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p. xxiip. 11. A new science is bornlocked

  • Maxwell Irvine

Abstract

By the end of the nineteenth century, it was clear that matter had an atomic structure, but the precise structure of the atoms and the reasons for their exact masses were a complete mystery. ‘A new science is born’ charts the development of atomic theory through the early twentieth century. Ernest Rutherford laid the foundations of the new science of nuclear physics, and in the early 1930s Cockcroft and Walton developed an accelerator which could increase the energy of charged particles, including alpha particles. Enrico Fermi and Leo Szilard developed the idea of a primitive self-sustaining reactor. The advances made by Paul Villard and Paul Dirac are explained.

By the end of the 19th century, it was clear that matter had an atomic structure and that relative weight could be attached to the atoms of different chemical elements. Many of these atomic weights were close to being integer multiples of the weight of the lightest element, hydrogen. However, there were many significant exceptions to this. It was known that the atoms contained electric charges and that, since most matter is electrically neutral, there must be a balance of positive and negative charges. The precise structure of these atoms and the reasons for their exact masses was a complete mystery. Chemists had developed a table listing the elements labelled by their measured atomic masses and electronic charges (Figure 1). This demonstrated a periodicity in the chemical properties of elements.

Only the naturally occurring elements are displayed in Figure 1. With the development of nuclear reactors and accelerators more than 20 man-made elements have been added to the actinide series – these are the transuranic elements. The elements are designated by their electronic charge numbers.

At the end of the 19th century, a time of tremendous scientific advance, two developments were to transform the situation. First, the discovery that certain materials emitted radiation, a phenomenon now called ‘radioactivity’, was to provide scientists p. 2

1. The periodic table of chemical elements

p. 3with probes to study subatomic structures. Second, the development of Einstein's theory of relativity and, shortly after, the emergence of quantum theory were to provide the intellectual framework for interpreting the structures that were revealed.

Einstein's theory of relativity revealed that ‘mass’ was simply another manifestation of ‘energy’. His equation E = Mc2, where E is the energy equivalent to a mass M and c is the velocity of light, became one of the most famous formulas in science.

There were three types of radioactive radiation discovered. The first to be identified were beams of exceptionally light, negatively charged particles, now known as electrons, discovered by the British physicist J. J. Thompson in 1897.

Thomson first identified electrons in experiments in a Crookes tube, a precursor to the modern TV cathode ray tube. Further study revealed that the electrons seen by Thomson were identical to the light, negatively charged particles emitted in radioactive decay.

In a series of studies begun in 1898, the New Zealand scientist Ernest Rutherford, working with Fredrick Soddy at McGill University in Canada, separated the radiation from radium into components according to their ability to penetrate matter and cause ionization. The least penetrative radiation, which Rutherford named ‘alpha rays’, had a positive electric charge. The electrons he called ‘beta rays’. Because alpha and beta rays had electric charges, their trajectories could be manipulated by passing them through electromagnetic fields. By studying these tracks, Rutherford was able to deduce relative charges and masses for the radiation. The electron was the lightest object to have ever been identified. Its mass was only 0.511 MeV. (In the subatomic world, it is usual to quote masses in energy units using Einstein's formula.) The energy standard is the electron-volt (eV), or approximately 1/2000th of the atomic mass of hydrogen, and its electric charge was −1.6 x 10−19 Coulombs. The alpha rays had a mass similar to that of the helium atom at 3,784 MeV, approximately four times p. 4heavier than hydrogen. The alpha particles had a positive charge that was twice the magnitude of that of the electron.

In 1900, the French scientist Paul Villard discovered an electrically neutral form of radiation similar to the X-rays discovered by Becquerel in 1896 which revealed them to be a particularly high-frequency form of electromagnetic radiation. Using Planck's energy frequency relationship E = hν‎, where h is Planck's constant and ν is frequency, X-rays corresponded to energies in the range 1 to 100 keV, while Villard's radiation was in the MeV range; Rutherford named these as ‘gamma rays’ in 1903.

The least penetrative radiation, the alpha rays, could be stopped in a sheet of cardboard; the beta rays were halted by a thin sheet of aluminium; while the most penetrative radiation, the gamma rays, required a high-density material like lead to halt their flow.

The alpha and beta particles carried an electric charge and hence could be accelerated in electric fields to produce more penetrative forms of radiation.

In 1907, Rutherford moved to the University of Manchester and continued his probing of matter with beams of alpha radiation. Working with an extraordinary group of exceptional scientists, Rutherford laid the foundations of the new science of nuclear physics.

First, in collaboration with Hans Geiger, he developed a detector for individual alpha particles. Then with John Nuttall and Ernest Marsden, he studied the scattering of alpha particle beams off thin gold films. In these experiments, some of the alpha particles were reflected back from the gold film. This indicated that they had encountered an object much more massive than themselves that had repelled them. The only things in the gold film were atoms of gold with an atomic mass number 190, almost 50 times heavier than the alpha particles. The atom was known to contain electric p. 5

2. Ernest Rutherford. Known as the ‘father of nuclear science’, Ernest Rutherford was born in Brightwater, New Zealand, 1871. He was awarded the Nobel Prize in 1908, while at the University of Manchester, for his investigations into the disintegration of the elements, and the chemistry of radioactivity. He died in Cambridge, UK, in 1937

p. 6charges, and Rutherford assumed that the repulsion was due to the familiar interaction between like charges, the positively charged alpha particles had encountered the source of the positive charge in the gold atom and it was associated with most of the mass of the atom.

Rutherford then developed a formula for the distribution of scattered alpha particles by a point concentration of positive charge which accurately reproduced the observations and allowed an estimate of the mass of the scattering centre. Thus Rutherford had demonstrated that all the positive charge in the gold atom was concentrated in a central core containing virtually all the mass of the atom.

This implied the existence of a new force in nature to add to the familiar classical forces of gravitation and electromagnetism. This force had to be attractive and much stronger than the electric repulsion between like charges in order to hold the nucleus together. It also had to be of extremely short range so as not to interfere in the scattering process.

If this was indeed the case, then Rutherford had a tool for obtaining an approximate measure of the size of this concentrated charge. The repulsive force between like electric charges is proportional to the two charges and inversely proportional to the square of the distance between them. However, at very short distances the force must change to reflect the stronger attractive force holding the positive charges in the atom together. Thus the Rutherford scattering formula should break down for alpha particle energies above E0 (Figure 3), the energy at which the distance of closest approach was equal to the radius of the concentration of the positive charges, RA. This was exactly what was observed. The early experiments by Rutherford and his colleagues in Manchester were restricted to alpha particles with the natural decay energy from radioactive elements. This meant that they could not explore the size of the nuclei but simply place an upper limit on their extent. When Rutherford moved to Cambridge, he was joined by John Cockcroft and Ernest Walton. p. 7

3. A schematic of Rutherford's model of alpha particle scattering

In the early 1930s, Cockcroft and Walton developed an accelerator which could increase the energy of charged particles, including alpha particles. With the more flexible beams, it was possible to obtain a clearer picture of nuclear sizes. The radii of nuclei were of order 10−15m and increased with the cube root of the mass number, RA = r0A1/3, where r0 was measured to be of order 10−15m. This is consistent with the close packing of a number of particles each of the same size r0.

The curve in Figure 3 represents the potential energy of interaction between the alpha particle and the nucleus. At large distances, this is the familiar repulsion between like charges. At short distances, less than RA, the alpha particle experiences the nuclear attractive force. Rutherford developed a classical, that is, pre-quantum theory, formula for the scattering of alpha particles from a point nucleus. For incident alpha particle energies E less than E0, the formula accurately replicated his experimental observations. For p. 8

4. Neutron beta decay

alpha particles (charge +2e) scattering from gold (charge 79e and mass number A=197), E0 = 5.5 MeV and RA =5.8 x 10−15m approximately.

The atomic nucleus could now be identified by two numbers: a nuclear mass number (A) and a charge number (Z). Only for hydrogen was A = Z = 1. The hydrogen nucleus was called the ‘proton’. For all heavier, stable nuclei, A was equal to or greater than 2Z. This suggested that the nucleus contained electrically neutral particles, now called neutrons, similar in mass to the protons. Assuming the number of neutrons is N, then A = N + Z. For the next 20 years, models of the nucleus were developed assuming the presence of these particles, until in 1932 James Chadwick, working with Rutherford in Cambridge, finally identified the neutron with a mass of 939.55 MeV compared with the proton mass at 938.256 MeV. The collective name for protons and neutrons is nucleons.

The discovery of the neutron answered two problems. First, atoms of the same Z (chemical element) could exist with different numbers of neutrons. These are called ‘isotopes’, meaning at the same place in the chemical periodic table. Thus a chemical sample could include a p. 9mixture of isotopes and the chemically measured atomic weight would then be the weighted average of the nuclear mass numbers and hence not an integer. For example, chlorine has Z = 17 and the isotopes chlorine‐35, −36, and −37 occur in nature with abundances 75.77%, traces, and 24.23%, respectively, leading to the atomic mass of 35.45. Second, since the neutron mass was greater than the proton mass by 1.29 MeV, which is more than the mass of the electron, it was possible to identify the source of beta decay as the decomposition of a neutron into a proton plus an electron. However, if this was the case then the electrons (beta particles) should all emerge with an energy of 0.78 MeV. In fact, the electrons appeared with a range of energies all less than 0.78 MeV, suggesting that some as yet unidentified object was simultaneously emitted.

This object had to be electrically neutral and of almost zero mass. In 1930, Wolfgang Pauli had postulated the existence of such a particle in order to explain the spectrum of beta decay energies. With Chadwick's confirmation of the neutron hypothesis, Enrico Fermi named this new particle the ‘neutrino’, or little neutron.

In 1930, Paul Dirac had speculated that the relativistic version of quantum mechanics seemed to allow for the existence of antimatter, that is, particles identical to those familiar in the laboratory but with their properties reversed. In 1932, Carl Anderson found cosmic ray tracks that looked like an electron but with a positive electric charge. This was the first antiparticle and was named the positron. While it is energetically impossible for a free proton to emit a positron and change itself into a neutron, within the nucleus an isotope could be formed with a depletion of neutrons such that this form of beta decay could be realized. The two forms of beta decay are designated β and β+ depending on whether an electron or positron is emitted.

It soon became clear that beta decay that resulted in the emission of an electron was accompanied by the emission of an antineutrino, while a positron was accompanied by the emission of a neutrino.

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5. Binding energy per nucleon for the most stable isotopes as a function of mass number A. The broken line indicates that all nuclei heavier than lead-208 are unstable

With virtually no mass and no electric charge, the detection of neutrinos is extremely difficult. Neutrinos are the most penetrative radiation yet detected, and antineutrinos are the dominant form of radiation emitted by a nuclear reactor. In 1956, a US group led by Cowen and Reines was able to detect the antineutrinos from a reactor the first time.

According to Einstein's mass–energy equation, the mass of any composite stable object has to be less than the sum of the masses of the parts; the difference is the binding energy of the object. In Figure 5, we display the measured binding energy per nucleon for the most stable isotopes. We see a generally smooth curve rising sharply in the light nuclei reaching a maximum of 8.8 MeV for iron-56 before falling to a value of 7.6 MeV for the heaviest naturally occurring isotope of uranium-238. All nuclei above lead-208 are radioactively unstable.

p. 11Among the very light nuclei, there are sharp peaks indicating significantly greater stability for the alpha particle (helium-4), the isotopes carbon-12 and oxygen-16. Other particularly stable nucleon numbers are indicated.

The general features of the binding energies are simply understood as follows.

We have seen that the measured radii of nuclei increased with the cube root of the mass number A. This is consistent with a structure of close packed nucleons. If each nucleon could only interact with its closest neighbours, the total binding energy would then itself be proportional to the number of nucleons. However, this would be an overestimate because nucleons at the surface of the nucleus would not have a complete set of nearest neighbours with which to interact (Figure 6). The binding energy would be reduced by the number of surface nucleons and this would be proportional to the surface area, itself proportional to A2/3. So far we have considered only the attractive short-range nuclear binding. However, the protons carry an electric charge and hence experience an electrical repulsion between each other. The electrical force between two protons is much weaker than the nuclear force at short distances but dominates at larger distances. Furthermore, the total electrical contribution increases with the number of pairs of protons.

The main characteristics of the empirical binding energy of nuclei exhibited in Figure 5 can now be explained. For the very light nuclei, all the nucleons are in the surface, the electrical repulsion is negligible, and the binding energy increases as the volume and number of nucleons increases. Next, the surface effects start to slow the rate of growth of the binding energy yielding a region of most stable nuclei near charge number Z = 28 (iron). Finally, the electrical repulsion steadily increases until we reach the most massive stable nucleus (lead-208). Between iron and lead, not only does the binding energy decrease so also do the proton to neutron ratios since the neutrons do not experience the electrical repulsion.

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6. Nucleus of radius RA containing nucleons with a range of interaction ro. Deeply imbedded nucleons can interact with all other nucleons within the interaction radius. Nucleons at the surface can only interact with those within the nucleus. The number of surface nucleons is proportional to the surface area of the nucleus, 4π‎RA2

This leaves the sharp peaks amongst the lightest nuclei and the residual peaks at specific numbers of neutrons and protons culminating in lead-208 (Z = 82, N-126). For an explanation of these peaks, we must turn to the quantum nature of the problem. In explaining the electronic structure of the atom, Bohr had demonstrated that, while in classical physics there was a continuum of electronic orbits, in the quantum analysis only a restricted number of orbits could be realized. These orbits form shells with each shell having a specific number of orbits in it. Filled shells corresponded to particularly stable electronic structures identified as the inert rare gasses. This shell structure explained the periodicity of the chemical properties of elements. In the nuclear case, a shell structure also exists separately for both the neutrons and the protons. The light nuclei helium-4, carbon-12, and oxygen-16 represent the first three doubly closed-shell nuclei. This shell structure continues with calcium-40, zirconium-90, and lead-208. While for the light nuclei helium-4 to calcium-40, these closed shells are occupied by equal numbers of neutrons and protons, as the nuclei get heavier the Coulomb repulsion term requires an increasing number of neutrons for stability, thus zirconium has Z = 40 and N = 50, while the heaviest stable nucleus, p. 13lead-208, has Z = 82 and N = 126. In the case of nuclei, the closed-shell nuclei are once more particularly stable. The nuclear periodicity does not strictly follow the chemical periodicity but is once more explained by the quantum analysis of allowed nucleon orbits inside the nucleus. Closed-shell nuclei are referred to as ‘magic number’ nuclei.

Finally, if we look at the two nucleon systems, we find that the dineutron and the diproton (helium-2) are not bound, while the neutron–proton system called the deuteron, or heavy hydrogen (hydrogen-2), is bound and found in nature. Thus there is a particular stability for nuclei with equal numbers of protons and neutrons. This is particularly obvious for the light nuclei, and for the heavier nuclei it becomes a balancing act between this nuclear symmetry between neutrons and protons and the additional electrical repulsion between the protons, as illustrated in Figure 7.

Figure 7 displays the isotopes of nuclei. The ‘most stable line’ of black squares represents the isotopes of Figure 5. All nuclei above calcium-40 (N = 20, Z = 20) have a neutron excess in the most stable isotopes.

As we move off the line of stable nuclei, by adding or subtracting neutrons, the isotopes become increasingly less stable indicated by increasing levels of beta radioactivity. Nuclei with a surfeit of neutrons emit an electron, hence converting one of the neutrons into a proton, while isotopes with a neutron deficiency can emit a positron with the conversion of a proton into a neutron. For the heavier nuclei, the neutron to proton ratio can be reduced by emitting an alpha particle. All nuclei heavier than lead are unstable and hence radioactive alpha emitters.

Radioactive decay is a spontaneous event and when it will occur for a given isotope cannot be predicted. However, for a large sample of identical isotopes a mean lifetime can be defined. We shall consistently refer to the half-life, denoted by t1/2. This is the p. 14

7. A chart of the nuclei

time over which half of the members of the sample will have decayed. Thus after two cycles, only one-quarter of the original isotopes will remain, and after three cycles only one-eighth will be present, and so on. Lifetimes vary considerably; a free neutron has a half-life of 15 minutes, tritium (hydrogen-3) 12.32 years, p. 15radio-carbon (carbon-14) 6,000 years, and uranium-238 4.5 billion years.

The decay of uranium-238 is illustrative:

U238 -α‎‐〉Τ‎h234-β-〉Pa234-β-〉U344-α‎-〉Th230-α‎-〉Ra226-α‎-〉Rn222-α‎-〉Po218-α‎-〉Pb214-β-〉Bi214-α‎-〉Ti210-β-〉Pb210-β-〉Bi210-β-〉Po210-α‎-〉 Pb210 (stable)

Here the nomenclature indicate that uranium-238 decays by alpha particle emission to form thorium-234, which in turn emits an electron to become palladium-234, and so on.

The fact that almost all the radioactive isotopes heavier than lead follow this kind of decay chain and end up as stable isotopes of lead explains this element's anomalously high natural abundance. The existence of isotopes heavier than lead is due to the long half-life of uranium-238, comparable to the age of the solar system.

We have seen that Rutherford was able to develop a classical scattering formula to explain alpha particle scattering from heavy nuclei. In 1928, George Gamow used the new quantum mechanics to describe alpha decay. The only possible source of the alpha particles was the nucleus. Quantum mechanics introduces the concept of the Heisenberg uncertainty principle which limits the precision with which the position and the momentum of a particle can simultaneously be known. If the alpha particle was constrained to be in the nucleus, its position was known to within the size of the nucleus (Figure 8). Quantum theory required the momentum of the alpha particle to be correspondingly uncertain. Thus while a classical particle would be trapped in the nucleus forever, a quantum particle would have an uncertain momentum and hence the possibility of escaping. Gamow calculated the relationship between the energy of an emitted alpha particle and p. 16

8. Gamow's model for alpha decay. For uranium-238, the parameters are RA = 6.2 x 10−15m and E0 = 5.9 MeV

the half-life of the decay and was able to replicate the experimental results of Geiger and Nuttall.

Figure 5 clearly shows that as heavy nuclei decay, they release energy, and that if the light isotopes of hydrogen are combined to form helium-4, carbon-12, or oxygen-16, energy is also released. The former is exploited in an atomic bomb or a thermal nuclear reactor; the latter is used to produce hydrogen bombs and is currently being developed to create a fusion reactor. We will explore both systems in this volume.

Spurred on by Curie and Joliot's demonstration that radioactivity could be induced in previously stable nuclei by bombarding them with radioactive radiations, Otto Hahn and Lise Meitner were joined in Berlin by Fritz Strassman in 1929 to continue to p. 17

9. Fission fragment yields from uranium-235. The solid curve represents the fragment yields induced by slow, thermal neutrons (keV). The points represent yields from fast neutrons (MeV) released in fission

investigate the phenomenon. Chadwick's 1932 discovery of the neutron led the Berlin group to investigate radioactivity induced by neutrons. They found that uranium could be induced to undergo a new form of decay. Instead of simply spitting out small objects such as alpha or beta particles, the uranium split into two large fragments. Enrico Fermi, working in Rome, began a series of studies of material bombarded by neutrons and discovered not only was energy released, but because the lighter fission fragment isotopes have a smaller neutron excess than uranium (Figure 7), a number of neutrons were simultaneously emitted. The fission fragments were not of equal size but favoured the particularly stable structures around the atomic numbers 90 and 140 (Figure 9).

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10. Enrico Fermi, builder of the first atomic pile (nuclear reactor). Fermi was awarded the Nobel Prize in 1938 for his demonstrations of the existence of new radioactive elements produced by neutron irradiation and for his related discovery of nuclear reactions brought about by slow neutrons while working at the University of Rome. He was born in Italy in 1908 and died in the USA in 1958

In 1933, the Hungarian scientist Leo Szilard had speculated about the possibility of nuclear chain reactions and now Fermi was quick to see the possibility of realizing this with neutron-induced fission of uranium. Leaving Europe for the USA ahead of the Second World War, Fermi continued his studies at Columbia University with Szilard and developed the idea of a primitive self sustaining reactor. However, his early studies convinced him that such a device had to be much larger than his research facilities would allow.

The exigencies of war were about to change the whole pace of development.