NUCLEAR PHYSICS

INTRODUCTION: the problem.
Rutherford's alpha scattering experiments showed that the atom is not solid, nor had a simple structure, but is mostly empty space and had a very small, very massive nucleus surrounded by a cloud of electrons. Now this raised the problem of the nature of this nucleus: what is the "stuff" out of which the nucleus was composed? Is it made of the primordial "substance" of the universe? What are its properties? To solve this problem, intensive effort was made to collect as much information as possible regarding the structure of the nucleus of the atom. Since radioactivity was recognized as involving the nucleus itself rather than the chemical activity of the atom, this investigation centered on the properties of the various particles given off during radioactivity. All the tools of physics and chemistry were used to unlock the secrets hidden within the nucleus of the atom.

ISOTOPES.
The discovery of so many seemingly new radioactive elements presented a perplexing problem. The "uranium-radium series" involves many substances that at first were given new names and symbols, such as, UX1, UX2, and RaA. And to add to this complexity, there was also a similar but quite independent series that was tracked back to thorium as the parent element (the thorium series). The thorium series has 11 members, and ends with the stable substance to which was given the name thorium D; later thorium D was found to have the chemical properties of lead. And there was a third series which had 12 members; it was once thought to originate from actinium (actinium series). Thus there was an embarrassing plenitude of seemingly new elements, and there was far too few empty spaces in the periodic table then available to handle them.
About a hundred years before Rutherford's work, the English physician William Prout (1785-1850) in 1815 suggested that all chemical elements were made up of multiples of hydrogen atoms, somehow bound together. He had been lead to this hypothesis by the fact that most elements have atomic weights that were nearly integral multiplies of the atomic weight of hydrogen. On this basis he believed that hydrogen was the single primordial substance of which all matter was composed. Prout's hypothesis, amply supported by the atomic weight data of 1815, was attractive and for a time was widely held. But later, the determination of more accurate atomic weight data showed that no atomic weight is an exact multiple of the atomic weight of hydrogen, and that some atomic weights are very different from multiples (the atomic weight of chlorine was 35.46) of the atomic weight of hydrogen as unity. Thus Prout's hypothesis was discarded.
With the closer study of radioactive elements, Prout's hypothesis of 1815 was revived, when Frederick Soddy (1877-1956) and others in 1913 showed that certain elements, such as radioactive ionium and radioactive thorium, which are chemically identical, have different atomic weights (ionium, 230, and thorium, 232). Ionium was first prepared from pitchblende, the ore in which radium was discovered, and it was found that freshly separated ionium gradually gives rise to a new radium. The thorium ordinarily found in its ores has atomic weight 232.12, and does not give rise to radium of the same kind that was discovered by the Curies. In chemical behavior, thorium and the new ionium could not be distinguish, and no difference between the bright-line spectra of the two substances could be distinguished. When the two atomic weights were determined with great care, there was no doubt that the atomic weight of ionium is lower than that of thorium. This and several other similar examples led Soddy to declare in 1910 that
"Chemical homogeneity is no longer a guarantee that any supposed element is not a mixture of several [elements] of different atomic weights, or that any atomic weight is not merely a mean number."
Thus Soddy proposed that thorium and ionium are two different forms of the same chemical element, unlike in mass but identical in chemical properties. He thus proposed that such elements, with identical chemical properties but with different atomic weights, be given the name "isotopes" (from Greek, iso, "same", and topos, "place"), and that such elements occupy the same place in the periodic table. The key observation here was that some of supposedly new elements in the radioactivity series had chemical properties identical with those of well-known elements, although their physical properties were different. For example, the great granddaughter of uranium UI, namely uranium UII, was found to have the same chemical properties as uranium UI itself. But they had different physical properties such as quite different half-lives, and the mass of a UII atom was much smaller than that of the UI atom by at least the mass of one alpha particle. Similarly, RaB and RaG turned out to have the same chemical properties of lead, as shown by the fact that if they are mixed, they cannot be separated by chemical means; yet RaB is radioactive and RaG is stable, and their atomic masses are not the same. Soddy's suggestion now was that a chemical element should be regarded as pure element in the sense that all its atoms have the same chemical properties, but as a mixture in that the atoms of one element may fall into several groups having different radioactive behavior and different atomic masses. This meant that Dalton's atomic-molecular theory had to be modified, namely, that the pure element are alike in all respects. It is only in their chemical properties that they are alike. Therefore, the several physically different species of atoms comprising a particular chemical element could occupy the same place in the periodic table, and have the same atomic number Z. Ionium is thus an isotope of thorium, with the same atomic number 90, but with a different atomic mass of 230.
Soddy also proposed that any chemical element may not only consist of mixture of atoms unlike in mass, but that their measured atomic weights may be no more than mean or "average" values, depending upon their individual atomic masses and the relative numbers of the two or more isotopes. The chemical atomic weight of chlorine, for example, is 35.46, reflects the fact that natural chlorine is a mixture of two kinds of atoms of mass numbers 35 and 37 in approximately 3:1 ratio. Another example, the chemical atomic weight of lithium which is 6.94 results from the presence of the small percentage of atoms of mass number 6 among the predominant variety of mass number 7.
In 1913 J. J. Thomson verified Soddy's hypothesis for the case of a nonradioactive element neon. Applying the same principles that he employed in the measurement of the charge-to-mass ratio of the electron, Thomson found that neon ions, all with same charge, exhibited two different charge-to-mass ratios. He thus proved the existence of two isotopes of neon, one with an approximately atomic mass of 20 and the other 22. (Thomson missed another isotope with atomic mass of 21, which is much rarer than the other two.). The apparatus that Thomson used in the experiments with neon was the precursor of the modern instrument of exceptional precision and versatility called the mass spectrometer. With this instrument, the isotopes of any element may be separated on the basis of slight differences of charge-to-mass ratios, and their masses may be determined with great precision.
NOMENCLATURE.
A new standard of mass was adopted to express the atomic mass of any isotope that was slightly different from that which was used for chemical atomic weights. At first hydrogen, then oxygen was adopted as the standard for chemical atomic weights. The chemical scale is defined by assigning the value of 16.00000 atomic weight units (awu) to ordinary oxygen. But oxygen was found to consist of three isotopes. Oxygen, long thought to consist only of O¹⁶ atoms, was found in 1929 to consist of minute traces of O¹⁷ and O¹⁸ atoms. So when the new standard for relative isotopic atomic masses was adopted, the mass of the most abundant isotope of oxygen was assigned the value of 16.00000, and used as the standard for the new physical scale of atomic masses. The difference between the two scales is slight, since the abundances of the other two heavier isotopes, ₈O¹⁷ and ₈O¹⁸, are very small. On the physical scale, the atomic mass unit, 1 amu, is defined as 1/16 of the mass of the neutral oxygen ₈O¹⁶ atom. Thus the weighted average of the atomic masses of the three oxygen isotopes as found naturally was determined to be 16.0045 amu. Thus 16.0045 amu = 16.0000 awu, or 1 amu = 0.9997 awu. The difference between the standards used by chemist and the nuclear physicist is only about 3 parts in 10,000. The relative masses of all known kinds of atoms have been determined by use of the mass spectrometer, and it turns out the Prout's hypothesis was correct after all! The masses of individual atoms are very nearly, though not quite exactly, integral multiples of the mass of the hydrogen atom.
The nomenclature used for the isotopes of oxygen, ₈O¹⁶, ₈O¹⁷, and ₈O¹⁸, has been introduced to make clear the distinction between them. The superscripts used in this system, called mass numbers and designated by A, are not atomic weights nor exponents, but the integers nearest the exact isotopic mass in each case. We will see later that these integers have a deeper significance. The forward subscript is called the atomic number, and designated by Z. Thus the isotopes of a chemical element X can be designated by writing the chemical symbol for element to which the isotope belong, placing a forward subscript to the left of the symbol to indicate its atomic number Z, and placing a superscript to the right of the symbol to indicate its mass number A. Thus any isotope of a chemical element X may be designated with the symbol _ZX^A. For example, the three isotopes of oxygen have the same atomic number Z = 8, but each has its own mass number A: 16, 17, 18. Thus, the three isotopes of oxygen may be designated by the symbols: ₈O¹⁶, ₈O¹⁷, and ₈O¹⁸. Of particular interest is that the two very lightest elements of hydrogen and helium exist in two stable isotopic forms. Hydrogen, whose chemical atomic weight is 1.0080, has two isotopes: ordinary or light hydrogen ₁H¹ and heavy hydrogen ₁H². Heavy hydrogen, also called deuterium (from the Greek, deuteros, second), was not discovered until 1931 because the atoms of ordinary hydrogen, ₁H¹, outnumber the deuterium atoms in natural sources by about 6000 to one. And atmospheric helium, whose chemical atomic weight is 4.003 and atomic number is 2, contains two isotopes: ₂He³ and ₂He⁴. Atmospheric helium is mostly atoms with a mass number of 4 and only about one ten-thousandth percent of the atoms with a mass number of 3. The alpha particle was found to be the nucleus of the heavy helium isotope, ₂He⁴.
The number of known chemical compounds has been greatly increased by the discovery of the isotopes. Of special importance was the discovery of "heavy" hydrogen by R. T. Brige, D. H. Menzel, and H. C. Urey in 1931. Consequently, this heavy hydrogen forms a compound with oxygen called "heavy" water, which has a molecular formula (₁H²)₂O. Heavy water differs from ordinary water in a number of physical properties; for example, its freezing and boiling points are, respectively, 3.8°C and 101.4°C. Naturally occurring water contains a slight trace of heavy water.
THE PROTON.
Rutherford meanwhile continued his investigations with the scattering of the alpha particles. In 1919, he tried shooting alpha particles into nitrogen gas and studied the effects. He assumed that the alpha particles with an atomic mass of 4, upon striking the heavier nitrogen nucleus with atomic mass of 14 would lose energy and momentum. Accordingly the nitrogen atoms would be given a smaller velocity and would not travel far. And they would be detected when they struck a zinc sulfide fluorescence screen. But to Rutherford's surprise he found that the alpha particles which should not be able to penetrate through the nitrogen gas for more than 7 cm, actually produced some kind of bright spots on the fluorescence screen that was 28 cm away from the source. What happened? Had new particles been produced when the nitrogen atoms were bombarded by the alpha particles? Since the alpha particles should not travel this distance after colliding with the nitrogen atoms, had the alpha particles produced an expulsion of some new, more penetrating particle from them? Further investigation were later carried out with a "cloud chamber", a device by which the passage of a particle through moist air could be traced. In this device, invented by C. T. R. Wilson in 1912, the high speed particles as they rushed past and through the atoms of the air in its chamber, they would tear off electrons, ionizing the atoms. Droplets of fog would then condense about these ionized atoms and, when properly illuminated, the path of the particle would be made clearly visible. A study of cloud chamber photographs convincingly revealed that a new particle was formed. When the alpha particle (leaving a wide track in the cloud chamber) collides with a nucleus of a nitrogen atom, a very thin, long track starts off from the point of collision. The particle was named the proton (from Greek protos, first) and this name was adopted for this particle in 1921, when it was generally accepted that it was the major constituent of the nucleus. In 1925 P. M. S. Brackett (1897-) was able to calculate from the characteristics of this track that the new particle formed had a mass of one quarter of that of the alpha particles and had a positive charge equal in magnitude to that of the electron. It was identical in mass to that of the nucleus of the hydrogen atom; it was the proton. Rutherford's experiment was the first example of artificial transmutation of matter. The alpha particle (the nucleus of the helium atom with mass number of 4) colliding at high velocity with the nitrogen nucleus (with mass number of 14) produced an isotope of oxygen (with mass number of 17) and a proton (hydrogen ion of atomic mass of 1). That is,
₂He⁴ + ₇N¹⁴ → ₈O¹⁷ + ₁H¹.
THE NEUTRON.
A theory about the nucleus was beginning to take shape, reviving Prout's hypothesis of a century before. Rutherford suggested that in the nucleus there were both protons and electrons with some of the protons closely combined with electrons as to constitute neutral particles to which the name "neutron" was given in 1921. Rutherford imagined that a nucleus consisting of a sufficient number (Z) of proton to account for its total charge, and in addition a sufficient number of proton-electron pairs, each pair having a zero net electric charge but enough mass to make the difference between the observed atomic mass and the atomic number. Thus the helium nucleus or alpha particle would consist of four protons and two electrons, giving a net charge of (+)2q_e
(where q_e is the quantity of electric charge on the electron:
q_e = 1.602 × 10^-19 coulombs)
and net mass of about 4 amu (the mass of the electron is only about 1/1836 of that of the proton and therefore contributes little to the total nuclear mass). At first it was believed that the electrons must exist free in the nucleus, since the emitted beta particles had been identified as electrons and because of their such high velocity precluded them from arising from the outer shell of electrons. Later, it was shown that free electrons cannot exist in the nucleus. Instead, they are firmly bound into the neutron. Today, nuclear physicists no longer think of the neutron as composed of a proton and an electron, but instead regard it as a fundamental particle in its own right. Also it is now known that the neutron can disintegrate when freed from its parent nucleus; the free neutron eventually changes into a proton by emitting a beta particle (and also a neutrino); the half-life T for the decay being about 12 minutes. But when inside the nucleus of a radioactive atom, the neutron does not act as it does in a free state. It remains stable except in certain radioactive transformations where beta emissions can be ascribed to a decay of a neutron. In this way no free electrons are needed to be considered to be within the nucleus, thus avoiding the many difficulties which this concept has raised. According to this modification of Rutherford's suggestion, the nucleus of every atom of every element contains a certain number of neutrons and protons. The total number of protons determines the atomic number of the element (designated by Z) and thus is the number of positive charges in the nucleus, that is, the proper nuclear charge is (+)Zq_e. The same number Z is also the number of electrons outside the nucleus of a neutral atom. Thus Z number determined the chemical properties of the element. Rutherford also postulated that the proton and the neutron have the same mass. Hence, the atomic mass (amu) of an isotope of an element (designated by A) was accounted for by the total number of nucleons, the name given collectively to the protons and neutrons. The number of neutrons (designated by N) in an isotope was equal to the difference between the atomic number and the mass number, that is, N = A - Z.
As was the case with many particles of matter, the existence of the neutron was suggested by theoretical considerations long before experimental confirmation was reached. A neutron is a very difficult particle to detect, since it carries no electric charge. It is not subject to electric or magnetic fields and cannot be deflected by them, and, hence, they are very penetrating. Thus they cannot be detected in cloud chamber because it produces no ionizing effect, leaving no cloud trail. In all these properties it resembles x-ray radiation. Its presence can be detected only when it strikes a nucleus. It took 10 years before direct evidence for the neutron was actually produced. In 1930 it was reported that when alpha particles given off by radioactive source of polonium struck a target of a sheet of beryllium, it emitted a radiation so penetrating that it was thought at first to consist of high-energy x-rays or gamma radiation. In 1932 the French physicists Frederic Joliot and his wife Irene Curie (the daughter of the discoverer of radium) noted that this reaction within beryllium which produced a very penetrating type of radiation, when it would impinge upon a sheet of paraffin (a hydrocarbon rich in hydrogen and carbon) it in turn caused protons to be emitted in large quantities with high energy. Their velocities could be measured by an ionization chamber. Immediately after the publication of their results, James Chadwick (1891-19??), who worked with Rutherford, pointed out that gamma rays could not eject the protons with the high speeds observed unless gamma rays behaved differently from electromagnetic radiation and had energies 10 times larger than the incident alpha particles. Chadwick showed in his 1932 paper "The existence of the neutron" that to balance the momentum and energy equations, the radiation from the beryllium could only be accounted for by assuming that it consisted of neutral particles having the same mass as a proton, and that they were neutrons. The reaction producing neutrons by bombarding beryllium with alpha particles can be expressed by the expression
₂He⁴ + ₄Be⁹ → ₆C¹² + ₀n¹,
where the term ₀n¹ represents a neutron with atomic number of zero (it has no positive charge) but has a mass number of one (the same mass as the proton). Note that the total mass (that is, the total number of nuclear particles or nucleons = 13) entering into the reaction is the same as leaving the reaction. Thus atomic mass is conserved in the reaction. This is true of all nuclear reactions, whether artificial or natural. This reaction produced a common isotope of carbon, ₆C¹², by transmuting the beryllium into carbon, like the transmutation of nitrogen into oxygen. Not enough carbon was produced by the bombardment to obtain direct evidence of its existence, but its existence can be inferred from the principles of conservation of charge and mass.

NATURAL RADIOACTIVITY.
Natural radioactivity usually results in the emission of alpha particles and gamma rays (high energy x-rays that have zero rest mass). Thus, the disintegration of radium is
₈₈Ra²²⁶ → ₈₆Rn²²² + ₂He⁴ + γ,
where ₈₆Rn²²² is an inert radioactive gas called radon and Greek letter γ represents the gamma radiation. There are three series of naturally radioactive elements which form a sequence of parent-daughter relationships: the uranium, the actinium, and thorium series. The uranium series is called the 4n + 2 series because the mass numbers of the atoms in it are given by this expression. The quantity n is an integer which decreases by unity in going from any radioelement to the next one below it. The actinium series can be represented by 4n + 3, and that of thorium by 4n. The value of n is not the same for the first element in each series.

The Uranium Series
Radioactive Element	Decay Emission	Half-life T
UI, ₉₂U²³⁸	α	4.51 × 10⁹ years
UX₁, ₉₀Th²³⁴	β, γ	24.1 days
UX₂, ₉₁Pa²³⁴	β, γ	1.18 minutes
UII, ₉₂U²³⁴	α	2.48 × 10⁵ years
Io, ₉₀Th²³⁰	α, γ	8.0 × 10⁴ years
Ra, ₈₈Ra²²⁶	α, γ	1620 years
Rn, ₈₆Rn²²²	α	3.82 days
RaA, ₈₄Po²¹⁸	α	3.05 minutes
RaB, ₈₂Pb²¹⁴	β, γ	26.8 minutes
RaC, ₈₃Bi²¹⁴	β, γ	19.7 minutes
RaC′, ₈₄Po²¹⁴	α	1.64 × 10^-4 seconds
RaD, ₈₂Pb²¹⁰	β, γ	19.4 years
RaE, ₈₃Bi²¹⁰	β	5.0 days
RaF, ₈₄Po²¹⁰	α, γ	138.4 days
RaG, ₈₂Pb²⁰⁶	(Stable Lead)

The Thorium Series
Radioactive Element Decay Emission Half-life T

Th, ₉₀Th²³² α 1.39 × 10¹⁰ years

MsTh 1, ₈₈Ra²²⁸ β 6.7 years

MsTh 2, ₈₉Ac²²⁸ β 6.13 hours

RdTh, ₉₀Ra²²⁸ α 1.90 years

ThX, ₈₈Ra²²⁴ α 3.64 days

Tn, ₈₆Em²²⁰ α 54.5 seconds

ThA, ₈₄Po²¹⁶ α 0.16 seconds

ThB, ₈₂Pb²¹² β 10.6 hours

ThC, ₈₃Bi²¹² α β 47 minutes

ThC', ₈₂Po²¹² α 3.0 × 10^-7 seconds

ThC'', ₈₁Tl²⁰⁸ β 2.1 minutes

ThD, ₈₂Pb²⁰⁸ (Stable Lead)

Some natural radioactive reactions involve the emission of beta particles (high energy electrons emitted from the nucleus). When this occurs, the atomic number Z is raised, since the emission of a negative charge leaves an additional positive charge on the nucleus, although the atomic mass is unchanged (the mass of the electron being considered negligible compared to the mass of the nucleons). Thus, one isotope of uranium, ₉₂U²³⁹, disintegrates according to the following reaction:
₉₂U²³⁹ → ₉₃Np²³⁹ + e^-,
where ₉₃Np²³⁹ is the isotope of the element neptunium which has the same mass as the uranium but is one higher in atomic number and therefore chemically distinct from uranium. Later on, we will see that this reaction must be modified by the addition of another particle, the neutrino, which is also emitted along with the electron. The neutrino carries no charge and has zero rest mass. It therefore affects neither the atomic number nor the atomic masses of the nuclei involved.

PARTICLE ACCELERATORS.
Up to 1932 the investigation of atomic nuclei was performed first by the study of naturally occurring spontaneous disintegration of the massive nuclei of the heavy elements uranium and thorium, or by observing of what happens when the high-speed alpha and beta particles from the naturally occurring radioactive elements bombarded various other elements, as in Rutherford's transmutation experiments with alpha particles. A third method was introduced, that is, the bombardment with charged particles, such as protons (₁H¹) and deuterion (₁H²), that was given very high speeds by artificial means. One of the great advantages of this method is that the particles which are produced and their speeds are controlled by the experimenter. The first to use this method successively were J. D. Cockcroft and E. T. S. Walton, also of Rutherford's Cavendish Laboratory. Protons were produced in the form of hydrogen ions in a discharge tube and accelerated by a potential difference of 600,000 volts. When in 1932 the beam of charged particles was directed onto a target of lithium, particles were emitted from the lithium that appeared to be alpha particles, as seen by their scintillations on a fluorescence screen, or by their tracks in the cloud chamber, etc. The nuclear reaction is given by the equation
₃Li⁷ + ₁H¹ → ₂He⁴ + ₂He⁴;
that is, each lithium nucleus absorbs a proton and at once splits into two alpha particles, or helium nuclei.
Many types of devices were invented for accelerating the charged particles to be used in the disintegration experiments. One of the most useful of particle accelerating instruments is the cyclotron, constructed in 1931 by E. O. Lawrence and M. S. Livingston at the University of California. The instrument consisted of a round flat metal box cut into two halves along a diameter of the box to form two D-shaped sections. These sections are placed into an evacuated chamber between the two poles of an electromagnet. The two halves or "dees" are connected to a high frequency electric generator, so that the potential difference between the dees changes sign several millions times per second. Near the center between the dees is a source of positively charged particles - protons, deuterion, or heavier particles. As the positively charged particles leaves the source they are attracted by negatively charged dee accelerating them toward the negative charged dee. But the magnetic field deflects them into a semicircular path. As the particle crosses the gap between the two dees the potential difference on the dees reverse and the particles are attracted in a reverse direction and accelerated toward the opposite dee. As the speed of particle increases the radius of their circular orbit increases and in successive orbits they spiral outwards from the center. At last the particles reach the periphery where they hit a target or, with a auxiliary electric field are deflected out through a thin window. The energy given to the particles at each crossing of the potential difference between the two dees accumulates until a beam from a modern cyclotron emerges with total energies per particle up to several hundred million electron volts. The unit used to measure the kinetic energy of the particles is called the electron-volt. One electron volt (1 ev) is defined as the amount of energy acquired by an electron as it falls through a potential difference of 1 volt. This is equivalent to 1.602 × 10^-19 joules, since the charge on the electron is 1.602 × 10^-19 coulombs. Thus
1 ev = (1.602 × 10^-19 coulombs) × (1 volt) = 1.602 × 10^-19 joules,
since 1 volt is equal to 1 joule per coulomb. This unit is too small for convenience in nuclear physics, so an unit of one million electron volts (Mev) is used and is equal to 1.602 × 10^-13 joules. Cockcroft's and Walton's original accelerator succeeded in accelerating protons to only 0.6 Mev, but that was sufficient to produce the nuclear reaction. Atomic mass can be expressed in Mev by using the mass-energy equivalence relation of the Special Theory of Relativity, that is, E = mc², so that 1 kgm is equal to
(2.9979 × 10⁸)² joules or 8.987 × 10¹⁶ joules.
Thus 1 amu = 1.66 × 10^-27 kgm = 1.492 × 10^-10 joules = 931 million electron volts = 931 Mev. And
1 ev = 1.074 × 10^-9 amu.
ARTIFICIAL RADIOACTIVITY AND POSITRONS.
Since 1934 a very large number of radioactive isotopes have been produced, and radioactive forms of the elements become known, The beta rays emanating from many of the radioactive isotopes are not just negatively charged electrons, but are also positrons, particles having the same mass m_e and quantity of charge q_e as the electron, but are positively charged. Neither of the positive or negative charged electrons are present in the nucleus, but they may be created, during radioactive decay, as a means of releasing energy. Charge is strictly conserved during the positron emission; the atomic number is decreased by one unit in this mode of decay. For example, when the radioactive isotope of phosphorus isotope ₁₅P³⁰ decays, it emits positrons to form stable atoms of silicon ₁₄Si³⁰. In 1934 when Irene Curie and F. Joliot were studying the effect of alpha particles upon the nuclei of light elements, they bombarded aluminum with alpha particles; neutrons were produced as expressed by the equation
₁₃Al²⁷ + ₂He⁴ → ₁₅P³⁰ + ₀n¹.
But in addition to the neutrons, another particle, a positively charged electron, called the positron, was also observed to come from the metal target. The positron whose symbol is (+)₁e⁰ had been discovered in 1932 by C. D. Anderson; it had been observed in a cloud chamber while studying cosmic rays and was identified by its electron like track which curved in the applied magnetic field as would a positive charged particle. The positrons were produced by the interaction of high-energy gamma radiation with matter. The energy of the gamma rays may be converted into a positron-electron pair, two particle with opposite charge but similar in all other respects. This process is a direct confirmation of the mass-energy equivalence predicted by Einstein's Special Theory of Relativity. The minimum energy that the gamma rays must have in order to produce the "pairs" is twice that equivalent to the "rest" energy of an electron; any excess goes into the kinetic energy of the particles. The inverse of this process may occur; when a positron and an electron meet, they may "annihilate" each other, with the production of a gamma ray. Since electrons and positrons may be created by a process outside the nucleus, it is not unreasonable to suppose that either may be created within the nucleus.
Now the Joliots had found positrons as a result of alpha bombardment. The emission of the positrons did not cease as the neutron emission did when the bombardment of the aluminum by alpha particles was stopped. "The foil remains radioactive, and the emission of the (+)₁e⁰ decays exponentially as for an ordinary radio-element." The Joliots pointed out that the isotope ₁₅P³⁰ of phosphorus was required in the equation to explain the emission of the neutrons and that it had also been identified by chemical analysis of the target foil, but it had never been observed in nature. It therefore was reasonable to conclude that the isotope ₁₅P³⁰ was a short-lived radioactive material, spontaneously decaying with the emission of a positron, as expressed by the equation
₁₅P³⁰ → ₁₄Si³⁰ + (+)₁e⁰.
By experiment it was determined that the half-life of this artificial radioactive isotope is 2.5 minutes and it produced a daughter-product that is a common isotope of silicon and is stable. Since all nuclei are assumed to consist of protons and neutrons, it must be assumed that a proton in the nucleus of ₁₅P³⁰ can break up into a neutron which remains in the nucleus and a positron and a neutrino, which are at once expelled from the nucleus.
BINDING ENERGIES AND NUCLEAR STABILITY.
The nuclei of atoms seem to be composed of protons and neutrons, particles which themselves possess substructures. The number of protons in a nucleus is its atomic number Z, and the sum of number of protons and number of neutrons is its mass number. At very short distances, of the order of 10^-13 centimeters, these particles must attract each other sufficiently to provide a cohesive force that holds the nucleus together. Work must be done to separate a nucleus into its constituent protons and neutrons, and the quantity of such work is a measure of the stability of a particular nucleus. This quantity of work is called the "binding energy", an amount of energy that a nucleus does not have in comparison with the total energy of its separated protons and neutrons. This is analogous to the energies involved in the formation of chemical compounds, but the amount of work required to separate the components of nuclei is generally much more than a million times greater than that needed to separate the constituent atoms of molecules. The energies of nuclear reaction are about a million times greater than those of chemical reactions, on the average.
A quantitative measure of nuclear binding energy is found by measuring what is called mass defect. The masses of the neutron and the proton, as these particles exist outside the nucleus, are known:
m_proton = 1.00814 amu,
m_neutron = 1.00898 amu.
If these particles correspond to Prout's universal atomic building blocks, then the sum of their masses present in the nucleus, calculated with these numbers, should correspond exactly to the mass of the nucleus. Now the nuclear masses have been determined very accurately with mass spectrometers; for nuclei of all kinds it was found that this sum is greater than the measured value, and it is the difference that is called mass defect.
The alpha particle or helium nucleus, for example, contains two neutrons and two protons (₂He⁴). Its mass is known to be 4.00396 amu. The sum of the masses of the two protons and two neutrons, calculated from the given values above, is 4.03424 amu. This sum is greater than the measured mass by 0.03028 amu, the mass defect of the helium nucleus. Since mass is equivalent to energy, this mass difference as energy may be calculated and it corresponds to 0.0303 × 931 = 28.2 Mev of energy. This is known as the binding energy of the protons and neutrons in the alpha particles. To break up the nucleus into its constituents, 28.2 Mev of energy would have to be supplied. Conversely, if somehow the helium nuclei can somehow be synthesize from neutrons and protons, 28.2 Mev of energy would be released per nucleus formed. For comparison with chemical energies, the energy released in the combustion of one carbon atom to form carbon dioxide is only 4.4 ev, more than six million times smaller.
Relatively few of the infinite number of mathematically possible combinations of protons and neutron actually form stable nuclei. Many of the stable nuclei of lighter elements contain equal number of protons and neutrons, for example, ₂He⁴, ₅B¹⁰, ₈O¹⁶, ₁₀Ne²⁰. As we go to heavier elements, the neutrons become increasingly more numerous than the protons; for example, ₅₂I¹²⁷ has 52 protons and 74 neutrons, and ₈₂Pb²⁰⁶ has 82 protons and 124 neutrons. The isotope of uranium, ₉₂U²³⁸, which is not a stable nucleus, has 92 protons and 146 neutrons. It appears that the specifically nuclear forces, those responsible for holding the nucleus together, act most strongly on the light nuclei containing equal numbers of protons and neutrons, even though at the very short distances of separation within a nucleus the protons must repel each other strongly because of their like charges. This repulsion would account for the relative shortage of protons and excess of neutrons found among stable nuclei of high atomic number. Among the very heaviest atoms, this same strong repulsive force becomes reflected in the radioactivity instability. For all elements of atomic number 84 and above, no excess of neutrons, which contribute only attractive force, is sufficient to offset this repulsive force entirely.
The binding energy of any nucleus is a measure of its stability, although not directly. The binding energies of very heavy nuclei are higher than those of lighter nuclei simply because they contain more particles, but they are not necessarily more stable. To compare the stabilities of different nuclei, the binding energy per particle, that is the total binding energy divided by mass number, is used. These quantities can be plotted against the mass numbers. The points shown correspond to the most stable nuclei known for each of the mass numbers considered; the points have been derived from the results of many careful mass measurements. When the binding energy axis is arranged negatively, the lowest point corresponds to nuclei of greatest binding energy per particle, hence with greatest stability. It should be noted that the nuclei of greatest stability have mass numbers in the range 50 to 60 (iron and nickel) although the region of greatest binding energy per particle forms a rather wide and shallow trough. Matter in its state of lowest energy would contain only atoms whose nuclei lie within this trough.
This curve will show what general kinds of nuclear reactions may be expected to release energy. When a heavy nucleus emits an alpha particle, for example, the mass number is decreased; the new atom lies farther toward the left along the curve and has less energy. Remember that binding energy corresponds to energy given up when a nucleus is formed, so that nuclei of high binding energy contain less energy than those of lower binding energy. If an atom of very high mass number could somehow be split in two, the new nuclei would necessarily lie closer to the stability "trough" than the original. Splitting, or fission reactions, in heavy nuclei should therefore release energy. Note that the very lightest nuclei have smaller binding energies per particle than nuclei that are somewhat heavier. Accordingly, if light nuclei could somehow be made to combine to form heavier ones, in a fusion reaction, energy should also be released.
NUCLEAR FISSION.
The atomic bomb or, more accurately, the nuclear bomb, involves a nuclear reaction in which a neutron strikes an atom of uranium setting off a chain reaction causing the uranium atoms to "fission". Early in 1938 two German physical chemists, Otto Hahn (1879-1968), formerly an assistance of Rutherford, and Friz Strassmann (1902-?) found in the neutron-bombardment of uranium caused the fission of the uranium. A typical fission reaction is the following one, involving uranium 238:
₀n¹ + ₉₂U²³⁸ → ₉₂U²³⁹ → ₅₆Ba¹⁴⁵ + ₃₆Kr⁹² + ₀n¹ + ₀n¹,
where the intermediate uranium isotope ₉₂U²³⁹ is first formed and then it breaks down into two large fragments, barium and krypton nuclei, plus two neutrons, each of which is available as a "bullet" to disintegrate other neighboring atoms of uranium, carrying on the chain reaction. There are many possible ways in which atoms split. On January 16, 1939, two Austrian physicists, Miss Lise Meitner (1878-1968), formerly Hahn's colleague, and Otto R. Frisch, both at that time in Sweden as a refugees from Nazi Germany, in a paper of that date, proposed that the neutron initiated an explosion of an uranium nucleus into "two nuclei of roughly equal size", a process that they referred to as nuclear fission. The fragments were predicted to have great kinetic energy and would be radioactivity, which would account for the beta-emissions. These predictions were quickly fulfilled by experiment and the following equation is the nuclear fission of ₉₂U²³⁵.
₉₂U²³⁵ + ₀n¹ → ₅₆Ba¹⁴⁰ + ₃₆Kr⁹⁴ + 2₀n¹ + 200 Mev,
where the two nuclei of barium ₅₆Ba¹⁴⁰ and krypton ₃₆Kr⁹⁴ are not found in nature and are unstable; they are radioactive and decay into stable isotopes with the emission of beta particles, β. This is what makes possible the controlled chain nuclear reaction of a nuclear reactor, or pile, and the uncontrolled reaction in the nuclear bomb. Only a few kinds of nuclei are so readily fissionable that they can maintain a chain reaction; and ₉₂U²³⁵, an isotope of only 1 percent of naturally occurring uranium, is the only one that is found in nature. Other fissionable materials have been manufactured in quantity, among which is notably ₉₂U²³³ and ₉₄Pu²³⁹, an isotope of the new transuranic element called plutonium. The first of these two isotopes is produced in a nuclear reactor by the reaction of neutrons and thorium, and the second is made similarly from the abundant isotope of uranium ₉₂U²³⁸.

The Thorium Series
Radioactive Element	Decay Emission	Half-life T
Th, ₉₀Th²³²	α	1.39 × 10¹⁰ years
MsTh 1, ₈₈Ra²²⁸	β	6.7 years
MsTh 2, ₈₉Ac²²⁸	β	6.13 hours
RdTh, ₉₀Ra²²⁸	α	1.90 years
ThX, ₈₈Ra²²⁴	α	3.64 days
Tn, ₈₆Em²²⁰	α	54.5 seconds
ThA, ₈₄Po²¹⁶	α	0.16 seconds
ThB, ₈₂Pb²¹²	β	10.6 hours
ThC, ₈₃Bi²¹²	α β	47 minutes
ThC', ₈₂Po²¹²	α	3.0 × 10^-7 seconds
ThC'', ₈₁Tl²⁰⁸	β	2.1 minutes
ThD, ₈₂Pb²⁰⁸	(Stable Lead)

NUCLEAR FUSION.
If very light atoms can be combined (fused) to form heavier atoms, then energy will be released. This kind of thermonuclear reaction can occur only at very high temperatures; the particles must be traveling at enormous speeds to get close enough to react despite their mutual electrical repulsion. Thus far, such reaction have been studied in detail only by use of the high-energy particles produced by cyclotrons and other accelerating machines. In the so-called "hydrogen" bomb, a fission ("atomic") bomb is used to provide the high temperature necessary for the initiation of thermonuclear reactions. Sufficiently high temperatures occur in the sun and other stars, and nuclear fusion is almost certainly the source of stellar energy.

Until recently it was difficult to conceive of a mechanism to explain how the sun and other stars should keep on pouring out such enormous quantities of energy over a period of billion of years. If the source was any chemical reaction, all the material would be consumed after a few thousand years. Even a nuclear fission cannot be held responsible, because of the low abundance in the sun of the elements that undergo fission. In fact, the main part of the sun's mass consists of the light elements, hydrogen and helium accounting for 90 percent of its mass. The present thinking about the source of the energy of the sun and other stellar bodies is a thermonuclear reaction in which hydrogen nuclei are transmuted into helium nuclei in cyclic sequence, such as the so-called proton-proton chain, consisting of three steps:
(a) ₁H¹ + ₁H¹ → ₁H² + (+)₁e⁰ + γ,
(b) ₁H² + ₁H¹ → ₂He³ + γ,
(c) ₂He³ + ₂He³ → ₂He⁴ + ₁H¹ + ₁H¹.
In the first step two protons fuse into deuterion, with the emission of a positron and radiant energy in form of gamma radiation. In the second step the deuterion thus formed reacts with another proton to form a light isotope of helium called tritium, ₂He³. Finally in the third step, two light helium nuclei so generated fuse to form a highly staple form of helium which is also called alpha particle and two protons. Note that two reaction in step (a) must take place so that the reaction in step (c) may occur. As a result four protons produces two tritium atoms. And two occurrences of the reaction in step (b) must occur so that the reaction in step (c) may occur. That is, two tritium nuclei must be produced so that one helium nuclei ₂He⁴ may be formed. The net result of this cycle of five fusion reactions is that four protons have been converted into one alpha particle and two positrons (the latter will soon encounter two electrons and produce two gamma photons). Also a good amount of energy is made available by these reactions, as is made clear by comparing the rest masses after and before the reactions:

AFTER THE CYCLE:

Mass of alpha particle = 4.0027 amu

Mass of 2 positrons = 0.0011 amu

----------

Sum = 4.0038 amu

BEFORE THE CYCLE:

Mass of 4 protons = 4.0304 amu

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Difference = -0.0266 amu

The reduction in rest mass by nearly 0.027 amu is accompanied by the release of 0.027 × 931 = 25 Mev of energy, some as gamma photons but most in the form of kinetic energy of the particles produced. The particles involved in these reactions will be in a high state of agitation as shown by the high corresponding temperatures. This would account for the high temperature of the sun, which is believed to be twenty million degrees Celsius. It is estimated that only about 1 percent of the sun's mass is consumed in a billion years; still, many million of tons of its mass is "lost" into space each minute. In the sun, the high temperature assures the speeds of approach of the nuclei necessary for the fusion. On earth, the high speeds of the atoms of the material necessary for a fusion reaction to occur in it can be obtained by heating the material initially by means of a violent explosion - perhaps an explosive fission reaction set off in the sample. Such a thermonuclear reaction is one of the processes involved in the so-called "hydrogen bomb" or "H-bomb", first tested in 1952, in which hydrogen fusion reactions was kindled by sudden local heating from the explosion of a small "atom" or fission bomb. The fusion process utilized may be a single reaction instead of the three step sequence or process that was believed to occur in the sun. Three possibilities are
₁H² + ₁H² → ₂H³ + ₀n¹, Q = 3.3 Mev,
₁H² + ₁H² → ₁H³ + ₁H¹, Q = 4.0 Mev,
₁H² + ₁H³ → ₂He⁴ + ₀n¹, Q = 17.6 Mev.
The hydrogen isotope ₁H³, tritium, is not found in nature in significant amounts, but can be manufactured for example by letting deuterium (₁H²) absorb low speed neutrons.

AFTER THE CYCLE:
Mass of alpha particle	=	4.0027 amu
Mass of 2 positrons	=	0.0011 amu
		----------
Sum	=	4.0038 amu
BEFORE THE CYCLE:
Mass of 4 protons	=	4.0304 amu
		----------
Difference	=	-0.0266 amu