-0, results in a change such as
O16 → C12 + He416-0 → 12-0 + 4-0
Since rotational vibration exists only as a modifier of rotation, there are no separate units of vibrational mass that can be added or subtracted directly in the manner of the alpha particle. But the mass of the compound neutron has the same single (atomic weight) unit value as the vibrational mass unit, and like the latter, it is a single rotating system (from the material standpoint). It is therefore interchangeable with the vibrational mass. In our numerical notation, it can be expressed as 0-1. This equivalence of the neutron mass and the unit of vibrational mass makes it possible to modify isotopes by adding or removing compound neutrons. Thus we may start with the mass two isotope of hydrogen, H2, and by adding a compound neutron obtain the mass three isotope, H3.
H2 + n → H3
2-0 + 0-1 → 2-1
Beta radioactivity is a conversion process rather than an ordinary addition process. An isotope that is above the zone of stability has one or more units of magnetic displacement, ½-½-0, in the form of rotational vibration, superimposed on units of the magnetic rotation of the atom. These vibrational units are only half the size of the rotational units. Addition of a second half-size unit to one of the combinations of unit rotation and unit rotational vibration is therefore required to produce an additional rotational unit. This cannot be accomplished by direct addition, as a rotational unit is not capable of accepting more than one vibrational unit. However, an unstable isotope is subject to influences that cause it to eject displacement. (That is what makes it unstable.) An isotope above the stability zone ejects a cosmic neutrino, (½)-(½)-1 and an electron, 0-0-(1). This ejection is equivalent to addition of displacement ½-½-0, the addition that is required to convert one of the half size vibrational units to a rotational unit.
Neither of the ejected particles has any effective primary mass. No change in mass therefore takes place in this process (b-radioactivity). The original isotope with rotational mass 2Z and vibrational mass n becomes an isotope with rotational mass 2(Z+1)—that is, an isotope of the next higher element—and vibrational mass n-2. The total mass of the combination of motions remains the same, but two units of vibrational mass have been converted to rotational mass, and the combination has moved closer to the zone of stability. If it is still outside that zone, the ejection process is repeated.
Where an isotope is below the zone of stability (deficient in vibrational mass) the process described in the foregoing paragraphs is reversed. In this process, b+ radioactivity, a unit of rotational mass is converted to two units of vibrational mass by ejection of a material neutrino, ½-½-(1), together with a positron, 0-0-1. The isotope of element Z, with rotational mass 2Z and vibrational mass n then becomes an isotope of element Z-1, with rotational mass 2(Z-1) and vibrational mass n+2.
These are the basic radioactive processes. The actual course of events in any particular case depends on the initial situation. It may involve only one such event; it may consist of several successive events of the same kind, or a combination of the basic processes may be required to complete the transition to a stable condition. In natural beta radioactivity under terrestrial conditions a single beta emission is usually sufficient, as the unstable isotopes are seldom very far outside the zone of beta stability. However, under some other environmental conditions the amount of radioactivity required in order to attain beta stability is very substantial, as we will see in Volume III.
In natural alpha radioactivity, the mass that must be ejected may amount to the equivalent of several alpha particles even in the terrestrial environment. The loss of this rotational mass necessitates beta emission to restore the equilibrium between rotational and vibrational mass. Alpha radioactivity is thus usually a complex process. As an example, we may trace the steps involved in the radioactive decay of uranium. Beginning with U238, which is just over the borderline of stability, and has the long half life of 4.5×109 years, the first event is an alpha emission.
U238 → Th234 + He4184-54 → 180-54 + 4-0
This puts the vibrational mass outside the zone of stability, and two successive beta events follow promptly, bring the atom back to another isotope of uranium.
Th234 → Pa234180-54→ 182-52
Pa234 → U234 182-52 → 184-50
Two successive alpha emissions now take place, with a considerable delay between stages, as both U234 and the intermediate product Th230 have relatively long half lives. These two events bring the atomic structure to that of radium, the prototype of the radioactive elements.
U234 → Th230 + He4184-50 → 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 phase of the decay range from days down to as low as seconds. Three more alpha emissions start the sequence.
Ra226 → Rn222 + 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 event is therefore a beta emission.
Pb214 → Bi214
164-50 → 166-48
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. In either case, the emission is followed by one of the alternate kind, and the net result of the two events is the same regardless of which step is taken first. We may therefore regard this as a double decay.
Bi214 → Pb210 + He4
166-48 → 164-46 + 4-0
After some delay due to a 22 year half life of Pb210, two successive beta emissions and one alpha event occur.
Pb210 → Bi210
164-46 → 166-44
Bi210 → Po210
166-44 → 168-42
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 ratio of vibrational to rotational mass (beta). The radioactivity therefore ends at this point.
The unstable isotopes that are responsible for natural beta radioactivity in the terrestrial environment originate either as by-products of alpha radioactivity or as a result of atomic transformations originated by high energy processes, such as those initiated by incoming cosmic rays. Alpha radioactivity is mainly the result of past or present inflow of material from regions where the magnetic ionization level is below that of the local environment.
In those regions where the magnetic ionization level is zero, or near zero, all of the 117 possible elements are stable, and there is no alpha radioactivity. The heavy element content of young matter is low because atom building is a cumulative process, and this young matter has not had time to produce more than a relatively small number of the more complex atoms. But probability considerations make it inevitable that some atoms of the higher groups will be formed in the younger aggregates, particularly where older matter dispersed into space by explosive processes has been accreted by these younger structures. Thus, although aggregates composed primarily of young matter have a much lower heavy element content than those composed of older matter, they do contain an appreciable number of the very heavy elements, including the trans-uranium elements that are absent from terrestrial matter. The significance of this point will be explained in Volume III.
If matter from a region of zero magnetic ionization is transferred to a region such as the surface of the earth, where the ionization level is unity or above, the stability limit in terms of atomic number drops, and radioactivity is initiated. Whether the material constituents of the earth acquired the unit magnetic ionization level at the time that the earth 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 suggesting that this change took place in a considerably earlier era, but in any event the situation with respect to the activity of the elements now undergoing alpha radioactivity is essentially the same. They originated in a region of zero, or near zero, magnetic ionization, and either remained in that region while the magnetic ionization level increased, or in some manner, the nature of which is immaterial in the present connection, were transferred to their present locations, where they have become radioactive for the reasons stated.
As noted above, another source of natural radioactivity is atomic rearrangement resulting from interaction of material atoms with high energy particles, principally the cosmic rays and their derivatives. In such reactions stable isotopes of one kind or another are converted into unstable isotopes, and the latter than become sources of radioactivity, mostly of the beta type. The level of the beta radioactivity produced in this manner is quite low. The very intense activity of the same general nature that is indicated by the radio and x-ray emission from certain kinds of astronomical objects originates by means of a different process, examination of which will be deferred until the nature and behavior of the objects from which the emissions are observed are developed in Volume III.
The processes that constitute natural radioactivity can be duplicated experimentally, together with a great variety of similar atomic transformations which presumably also occur naturally under appropriate circumstances, but have been observed only under 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. Essentially, these transformations, regardless of the number and type of atoms or particles involved, are no different from the simple addition and decay reactions previously discussed. The most convenient way 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 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 transformations actually take place, 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 first artificial radioactive reaction discovered, may be represented as
Al27 + He4 → P30 + n1
26-1 + 4-0 → 30-1 → 30-0 + 0-1
In this case the two phases of the reaction are independent, in the sense that any combination which adds up to 30-1 can produce P30 + n1, while there are many ways in which the 30-1 resultant of the combination of Al27 + He4 can be broken down. The final product may, for instance, be Si30 + H1.
The usual method of conducting transformation experiments is to accelerate a small atomic or sub-atomic 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 on the relative stability of those 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 get results similar to those produced in the Al27 + He4 reaction previously discussed. Typical equations are
Al27 + H1 → Mg24 + He4
26-1 + 2-(1) → 28-0 → 24-0 + 4-0
Al27 + H1 → Si27 + n1
26-1 + 2-(1) → 28-0 → 28-(1) + 0-1
Greater energies cause further fragmentation and result in such rearrangements as
Al27 + H1 → Na24 + 3 H1 + n126-1 + 2-(1) → 28-0 → 22-2 + 6-(3) + 0-1
The 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. In this case, the process is known as fission. The difference between the fission process and the transformation reactions previously described in merely a matter of degree, and the same relationships apply.
Although it is possible in some instances to transform one stable isotope into another by an appropriate process, the more general rule is that if the original reactants are stable the major product is unstable, and therefore radioactive. The reason is, of course, that the stable isotopes have vibrational to rotational mass ratios within the stability zone, and any change in the ratio tends to move it out of that zone. As an example, the P30 isotope formed in the reaction between aluminum and helium atoms is below the stability zone; that is, it is deficient in vibrational mass. It therefore decays by the b+ process to form a stable silicon isotope.
P30 → Si30
30-0 → 28-2
In the radioactive reactions of the heavy elements the products often have substantial excesses of vibrational mass, and in these cases successive beta emissions take place, resulting in decay chains in which the unstable isotopes move step by step toward stability. One of the relatively long chains of this type that has been identified is the following:
|
Xe140 |
→ | Cs140 | → | Ba140 | → | La140 | → | Ce140 | |
| 108-32 | → | 110-30 | → | 112-28 | → | 114-26 | → | 116-24 | |
| (19) | (19) | (20) | (21) | (22) | |||||
The figures in parentheses refer to the number of units of vibrational mass corresponding to the center of the zone of stability, as calculated for each element from equation 24-1. The original product Xe140 has 13 excess vibrational units, and is thus far outside the stability zone. Successive beta emissions convert two-unit quantities of vibrational mass to rotational mass, while the stable amount of vibrational mass gradually increases as the atomic number rises. On reaching Ce140 the excess has been reduced to two units. This is within the stability margin, and the radioactivity therefore ceases.
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 relations, which will be discussed in Chapter 27. The electric charges carried by some of the reacting substances, or the reaction products, have no significance in the present connection, as they only affect the energy relations.
On first consideration it might appear that the addition processes discussed in the preceding pages would provide the answer to the problem of accounting for the existence of the heavier members of the series of chemical elements. In current practice this is taken for granted, and the question to be answered is accepted as being merely the issue as to what specific one or more of these processes is operative.
The currently accepted hypothesis is that the raw material from which the elements are formed is hydrogen, and that mass is added to hydrogen by means of the addition processes. It is recognized that (with certain exceptions that will be considered later) the addition mechanisms are high energy processes. Atoms approaching each other at low or moderate speeds normally rebound, and take up positions at equilibrium distances. The additions take place only where the speeds are high enough to overcome the resistance, and these speeds generally involve disruption of the structure of the target atoms, followed by some recombination.
The only place now known in our galaxy where the energy concentration is at the level required for operation of these processes on a major scale is in the interiors of the stars. The accepted hypothesis therefore is that the atom building takes place in the stellar interiors, and that the products are subsequently scattered into the environment by supernova explosions. It has been demonstrated by laboratory experiments, and more dramatically in the explosion of the hydrogen bomb, that the mass 2 and mass 3 isotopes of hydrogen can be stimulated to combine into the mass 4 isotope of helium, with the release of large quantities of energy. This hydrogen conversion process is currently the most powerful source of energy known to science (aside from some highly speculative ideas that involve carrying gravitational attraction to hypothetical extremes). The attitude of the professional physicists has always been that the most energetic process known to them must necessarily be the process by which energy is generated in the stars (even though they have had to revise their concept of the nature of this process twice already, the last time under very embarrassing circumstances). The current belief of both the physicists and the astronomers therefore is that the hydrogen conversion process is unquestionably the primary stellar energy source. It is further assumed that there are other addition processes operating in the stars by which atom building beyond the helium level is accomplished.
It will be shown in Volume III that there is a mass of astronomical evidence demonstrating conclusively that this hydrogen conversion process cannot be the means by which the stellar energy is generated. But even without this evidence that demolishes the currently accepted assumption, any critical examination of the fundamentals of atom building will make it clear that high energy processes—inherently destructive—are not the answer to the problem. It is true that the formation of helium from isotopes of hydrogen proceeds in the right direction, but the fact is that the increase in atomic mass that results from the hydrogen conversion reaction is an incidental effect of a process that operates toward a different end. The primary objective of that process, the objective that supplies the probability difference that powers the process, is the conversion of unstable isotopes into stable isotopes.
The fuel for the known hydrogen conversion process, that of the hydrogen bomb and the experiments aimed at developing fusion power, is a mixture of these unstable hydrogen isotopes. The operating principle is merely a matter of speeding up the conversion, causing the reactants to do rapidly what they will do slowly, of their own accord, if not subjected to stimulation. It is freely asserted that this is the same process as that by which energy is generated in the stars, and that the fusion experiments are designed to duplicate the stellar conditions. But the hydrogen in the stars is mainly in the form of the stable mass one isotope, and there is no justification for assuming that this stable atomic structure can be induced to undergo the kind of a reaction to which the unstable isotopes are subject by reason of their instability. The mere fact that the conversion process would be exothermic, if it occurred, does not necessarily mean that it will take place spontaneously. The controlling factor is the relative probability, not the energy balance, and so far as we know, the mass one isotope of hydrogen is just as probable a structure as the helium atom under any physical conditions, other than those, to be discussed in Chapter 26, that lead to atom building.
At high temperatures the chances of atomic break-up are improved, but this does not necessarily increase the proportion of helium in the final product. On the contrary, as noted earlier, a greater kinetic energy results in more fragmentation, and it therefore favors the smaller unit rather than the larger. A certain amount of recombination of the fragments produced under these high temperature conditions can be expected, particularly where the extreme conditions are only temporary, as in the explosion of the hydrogen bomb, but the relative amounts of the various possible products of recombination are determined by probability considerations. Inasmuch as stable isotopes are more probable than unstable isotopes (that is what makes them stable), formation of the stable helium isotope from the atomic and sub-atomic fragments takes precedence over recombination of the unstable isotopes of hydrogen. But the mass one hydrogen isotope that is the principal constituent of the stars is just as stable as helium, and it has the advantage, in a high energy environment, of being the smaller unit, which makes it less susceptible to fragmentation, and more capable of recombination if disrupted. Thus it cannot be expected that recombination of fragments into helium, under high energy conditions, will occur on a large enough scale to constitute a major source of stellar energy.
In this connection, it should be noted that the general tendency of high energy reactions in the material sector of the universe is to break down existing structures rather than build larger ones. The reason for this should be evident. The material sector is the low speed sector, and the lower the speed of matter the more pronounced its material character becomes; that is, the more it deviates from the speeds of the cosmic sector. It follows that, in general, the lower the speed the greater the tendency to form combinations of the material type. Conversely, higher speeds lessen the material character of the matter, and not only inhibit further combination, but tend to disrupt the combinations already existing. Furthermore, this increase in the amount of negative displacement (thermal or translational motion) is not conducive to building up positive displacement in the form of mass. Thus the net result of the reactions in the high speed environment of the stellar interiors can be expected to decrease, rather than increase, the average atomic weight of the matter participating in these reactions.
An analogous process in a more familiar energy range is the pyrolysis of petroleum. Cracking of a paraffinic oil, for instance, yields products that, among other things, include substantial quantities of complex aromatic compounds. For example, one of those that makes it appearance is anthracene, a 24-atom molecule. There are few, if any, of the ring compounds, even the smaller ones, in the original material. Thus it is evident that the high temperatures of this process have not only broken down the original hydrocarbon molecules into smaller molecules or atoms, but have also allowed some recombination into larger molecular units. Nevertheless, the general result of the cracking process is a drastic reduction in the average size of the molecules, the greater part of the mass being reduced to hydrogen, methane, and carbon.
The point that needs to be recognized is that this is what high energy processes do to combinations such as atoms, regardless of whether those atoms are combinations of particles, as contended by conventional physics, or combinations of different forms of motion, as deduced from the postulates of the theory of the universe of motion. Such processes disrupt some or all of the original combinations. In the chaotic conditions generated by the application of powerful forces there is a certain amount of recombination going on alongside the disintegration. This may result in the appearance of some new combinations (isotopes), which may suggest that atom building is occurring. But, in fact, these constructive events are merely incidental results of a destructive process.
In the universe of motion, the raw material for atom building consists of massless particles, the decay products of the cosmic rays. Conversion of these particles into simple atoms of matter, and production of increasingly more massive atoms from the original units, is a slow and gradual constructive process, not a high energy destructive process. This assertion as to the general character of the atom building process is confirmed by the astronomical evidence, which, as will be brought out in Volume III, shows that atom building is taking place throughout the universe, not merely at special locations and under special conditions, as envisioned in present-day theories. The details of the atom building processes in the universe of motion will be the subject of the next chapter.