Nuclear Energy

    The purpose of this webpage entitled Nuclear Energy is to provide a non-technical introduction to some of the most important concepts of physics required for a general  understanding of the generation of energy through the use of the fission of the nucleus of Uranium 235 (U235). Inherent in any discussion on the structure of matter and certainly in the discussion of the production of electrical energy through the fission of nuclear material are some of the topics of modern physics: Quantum Mechanics and Special Relativity.
    In this introduction to nuclear physics we shall consider only those laws of mechanics, thermodynamics and hydraulics which can appropriately be discussed in the guise of “Rational Mechanics”, and we will use the concepts which form the basis of modern Physics: Quantum Mechanics and Special Relativity only when absolutely necessary to impart the information needed to the reader to continue the study in this white paper.
    The discovery of fission in 1939 was and event of epochal significance in the annals of physics because it ushered in the age of the atom.  This discovery opened up the prospect of an entirely new source of power utilizing the internal binding energy of the atom.
    The operation of a nuclear reactor depends upon various interactions of neutrons with atomic nuclei.  In order to appreciate the complexities of a nuclear reactor it is desirable to consider briefly some of the fundamental of atomic and nuclear physics.  This paper was produced to provide such an introduction.


    1.1   History of Structure of Matter
    Early Greek philosophers speculated that the earth was made up of different combinations of basic substances, or elements. They considered these basic elements to be earth, air, water, and fire. Modern science shows that the early Greeks held the correct concept that matter consists of a combination of basic elements, but they incorrectly identified the elements.
    In 1661 the English chemist Robert Boyle published the modern criterion for an element. He defined an element to be a basic substance that cannot be broken down into any simpler substance after it is isolated from a compound, but can be combined with other elements to form compounds. To date, 105 different elements have been confirmed to exist, and researchers claim to have discovered three additional elements. Of the 105 confirmed elements, 90 exist in nature and 15 are man-made.
    Another basic concept of matter that the Greeks debated was whether matter was continuous or discrete. That is, whether matter could be continuously divided and subdivided into ever smaller particles or whether eventually an indivisible particle would be encountered. Democritus in about 450 B.C. argued that substances were ultimately composed of small, indivisible particles that he labeled “atoma”. He further suggested that different substances were composed of different atoms or combinations of atoms, and that one substance could be converted into another by rearranging the atoms. It was impossible to conclusively prove or disprove this proposal for more than 2000 years.
    The modern proof for the atomic nature of matter was first proposed by the English chemist John Dalton in 1803. Dalton stated that each chemical element possesses a particular kind of atom, and any quantity of the element is made up of identical atoms of this kind. What distinguishes one element from another element is the kind of atom of which it consists, and the basic physical difference between kinds of atoms is their weight.

    1.2   Subatomic Particles
    For almost 100 years after Dalton established the atomic nature of atoms, it was considered impossible to divide the atom into even smaller parts. All of the results of chemical experiments during this time indicated that the atom was indivisible. Eventually, experimentation into electricity and radioactivity indicated that particles of matter smaller than the atom did indeed exist.
    In 1906, J. J. Thompson won the Nobel Prize in physics for establishing the existence of electrons. Electrons are negatively-charged particles that have 1/1835 the mass of the hydrogen atom. Soon after the discovery of electrons, protons were discovered. Protons are relatively large particles that have almost the same mass as a hydrogen atom and a positive charge equal in magnitude (but opposite in sign) to that of the electron. The third subatomic particle to be discovered, the neutron, was not found until 1932. The neutron has almost the same mass as the proton, but it is electrically neutral.

    1.3  Bohr Model of the Atom
    The British physicist Ernest Rutherford postulated that the positive charge in an atom is concentrated in a small region called a nucleus at the center of the atom with electrons existing in orbits around it.
    Niels Bohr, coupling Rutherford’s postulation with the newly minted theories of quantum mechanics introduced by Max Planck, proposed that the atom consists of a dense nucleus of protons surrounded by electrons traveling in discrete orbits at fixed distances from the nucleus.
    An electron in one of these stationary orbits or shells has a specific or discrete quantity of energy (quantum). When an electron moves from one allowed orbit to another allowed orbit, the energy difference between the two states is emitted or absorbed in the form of a single quantum of radiant energy called a photon.
    The Quantum of energy emitted from this jump from one stationary state to another is given by the so called Plank formula:
    Where h = Planck’s constant = 6.63 x 10-34 J-s
    [latex]\nu[/latex]= frequency of the photon.
    Bohr’s theory was the first to successfully account for the discrete energy levels of this radiation as measured in the laboratory. Although Bohr’s atomic model was designed specifically to explain the hydrogen atom, his theories apply generally to the structure of all atoms. Additional information on electron shell theory can be found in any introductory book on Quantum Mechanics.

    1.4  Measuring Units on the Atomic Scale
    The size and mass of atoms are so small that the use of normal measuring units, while possible, is often inconvenient. Units of measure have been defined for mass and energy on the atomic scale to make measurements more convenient to express.
    The unit of measure for mass is the atomic mass unit (amu). One atomic mass unit is equal to 1.66×1024 grams. The reason for this particular value for the atomic mass unit will be made clear later in this introduction. Note that the mass of a neutron and a proton are both about 1 amu.
    The unit for energy is the electron volt (eV). The electron volt is the amount of energy acquired by a single electron when it falls through a potential difference of one volt. One electron volt is equivalent to 1.602×10-19  joules or 1.18 x10-19 foot-pounds.

    1.5  Nuclides
    The total number of protons in the nucleus of an atom is called the atomic number of the atom and is given the symbol Z. The number of electrons in an electrically-neutral atom is the same as the number of protons in the nucleus.
    The number of neutrons in a nucleus is known as the neutron number and is given the symbol N. The mass number of the nucleus is the total number of nucleons, that is, protons and neutrons in the nucleus. The mass number is given the symbol A and can be found by the equation
    A=  Z + N.
    Each of the chemical elements has a unique atomic number because the atoms of different elements contain a different number of protons. The atomic number of an atom identifies the particular element.
    Each type of atom that contains a unique combination of protons and neutrons is called a nuclide. Not all combinations of numbers of protons and neutrons are possible, but about 2500 specific nuclides with unique combinations of neutrons and protons have been identified. Each nuclide is denoted by the chemical symbol of the element with the atomic number written as a subscript and the mass number written as a superscript.
    Because each element has a unique name, chemical symbol, and atomic number, only one of the three is necessary to identify the element. For this reason nuclides can also be identified by either the chemical name or the chemical symbol followed by the mass number (for example, U-235 or uranium-235).
    Another common format is to use the abbreviation of the chemical element with the mass number superscripted (for example, U235). In this white paper the format used will usually be the element’s name followed by the mass number as a superscript.

    1.6  Isotopes
    Isotopes are nuclides that have the same atomic number and are therefore the same element, but differ in the number of neutrons. Most elements have a few stable isotopes and several unstable, radioactive isotopes. For example, oxygen has three stable isotopes that can be found in nature (oxygen16, oxygen17, oxygen18, and eight radioactive isotopes. Another example is hydrogen, which has two stable isotopes (hydrogen-1, hydrogen1 and hydrogen-2, hydrogen2,) and a single radioactive isotope (hydrogen-3, hydrogen3).
    The isotopes of hydrogen are unique in that they are each commonly referred to by a unique name instead of the common chemical element name. Hydrogen-1 is almost always referred to as hydrogen, but the term protium is infrequently used also. Hydrogen-2 is commonly called deuterium and Hydrogen-3 is commonly called tritium.

    1.7  Atomic and Nuclear Radii
    The size of an atom is difficult to define exactly due to the fact that the electron cloud, formed by the electrons moving in their various orbitals, does not have a distinct outer edge. A reasonable measure of atomic size is given by the average distance of the outermost electron from the nucleus.
    Except for a few of the lightest atoms, the average atomic radii are approximately the same for all atoms, about 2 x 10-8 cm.  Like the atom the nucleus does not have a sharp outer boundary. Experiments have shown that the nucleus is shaped like a sphere with a radius that depends on the atomic mass number of the atom.

    1.8  Nuclear Forces
    In the Bohr model of the atom, the nucleus consists of positively-charged protons and electrically neutral neutrons. Since both protons and neutrons exist in the nucleus, they are both referred to as nucleons. One problem that the Bohr model of the atom presented was accounting for an attractive force to overcome the repulsive force between protons.
    Two of the four forces present in the nucleus are;
    1.      Electrostatic forces between charged particles
    2.      Gravitational forces between any two objects that have mass.
    It is possible to calculate the magnitude of the gravitational force and electrostatic force based upon principles from classical physics.  Newton stated that the gravitational force between two bodies is directly proportional to the masses of the two bodies and inversely proportional to the square of the distance between the bodies. This relationship is shown in the equation below.
    Fg = (G x m1 x m2)/ r12
    Fg = gravitational force (newtons)
    m1 = mass of first body (kilograms)
    m2 = mass of second body (kilograms)
    G = gravitational constant (6.67 x 10 -11 N-m2/kg2)
    r = distance between particles (meters)
    The equation illustrates that the larger the masses of the objects or the smaller the distance between the objects, the greater the gravitational force. So even though the masses of nucleons are very small, the fact that the distance between nucleons is extremely short may make the gravitational force significant. It is necessary to calculate the value for the gravitational force and compare it to the value for other forces to determine the significance of the gravitational force in the nucleus. The gravitational force between two protons that are separated by a distance of 10-20  meters is about 10-24  newtons.
    Coulomb’s Law can be used to calculate the force between two protons. The electrostatic force is directly proportional to the electrical charges of the two particles and inversely proportional to the square of the distance between the particles.
    Coulomb’s Law is stated as the following equation:
    Fe = (K x Q1 x Q2 )/r12
    Fe = Electrostatic force (newtons)
    K = electrostatic constant (9.0 x 109 N-m2/C2)
    Q1 = charge of first particle (coulombs)
    Q2 = charge of second particle (coulombs)
    r12 = Distance between particles (meters)
    Using this equation, the electrostatic force between two protons that are separated by a distance of 10-20  meters is about 1012 newtons. Comparing this result with the calculation of the gravitational force (10-24 newtons) shows that the gravitational force is so small that it can be neglected.
    If only the electrostatic and gravitational forces existed in the nucleus, then it would be impossible to have stable nuclei composed of protons and neutrons. The gravitational forces are much too small to hold the nucleons together compared to the electrostatic forces repelling the protons. Since stable atoms of neutrons and protons do exist, there must be another attractive force acting within the nucleus. This force is called the nuclear force.
    The nuclear force is a strong attractive force that is independent of charge. It acts equally only between pairs of neutrons, pairs of protons, or a neutron and a proton. The nuclear force has a very short range; it acts only over distances approximately equal to the diameter of the nucleus (10-13 cm). The attractive nuclear force between all nucleons drops off with distance much faster than the repulsive electrostatic force between protons.

    1.9  Atomic Nature of Matter Summary
    Structure of the Atom
    An atom consists of a positively charged Nucleus  surrounded by a number of negatively charged particles, called electrons, so that the atom as a whole is electrically neutral.  The atomic nuclei are built up of two kinds of primary particles, namely protons and neutrons, which can be ordinarily referred to as Nucleons. The masses of the protons and neutrons are similar and much heavier than an electron, by a factor of 1840.  As the nucleus contains all the protons and neutrons, it follows that the mass of the atoms are concentrated in the nucleus.
    The proton carries a single unit of charge and the neutron is electrically neutral. The unit of charge carried by the proton is equal in magnitude and opposite in sign, to the charge on the electron.  This charge is often referred to in physics as the fundamental charge.
    Each electron carries a unit of negative charge equal to the charge on the proton.  The number of orbital electrons is equal to the number of protons in the nucleus so that the their charge balances and overall the atom is electrically neutral.  If the atom loses or gains a planetary electron, it is left with a residual electrical charge and the atom is said to be ionized.
    The number of protons in the nucleus determines the number of orbital electrons.  It is the electronic structure of the atom, in particular the outermost orbiting electrons, that give the atoms its chemical properties.  Chemical reactions are due to electronic interactions.
    In this paper we will only mention that the electron, in a stable orbit around the nucleus occupies a stationary state, often referred to in Physics as an Eigenstate or an Eigunfunction of the orbital decomposition of the central field problem.  The solution of the electronic motion of an electron in a central field of force will not be addressed here. The force which holds the electron to the nucleus is the electrostatic force of electromagnetic theory and is accurately describe by an inverse square law of force, similar the Newton’s law of gravitation.

    2.1  Atomic Number and Chart of Nuclides
    As has been previously stated the nucleus consists of protons and neutrons. For a given element, the number of protons present in the atomic nucleus, which is the same as the number of positive charges it carries, is called the atomic number.  This number is identical with the ordinal number of the element which is used in the familiar Periodic table of the elements.  Thus the atomic number of hydrogen is 1, of helium 2, and lithium 3, up to 92 for Uranium, the element of highest atomic number existing in nature to any extent.  A large number of heavier elements have been produced artificially, of these elements, plutonium, atomic number 94, is the most important because of it’s connection with nuclear weapons.
    The total number of Nucleons, i.e. of protons and neutrons, in an atomic nucleus is referred to as the mass number.  Since the masses of neutrons and protons and very nearly identical, it is evident that the mass number is the integer nearest to the atomic weight of the species under considerations.
    It is the atomic number, i.e. the number of protons in the nucleus, which determines the chemical nature of an element.  This is because the chemical properties depend on the (orbital ) electrons, surrounding the nucleus, and their number must be equal to the number of protons in the nucleus since the atom must be electrically neutral.  Consequently, atoms with nuclei containing the same numbers of protons, i.e. with the same atomic number, but with different numbers of neutrons, i.e. with different mass number, are essentially identical chemically.  Such species having the same atomic number but different mass numbers are called Isotopes.  Isotopes are, in general, chemically identical but have different atomic weight.  They are, in general, indistinguishable chemically, but have different atomic weights.  As of January 1, 1962, all atomic weights are expressed on a single scale which assigns a value of 12 to the common isotope of C12.
    In Nuclear physics, and related fields, the masses of atoms, of nuclei, and of nuclear particles are invariably expressed on the so-called physical scale.  The Atomic Mass unit (amu) is then defined as exactly one-twelfth  of the mass of the C12  atom.

    2.2  Chart of the Nuclides
    A tabulated chart called the Chart of the Nuclides lists the stable and unstable nuclides in addition to pertinent information about each one. This chart plots a box for each individual nuclide, with the number of protons (Z) on the vertical axis and the number of neutrons (N = A – Z) on the horizontal axis.  The chart indicates stable isotopes.
    Some isotopes are artificially radioactive, meaning that they are produced by artificial techniques and do not occur naturally.

    A.  Information for Stable Nuclides
    For the stable isotopes, in addition to the symbol and the atomic mass number, the number percentage of each isotope in the naturally occurring element is listed, as well as the thermal neutron activation cross section and the mass in atomic mass units (amu).

    B.  Information for Unstable Nuclides
    For unstable isotopes the additional information includes the half life, the mode of decay (for example, b-, a), the total disintegration energy in MeV (million electron volts), and the mass in amu when available

    C.  Neutron – Proton Ratios
    If you plot the number of protons on the x-axis and the number of neutrons on the y axis, then you will see that as the mass numbers become higher, the ratio of neutrons to protons in the nucleus becomes larger. For helium-4 (2 protons and 2 neutrons) and oxygen-16 (8 protons and 8 neutrons) this ratio is unity. For indium-115 (49 protons and 66 neutrons) the ratio of neutrons to protons has increased to 1.35, and for uranium-238 (92 protons and 146 neutrons) the neutron to-proton ratio is 1.59.

    D.  Natural Abundance of Isotopes
    The relative abundance of an isotope in nature compared to other isotopes of the same element is relatively constant. The Chart of the Nuclides presents the relative abundance of the naturally occurring isotopes of an element in units of atom percent. Atom percent is the percentage of the atoms of an element that are of a particular isotope.
    Atom percent is abbreviated as a/o. For example, if a cup of water contains 8.23 x 1024 atoms of oxygen, and the isotopic abundance of oxygen-18 is 0.20%, then there are 1.65 x 1022 atoms of oxygen-18 in the cup.

    E.  Atomic Weight
    The atomic weight for an element is defined as the average atomic weight of the isotopes of the element. The atomic weight for an element can be calculated by summing the products of the isotopic abundance of the isotope with the atomic mass of the isotope.

    3.1   MASS DEFECT
    Careful measurements have shown that the mass of a particular atom is always slightly less than the sum of the masses of the individual neutrons, protons, and electrons of which the atom consists. The difference between the mass of the atom and the sum of the masses of its parts is called the mass defect (Dm ).
    The mass defect can be calculated using the equation show below. In calculating the mass defect it is important to use the full accuracy of mass measurements because the difference in mass is small compared to the mass of the atom. Rounding off the masses of atoms and particles to three or four significant digits prior to the calculation will result in a calculated mass defect of zero.
    Dm  = [ Z(mp + me) + (A-Z)mn ] – matom
    Dm  = mass defect (amu)
    mp = mass of a proton (1.007277 amu)
    mn = mass of a neutron (1.008665 amu)
    me = mass of an electron (0.000548597 amu)
    matom = mass of nuclide (amu)
    Z = atomic number (number of protons)
    A = mass number (number of nucleons)

    3.2  Binding Energy
    The loss in mass, or mass defect, is due to the conversion of mass to binding energy when the nucleus is formed. Binding energy is defined as the amount of energy that must be supplied to a nucleus to completely separate its nuclear particles (nucleons). It can also be understood as the amount of energy that would be released if the nucleus was formed from the separate particles.
    Binding energy is the energy equivalent of the mass defect. Since the mass defect was converted to binding energy (BE) when the nucleus was formed, it is possible to calculate the binding energy using a conversion factor derived by the mass-energy relationship from Einstein’s Theory of Relativity.
    Einstein’s famous equation relating mass and energy is;
     E = mc2
    E = Energy in Joules
    m = mass in kilograms
    c = is the velocity of light (c = 3 x 108 meters/sec).
    The energy equivalent of 1 amu can be determined by inserting this quantity of mass into Einstein’s equation and applying conversion factors.
    1 amu = 1.6606 x 10-27 kg

    3.3.  Energy Levels of Atoms
    The electrons that circle the nucleus move in fairly well-defined orbits. Some of these electrons are more tightly bound in the atom than others. For example, only 7.38 eV is required to remove the outermost electron from a lead atom, while 88,000 eV is required to remove the innermost electron.
    The process of removing an electron from an atom is called ionization, and the energy required to remove the electron is called the ionization energy.  In a neutral atom (number of electrons = Z) it is possible for the electrons to be in a variety of different orbits, each with a different energy level. The state of lowest energy is the one in which the atom is normally found and is called the ground state. When the atom possesses more energy than its ground state energy, it is said to be in an excited state.
    An atom cannot stay in the excited state for an indefinite period of time. An excited atom will eventually transition to either a lower-energy excited state, or directly to its ground state, by emitting a discrete bundle of electromagnetic energy called an x-ray. The energy of the x-ray will be equal to the difference between the energy levels of the atom and will typically range from several eV to 100,000 eV in magnitude.

    3.4.  Energy Levels of the Nucleus
    The nucleons in the nucleus of an atom, like the electrons that circle the nucleus, exist in shells that correspond to energy states. The energy shells of the nucleus are less defined and less understood than those of the electrons.
    There is a state of lowest energy (the ground state) and discrete possible excited states for a nucleus. Where the discrete energy states for the electrons of an atom are measured in eV or keV, the energy levels of the nucleus are considerably greater and typically measured in MeV.
    A nucleus that is in the excited state will not remain at that energy level for an indefinite period. Like the electrons in an excited atom, the nucleons in an excited nucleus will transition towards their lowest energy configuration and in doing so emit a discrete bundle of electromagnetic radiation called a gamma ray (g-ray). The only differences between x-rays and g-rays are their energy levels and whether they are emitted from the electron shell or from the nucleus.

    Most atoms found in nature are stable and do not emit particles or energy that change form over time. Some atoms, however, do not have stable nuclei. These atoms emit radiation in order to achieve a more stable configuration.

    [latex]\mbox{\textbf{4.1 Stability of Nuclei}}[/latex]
    As mass numbers become larger, the ratio of neutrons to protons in the nucleus becomes larger for the stable nuclei. Non-stable nuclei may have an excess or deficiency of neutrons and undergo a transformation process known as beta (b) decay.
    Non-stable nuclei can also undergo a variety of other processes such as alpha (a) or neutron (n) decay. As a result of these decay processes, the final nucleus is in a more stable or more tightly bound configuration.

    [latex]\mbox{\textbf{4.2 Natural Radioactivity}}[/latex]
    In 1896, the French physicist Becquerel discovered that crystals of a uranium salt emitted rays that were similar to x-rays in that they were highly penetrating, could affect a photographic plate, and induced electrical conductivity in gases. Becquerel’s discovery was followed in 1898 by the identification of two other radioactive elements, polonium and radium, by Pierre and Marie Curie.
    Heavy elements, such as uranium or thorium, and their unstable decay chain elements emit radiation in their naturally occurring state. Uranium and thorium, present since their creation at the beginning of geological time, have an extremely slow rate of decay. All naturally occurring nuclides with atomic numbers greater than 82 are radioactive.

    [latex]\mbox{\textbf{4.3 Nuclear Decay}}[/latex]
    Whenever a nucleus can attain a more stable (i.e., more tightly bound) configuration by emitting radiation, a spontaneous disintegration process known as radioactive decay or nuclear decay may occur. In practice, this “radiation” may be electromagnetic radiation, particles, or both. Detailed studies of radioactive decay and nuclear reaction processes have led to the formulation of useful conservation principles.
    The four principles of most interest in this white paper are discussed below.
    1.     Conservation of electric charge:  Conservation of electric charge implies that sum of the charges in the beginning of a process is equal to the sum of the charges after the interaction has occurred.
    2.     Conservation of mass number:  Conservation of mass number does not allow a net change in the number of nucleons. However, the conversion of a proton to a neutron and vice versa is allowed.
    3.     Conservation of mass and energy:  Implies that the total of the kinetic energy and the energy equivalent of the mass in a system must be conserved in all decays and reactions. Mass can be converted to energy and energy can be converted to mass, but the sum of mass and energy must be constant.
    4.     Conservation of momentum:  is responsible for the distribution of the available kinetic energy among product nuclei, particles, and/or radiation. The total amount is the same before and after the reaction even though it may be distributed differently among entirely different nuclides and/or particles.

    [latex]\mbox{\textbf{4.4 Alpha Decay}} (\alpha)[/latex]
    Alpha decay is the emission of alpha particles (helium nuclei) which may be represented as either He4or (a). When an unstable nucleus ejects an alpha particle, the atomic number is reduced by 2 and the mass number decreased by 4. An example is uranium-234, (U234) which decays by the ejection of an alpha particle accompanied by the emission of a 0.068 MeV gamma ray photon.
    The combined kinetic energy of the new nucleus (Thorium-230, Th 230) and the a particle is designated as KE. The sum of the KE and the gamma energy is equal to the difference in mass between the original nucleus U234 (Uranium-234) and the final particles (equivalent to the binding energy released, since  Dm = BE). The alpha particle will carry off as much as 98% of the kinetic energy and, in most cases, can be considered to carry off all the kinetic energy.

    [latex]\mbox{4.5 Beta Decay} (\beta)[/latex]
    Beta decay is the emission of electrons of nuclear rather than orbital origin. These particles are electrons that have been expelled by excited nuclei and may have a charge of either sign. If both energy and momentum are to be conserved, a third type of particle, the neutrino must be involved.
    The neutrino is associated with positive electron emission, and its antiparticle, the antineutrino, is emitted with a negative electron. These uncharged particles have only the weakest interaction with matter, no mass, and travel at the speed of light. For all practical purposes, they pass through all materials with so few interactions that the energy they possess cannot be recovered.
    The neutrinos and antineutrinos are included here only because they carry a portion of the kinetic energy that would otherwise belong to the beta particle, and therefore, must be considered for energy and momentum to be conserved. They are normally ignored since they are not significant in the context of nuclear reactor applications.
    Negative electron emission, effectively converts a neutron to a proton, thus increasing the atomic number by one and leaving the mass number unchanged. This is a common mode of decay for nuclei with an excess of neutrons.
    Positively charged electrons (beta-plus) are known as positrons. Except for sign, they are nearly identical to their negatively charged cousins. When a positron is ejected from the nucleus, the atomic number is decreased by one and the mass number remains unchanged. A proton has been converted to a neutron.

    [latex]\mbox{4.6 Electron Capture (EC, K-Capture)}[/latex]
    Nuclei having an excess of protons may capture an electron from one of the inner orbits which immediately combines with a proton in the nucleus to form a neutron. This process is called electron capture (EC). The electron is normally captured from the innermost orbit (the K-shell), and, consequently, this process is sometimes called K-capture.
    A neutrino is formed at the same time that the neutron is formed, and energy carried off by it serves to conserve momentum. Any energy that is available due to the atomic mass of the product being appreciably less than that of the parent will appear as gamma radiation. Also, there will always be characteristic x-rays given off when an electron from one of the higher energy shells moves in to fill the vacancy in the K-shell. Electron capture and positron emission result in the production of the same daughter product, and they exist as competing processes.
    For positron emission to occur, however, the mass of the daughter product must be less than the mass of the parent by an amount equal to at least twice the mass of an electron. This mass difference between the parent and daughter is necessary to account for two items present in the parent but not in the daughter. One item is the positron ejected from the nucleus of the parent. The other item is that the daughter product has one less orbital electron than the parent. If this requirement is not met, then orbital electron capture takes place exclusively.

    [latex]\mbox{4.7 Gamma Emissions} (\gamma)[/latex]
    Gamma radiation is a high-energy electromagnetic radiation that originates in the nucleus. It is emitted in the form of photons, discrete bundles of energy that have both wave and particle properties. Often a daughter nuclide is left in an excited state after a radioactive parent nucleus undergoes a transformation by alpha decay, beta decay, or electron capture. The nucleus will drop to the ground state by the emission of gamma radiation.

    [latex]\mbox{4.8 Internal Conversion}[/latex]
    The usual method for an excited nucleus to go from the excited state to the ground state is by emission of gamma radiation. However, in some cases the gamma ray (photon) emerges from the nucleus only to interact with one of the innermost orbital electrons and, as a result, the energy of the photon is transferred to the electron. The gamma ray is then said to have undergone internal conversion.
    The conversion electron is ejected from the atom with kinetic energy equal to the gamma energy minus the binding energy of the orbital electron. An orbital electron then drops to a lower energy state to fill the vacancy, and this is accompanied by the emission of characteristic x-rays.

    [latex]\mbox{4.9 Isomers and Isomeric Transitions}[/latex]
    Isomeric transition commonly occurs immediately after particle emission; however, the nucleus may remain in an excited state for a measurable period of time before dropping to the ground state at its own characteristic rate. A nucleus that remains in such an excited state is known as a nuclear isomer because it differs in energy and behavior from other nuclei with the same atomic number and mass number.
    The decay of an excited nuclear isomer to a lower energy level is called an isomeric transition. It is also possible for the excited isomer to decay by some alternate means, for example, by beta emission.

    [latex]\mbox{4.10 Decay Chains}[/latex]
    When an unstable nucleus decays, the resulting daughter nucleus is not necessarily stable. The nucleus resulting from the decay of a parent is often itself unstable, and will undergo an additional decay. This is especially common among the larger nuclides.
    It is possible to trace the steps of an unstable atom as it goes through multiple decays trying to achieve stability. The list of the original unstable nuclide, the nuclides that are involved as intermediate steps in the decay, and the final stable nuclide is known as the decay chain.

    [latex]\mbox{4.11 Predicting Type of Decay}[/latex]
    Radioactive nuclides tend to decay in a way that results in a daughter nuclide that lies closer to the line of stability. Due to this, it is possible to predict the type of decay that a nuclide will undergo based on its location relative to the line of stability.

    The rate at which a sample of radioactive material decays is not constant. As individual atoms of the material decay, there are fewer of those types of atoms remaining. Since the rate of decay is directly proportional to the number of atoms, the rate of decay will decrease as the number of atoms decreases.
    5.1  Definition Radioactivity
    Radioactivity is the property of certain nuclides of spontaneously emitting particles or gamma radiation. The decay of radioactive nuclides occurs in a random manner, and the precise time at which a single nucleus will decay cannot be determined. However, the average behavior of a very large sample can be predicted accurately by using statistical methods. These studies have revealed that there is a certain probability that in a given time interval a certain fraction of the nuclei within a sample of a particular nuclide will decay.
    This probability per unit time that an atom of a nuclide will decay is known as the radioactive decay constant. The units for the decay constant are inverse time such as 1/second, 1/minute, 1/hour, or 1/year.

    5.2  Activity
    The activity (A) of a sample is the rate of decay of that sample. This rate of decay is usually measured in the number of disintegrations that occur per second. For a sample containing millions of atoms, the activity is the product of the decay constant and the number of atoms present in the sample.The relationship between the activity, number of atoms, and decay constant is shown below;

    A = lN
    A = Activity of the nuclide (disintegrations/second)
    l = decay constant of the nuclide (second-1)
    N = Number of atoms of the nuclide in the sample
    Since l  is a constant, the activity and the number of atoms are always proportional.

    5.3  Units of Measurement for Radioactivity
    Two common units to measure the activity of a substance are the curie (Ci) and becquerel (Bq). A curie is a unit of measure of the rate of radioactive decay equal to 3.7 x 1010 disintegrations per second. This is approximately equivalent to the number of disintegrations that one gram of radium-226 will undergo in one second. A becquerel is a more fundamental unit of measure of radioactive decay that is equal to 1 disintegration per second.
    Currently, the curie is more widely used in the United States, but usage of the becquerel can be expected to broaden as the metric system slowly comes into wider use. The conversion between curies and becquerels is shown below.
    1 curie = 3.7 x 1010 becquerels

    5.4  Variation of Radioactivity Over Time
    The rate at which a given radionuclide sample decays is stated in section 5.2  as being equal to the product of the number of atoms and the decay constant.
    From this basic relationship it is possible to use calculus to derive an expression which can be used to calculate how the number of atoms present will change over time. The derivation is beyond the scope of this white paper  but the following equation is the useful result of the solution of this important differential equation:

    Nt = No elt
    Nt = number of atoms present at time t
    No = number of atoms initially present o
    l= decay constant (time-1)
    t = time

    5.5  Radioactive Half-Life
    One of the most useful terms for estimating how quickly a nuclide will decay is the radioactive half-life. The radioactive half-life is defined as the amount of time required for the activity to decrease to one-half of its original value. A relationship between the half-life and decay constant can be developed from the equation developed in section 5.4.
    Assuming an initial number of atoms No the population, and consequently, the activity may be noted to decrease by one-half of this value in a time of one half-life. Additional decreases occur so that whenever one half-life elapses, the number of atoms drops to one-half of what its value was at the beginning of that time interval. After five half-lives have elapsed, only 1/32, or 3.1%, of the original number of atoms remains. After seven half-lives, only 1/128, or 0.78%, of the atoms remains. The number of atoms existing after 5 to 7 half-lives can usually be assumed to be negligible.

    5.6  Plotting Radioactive Decay
    It is useful to plot the activity of a nuclide as it changes over time. Plots of this type can be used to determine when the activity will fall below a certain level. This plot is usually done showing activity on either a linear or a logarithmic scale. The decay of the activity of a single nuclide on a logarithmic scale will plot as a straight line because the decay is exponential. If a substance contains more than one radioactive nuclide, the total activity is the sum of the individual activities of each nuclide.  The initial activity of each of the nuclides would be the product of the number of atoms and the decay constant.

    5.7  Radioactive Equilibrium
    A.  Radioactive equilibrium exists when a radioactive nuclide is decaying at the same rate at which it is being produced. Since the production rate and decay rate are equal, the number of atoms present remains constant over time.

    B.  Transient radioactive equilibrium occurs when the parent nuclide and the daughter nuclide decay at essentially the same rate. For transient equilibrium to occur, the parent must have a long half-life when compared to the daughter. An example of this type of compound decay process is barium-140, which decays by beta emission to lanthanum-140, which in turn decays by beta emission to stable cerium-140.
    The decay constant for barium-140 is considerably smaller than the decay constant for lanthanum-140. Remember that the rate of decay of both the parent and daughter can be represented as lN. Although the decay constant for barium-140 is smaller, the actual rate of decay (lN )is initially larger than that of lanthanum-140 because of the great difference in their initial concentrations. As the concentration of the daughter increases, the rate of decay of the daughter will approach and eventually match the decay rate of the parent. When this occurs, they are said to be in transient equilibrium.

    C. Secular equilibrium occurs when the parent has an extremely long half-life. In the long decay chain for a naturally radioactive element, such as thorium-232, where all of the elements in the chain are in secular equilibrium, each of the descendants has built up to an equilibrium amount and all decay at the rate set by the original parent. The only exception is the final stable element on the end of the chain. Its number of atoms is constantly increasing.

    Neutrons can cause many different types of interactions. The neutron may simply scatter off the nucleus in two different ways, or it may actually be absorbed into the nucleus. If a neutron is absorbed into the nucleus, it may result in the emission of a gamma ray or a subatomic particle, or it may cause the nucleus to fission.
    6.1  Scattering
    A neutron scattering reaction occurs when a nucleus, after having been struck by a neutron, emits a single neutron. Despite the fact that the initial and final neutrons do not need to be (and often are not) the same, the net effect of the reaction is as if the projectile neutron had merely “bounced off,” or scattered from, the nucleus. The two categories of scattering reactions, elastic and inelastic scattering, are described below:

    A.  Elastic Scattering
    In an elastic scattering reaction between a neutron and a target nucleus, there is no energy transferred into nuclear excitation. Momentum and kinetic energy of the “system” are conserved although there is usually some transfer of kinetic energy from the neutron to the target nucleus. The target nucleus gains the amount of kinetic energy that the neutron loses. Elastic scattering of neutrons by nuclei can occur in two ways:
    1.     The more unusual of the two interactions is the absorption of the neutron, forming a compound nucleus, followed by the re-emission of a neutron in such a way that the total kinetic energy is conserved and the nucleus returns to its ground state. This is known as resonance elastic scattering and is very dependent upon the initial kinetic energy possessed by the neutron. Due to formation of the compound nucleus, it is also referred to as compound elastic scattering.
    2.      The second, more usual method, is termed potential elastic scattering and can be understood by visualizing the neutrons and nuclei to be much like billiard balls with impenetrable surfaces. Potential scattering takes place with incident neutrons that have an energy of up to about 1 MeV. In potential scattering, the neutron does not actually touch the nucleus and a compound nucleus is not formed. Instead, the neutron is acted on and scattered by the short range nuclear forces when it approaches close enough to the nucleus.

    B.  Inelastic Scattering
    In inelastic scattering, the incident neutron is absorbed by the target nucleus, forming a compound nucleus. The compound nucleus will then emit a neutron of lower kinetic energy which leaves the original nucleus in an excited state. The nucleus will usually, by one or more gamma emissions, emit this excess energy to reach its ground state.
    For the nucleus that has reached its ground state, the sum of the kinetic energy of the exit  Inelastic Scattering neutron, the target nucleus, and the total gamma energy emitted is equal to the initial kinetic energy of the incident neutron.

    6.2  Absorption Reactions
    Most absorption reactions result in the loss of a neutron coupled with the production of a charged particle or gamma ray. When the product nucleus is radioactive, additional radiation is emitted at some later time. Radiative capture, particle ejection, and fission are all categorized as absorption reactions and are briefly described below.
    A.  Radiative Capture:  In radiative capture the incident neutron enters the target nucleus forming a compound nucleus. The compound nucleus then decays to its ground state by gamma emission.

    B.  Particle Ejection:  In a particle ejection reaction the incident particle enters the target nucleus forming a compound nucleus. The newly formed compound nucleus has been excited to a high enough energy level to cause it to eject a new particle while the incident neutron remains in the nucleus. After the new particle is ejected, the remaining nucleus may or may not exist in an excited state depending upon the mass-energy balance of the reaction.
    C.  Fission:  One of the most important interactions that neutrons can cause is fission, in which the nucleus that absorbs the neutron actually splits into two similarly sized parts. Fission will be discussed in detail in the next chapter.

    Nuclear fission is a process in which an atom splits and releases energy, fission products, and neutrons. The neutrons released by fission can, in turn, cause the fission of other atoms.

    7.1   Fission
    In the fission reaction the incident neutron enters the heavy target nucleus, forming a compound nucleus that is excited to such a high energy level (E > E ) that the nucleus “splits” (fissions) into two large fragments plus some neutrons. A large amount of energy is released in the form of radiation and fragment kinetic energy.

    7.2.  Liquid Drop Model of a Nucleus
    The nucleus is held together by the attractive nuclear force between nucleons. The characteristics of the nuclear force are listed below:
    1.     Very short range, with essentially no effect beyond nuclear dimensions (10-13 cm)
    2.      Stronger than the repulsive electrostatic forces within the nucleus
    3.      Independent of nucleon pairing, in that the attractive forces between pairs of neutrons are no different than those between pairs of protons or a neutron and a proton
    4.      Saturable, that is, a nucleon can attract only a few of its nearest neighbors

    One theory of fission considers the fissioning of a nucleus similar in some respects to the splitting of a liquid drop. This analogy is justifiable to some extent by the fact that a liquid drop is held together by molecular forces that tend to make the drop spherical in shape and that try to resist any deformation in the same manner as nuclear forces are assumed to hold the nucleus together.
    By considering the nucleus as a liquid drop, the fission process can be described. the nucleus in the ground state is undistorted, and its attractive nuclear forces are greater than the repulsive electrostatic forces between the protons within the nucleus. When an incident particle (in this instance a neutron) is absorbed by the target nucleus, a compound nucleus is formed. The compound nucleus temporarily contains all the charge and mass involved in the reaction and exists in an excited state. The excitation energy added to the compound nucleus is equal to the binding energy contributed by the incident particle plus the kinetic energy possessed by that particle.
    The excitation energy thus imparted to the compound nucleus, which may cause it to oscillate and become distorted. If the excitation energy is greater than a certain critical energy, the oscillations may cause the compound nucleus to become dumbbell-shaped. When this happens, the attractive nuclear forces (short-range) in the neck area are small due to saturation, while the repulsive electrostatic forces (long-range) are only slightly less than before. When the repulsive electrostatic forces exceed the attractive nuclear forces, nuclear fission occurs,

    7.3.   Critical Energy
    The measure of how far the energy level of a nucleus is above its ground state is called the excitation energy. For fission to occur, the excitation energy must be above a particular value for that nuclide. The critical energy (Ecrit) is the minimum excitation energy required for fission to occur.

    7.4.  Fissionable, Fissile and Fertile Materials
    Theoretically, all nuclei heavier than iron have the potential to undergo fission, however the energy barrier that needs to be exceeded before fission can occur is impossibly high for all but the heavier elements.  It is only for mass numbers greater than about 230 that the fission activation energy may be less than 10 MeV.

    A.   Fissionable Materials
    Consider the compound nucleus Uranium 239 formed by the absorption of a neutron by U238For the neutron to induce fission the sum of the binding and kinetic energy transferred to the U239 compound nucleus must exceed its fission activation energy.  The activation energy of U239 is 7 MeV; the difference between the binding energy of U238 and U239 is 5.5 MeV.  Thus the kinetic energy of the incoming neutron must be at least 1.5 MeV.
    Materials, such as U238, which may undergo fission following absorption of fast neutrons of a few MeV kinetic energy are called Fissionable Materials.

    B.  Fissile Materials
    A fissile materialis composed of nuclides for which fission is possible with neutrons of any energy level. What is especially significant about these nuclides is their ability to be fissioned with zero kinetic energy neutrons (thermal neutrons). Thermal neutrons have very low kinetic energy levels (essentially zero) because they are roughly in equilibrium with the thermal motion of surrounding materials.
    Therefore, in order to be classified as fissile, a material must be capable of fissioning after absorbing a thermal neutron. Consequently, they impart essentially no kinetic energy to the reaction. Fission is possible in these materials with thermal neutrons, since the change in binding energy supplied by the neutron addition alone is high enough to exceed the critical energy. Some examples of fissile nuclides are U235 (uranium-235), U233 (uranium-233), and PU239 (plutonium-239).
    Consider the compound nucleus U236 formed from the absorption of a neutron by U235In this case the U236 fission activation energy is 6.5 MeV whereas the difference in binding energy between U235 and U236 is 6.8 MeV.  Thus neutrons of any kinetic energy can induce fission following absorption in U235U235 is the only naturally occurring fissile material.

    C.  Fertile Materials
    All of the neutron absorption reactions that do not result in fission lead to the production of new nuclides through the process known as transmutation. These nuclides can, in turn, be transmuted again or may undergo radioactive decay to produce still different nuclides. The nuclides that are produced by this process are referred to as transmutation products. Because several of the fissile nuclides do not exist in nature, they can only be produced by nuclear reactions (transmutation).
    The target nuclei for such reactions are said to be fertile. Fertile materials are materials that can undergo transmutation to become fissile materials. The fertile nuclides, thorium-232 and uranium-238 can be bombarded with neutrons to produce uranium-233 and plutonium-239, respectively.
    If a reactor contains fertile material in addition to its fissile fuel, some new fuel will be produced as the original fuel is burned up. This is called conversion. Reactors that are specifically designed to produce fissionable fuel are called “breeder” reactors. In such reactors, the amount of fissionable fuel produced is greater than the amount of fuel burnup. If less fuel is produced than used, the process is called conversion, and the reactor is termed a “converter.”
    A fissionable materialis composed of nuclides for which fission with neutrons is possible. All fissile nuclides fall into this category. However, also included are those nuclides that can be fissioned only with high energy neutrons. The change in binding energy that occurs as the result of neutron absorption results in a nuclear excitation energy level that is less than the required critical energy. Therefore, the additional excitation energy must be supplied by the kinetic energy of the incident neutron.
    The reason for this difference between fissile and fissionable materials is the so-called odd-even effect for nuclei. It has been observed that nuclei with even numbers of neutrons and/or protons are more stable than those with odd numbers. Therefore, adding a neutron to change a nucleus with an odd number of neutrons to a nucleus with an even number of neutrons produces an appreciably higher binding energy than adding a neutron to a nucleus already possessing an even number of neutrons. Some examples of nuclides requiring high energy neutrons to cause fission are Th232 (thorium-232), U238 (uranium-238), and Pu240 (plutonium-240).
    Uranium 239, which may be formed as the result of U238 absorbing a neutron, is radioactive and decays by b emission, with a half-life of 23-1/2 minutes, to Neptunium 239.  This neptunium 239 decays by b emission, with half  life of 2.3 days, to Plutonium 239, an a emitter of half life of 24,000 years.  It turns out that plutonium 239 is a fissile material; that is, as in the case of U235, it readily undergoes fission on absorption of neutrons of any energy including slow neutrons of very low energies. The uranium 238 is called a Fertile Material because the absorption of the neutrons, which we have seen previously it most readily does in the resonance capture mode, leads to the formation of the fissile material Pu239
    Similarly thorium 232 is also a fertile material because neutron absorption leads, via Protactinium 233, to the fissile material Uranium 233. 
    Thus the fertile materials U238 and Th232 yield the fissile materials Pu239 and U233, respectively.

    7.5  Natural Uranium
    Natural Uranium is found in ore deposits in many places around the world.  It is predominantly a mixture of the two isotopes 238, 234 and 235, in the proportions mentioned at the beginning of this white paper.  All three isotopes are radioactive.
    Therefore of the three fissile materials mentioned above, natural uranium is a direct source for one, U235and an indirect source for a second, Pu239 via the fertile U238.  These facts underscore the importance of natural uranium in the production of Nuclear Power.
    The third fissile material, U233, is of little significance at present, although of possibly important potential because of large ore reserves of the fertile thorium.
    Before returning to our discussion on fission it will be useful to summarize some of the properties of natural uranium and its isotopes. Natural uranium consists of:

    • 99.3% U238  a emitter half life  4.5 x 109 years. U238 is a fissionable material; it can undergo fission provided the absorbed neutron has an incident kinetic energy of at least 1.1 MeV.
    • 0.7% U235  a  emitter half life   7.1 x 108 years. U238 is a fertile material, forming fissile Pu239 following capture of a neutron. Neutrons of intermediate energy are readily captured in the resonance capture peaks of U238.
    • 0.1% U234  a  emitter half life  2.5 x 105 years. U235 is a fissile material; it can undergo fission with neutrons of any energy but is much more likely to do so the less energetic, or slower, the neutron.
    • The isotope uranium-235 is usually the desired material for use in reactors.

    7.6 Uranium Enrichment
    A vast amount of equipment and energy are expended in processes that separate the isotopes of uranium (and other elements). The details of these processes are beyond the scope of this white paper. These processes are called enrichment processes because they selectively increase the proportion of a particular isotope. The enrichment process typically starts with feed material that has the proportion of isotopes that occur naturally. In the case of uranium, the natural uranium ore is 0.72 a/o uranium-235. The desired outcome of the enrichment process is to produce enriched uranium.
    Enriched uranium is defined as uranium in which the isotope uranium-235 has a concentration greater than its natural value. The enrichment process will also result in the byproduct of depleted uranium.
    Depleted uranium is defined as uranium in which the isotope uranium-235 has a concentration less than its natural value. Although depleted uranium is referred to as a by-product of the enrichment process, it does have uses in the nuclear field and in commercial and defense industries.

    7.7  Critical Energies Compared to Binding Energy of Last Neutron
    Uranium-235 fissions with thermal neutrons because the binding energy released by the absorption of a neutron is greater than the critical energy for fission; therefore uranium-235 is a fissile material. The binding energy released by uranium-238 absorbing a thermal neutron is less than the critical energy, so additional energy must be possessed by the neutron for fission to be possible. Consequently, uranium-238 is a fissionable material.

    7.8  Binding Energy Per Nucleon (BE/A)
    As the number of particles in a nucleus increases, the total binding energy also increases. The rate of increase, however, is not uniform. This lack of uniformity results in a variation in the amount of binding energy associated with each nucleon within the nucleus. This variation in the binding energy per nucleon (BE/A) is easily seen when the average BE/A is plotted versus atomic mass number (A).
    This plot illustrates that as the atomic mass number increases, the binding energy per nucleon decreases for A > 60. The BE/A curve reaches a maximum value of 8.79 MeV at A = 56 and decreases to about 7.6 MeV for A = 238. The general shape of the BE/A curve can be explained using the general properties of nuclear forces. The nucleus is held together by very short-range attractive forces that exist between nucleons. On the other hand, the nucleus is being forced apart by long range repulsive electrostatic (coulomb) forces that exist between all the protons in the nucleus.
    As the atomic number and the atomic mass number increase, the repulsive electrostatic forces within the nucleus increase due to the greater number of protons in the heavy elements. To overcome this increased repulsion, the proportion of neutrons in the nucleus must increase to maintain stability. This increase in the neutron-to-proton ratio only partially compensates for the growing proton-proton repulsive force in the heavier, naturally occurring elements. Because the repulsive forces are increasing, less energy must be supplied, on the average, to remove a nucleon from the nucleus. The BE/A has decreased. The BE/A of a nucleus is an indication of its degree of stability. Generally, the more stable nuclides have higher BE/A than the less stable ones. The increase in the BE/A as the atomic mass number decreases from 260 to 60 is the primary reason for the energy liberation in the fission process. In addition, the increase in the BE/A as the atomic mass number increases from 1 to 60 is the reason for the energy liberation in the fusion process, which is the opposite reaction of fission.
    The heaviest nuclei require only a small distortion from a spherical shape (small energy addition) for the relatively large coulomb forces forcing the two halves of the nucleus apart to overcome the attractive nuclear forces holding the two halves together. Consequently, the heaviest nuclei are easily fissionable compared to lighter nuclei.

    Fission of heavy nuclides converts a small amount of mass into an enormous amount of energy. The amount of energy released by fission can be determined based on either the change in mass that occurs during the reaction or by the difference in binding energy per nucleon between the fissile nuclide and the fission products.

    8.1.  Calculation of Fission Energy
    Nuclear fission results in the release of enormous quantities of energy. It is necessary to be able to calculate the amount of energy that will be produced. The logical manner in which to pursue this is to first investigate a typical fission reaction. When the compound nucleus splits, it breaks into two fission fragments, rubidium-93, cesium-140, and some neutrons. Both fission products then decay by multiple – emissions as a result of the high neutron-to-proton ratio possessed by these nuclides.
    In most cases, the resultant fission fragments have masses that vary widely. The most probable pair of fission fragments for the thermal fission of the fuel uranium-235 have masses of about 95 and 140.
    Referring now to the binding energy per nucleon, we can estimate the amount of energy released by our “typical” fission by plotting this reaction on the curve and calculating the change in binding energy (DBE) between the reactants on the left-hand side of the fission equation and the products on the right-hand side. Plotting the reactant and product nuclides on the curve shows that the total binding energy of the system after fission is greater than the total binding energy of the system before fission. When there is an increase in the total binding energy of a system, the system has become more stable by releasing an amount of energy equal to the increase in total binding energy of the system. Therefore, in the fission process, the energy liberated is equal to the increase in the total binding energy of the system.

    8.2  Binding Energy per Nucleon Curve
    The energy released will be equivalent to the difference in binding energy ( BE) between the reactants and the products. The energy liberation during the fission process can also be explained from the standpoint of the conservation of mass-energy. During the fission process, there is a decrease in the mass of the system. There must, therefore, be energy liberated equal to the energy equivalent of the mass lost in the process.
    Again, referring to the “typical” fission reaction. E , the instantaneous energy, is the energy released immediately after the fission process. It is equal to the energy equivalent of the mass lost in the fission process. The total energy released per fission will vary from the fission to the next depending on what fission products are formed, but the average total energy released per fission of uranium-235 with a thermal neutron is 200 MeV.
    The majority of the energy liberated in the fission process is released immediately after the fission occurs and appears as the kinetic energy of the fission fragments, kinetic energy of the fission neutrons, and instantaneous gamma rays. The remaining energy is released over a period of time after the fission occurs and appears as kinetic energy of the beta, neutrino, and decay gamma rays.

    8.3.  Estimation of Decay Energy
    In addition to this instantaneous energy release during the actual fission reaction, there is additional energy released when the fission fragments decay by – emission. This additional energy is called decay energy, E . The energy released during the decay for each chain will be equivalent to the mass difference between the original fission product and the sum of the final stable nuclide and the beta particles emitted.

    8.4.  Distribution of Fission Energy
    The average energy distribution for the energy released per fission with a thermal neutron in uranium-235 is shown below:
    A.  Instantaneous Energy from Fission
    Kinetic Energy of Fission Products 167 Mev
    Energy of Fission Neutrons 5 MeV
    Instantaneous Gamma-ray Energy 5 MeV
    Capture Gamma-ray Energy 10 MeV
    Total Instantaneous Energy 187 MeV

    B.  Delayed Energy from Fission
    Beta Particles From Fission Products 7 Mev
    Gamma-rays from Fission Products 6 MeV
    Neutrinos 10 MeV
    Total Delayed Energy 23 MeV
    All of the energy released, with the exception of the neutrino energy, is ultimately transformed into heat through a number of processes. The fission fragments, with their high positive charge and kinetic energy, cause ionization directly as they rip orbital electrons from the surrounding atoms. In this ionization process, kinetic energy is transferred to the surrounding atoms of the fuel material, resulting in an increase in temperature. The beta particles and gamma rays also give up their energy through ionization, and the fission neutrons interact and lose their energy through elastic scattering.
    Of the 200 MeV released per fission, about seven percent (13 MeV) is released at some time after the instant of fission. When a reactor is shut down, fissions essentially cease, but energy is still being released from the decay of fission products. The heat produced by this decay energy is referred to as “decay heat.” Although decay energy represents about seven percent of reactor heat production during reactor operation, once the reactor is shut down the decay heat production drops off quickly to a small fraction of its value while operating. The decay heat produced is significant, however, and systems must be provided to keep the reactor cool even after shutdown.

    Different types of radiation interact with matter in widely different ways. A large, massive, charged alpha particle cannot penetrate a piece of paper and even has a limited range in dry air. A neutrino, at the other extreme, has a low probability of interacting with any matter, even if it passed through the diameter of the earth.

    9.1   Ionization
    Radiation can be classified into two general groups, charged and uncharged; therefore, it may be expected that interactions with matter fall into two general types. Charged particles directly ionize the media through which they pass, while uncharged particles and photons can cause ionization only indirectly or by secondary radiation.
    A moving charged particle has an electrical field surrounding it, which interacts with the atomic structure of the medium through which it is passing. This interaction decelerates the particle and accelerates electrons in the atoms of the medium. The accelerated electrons may acquire enough energy to escape from the parent atom. This process, whereby radiation “strips” off orbital electrons, is called ionization. Uncharged moving particles have no electrical field, so they can only lose energy and cause ionization by such means as collisions or scattering. A photon can lose energy by the photoelectric effect, Compton effect, or pair production.
    Because ionizing radiation creates ions in pairs, the intensity of ionization or the specific ionization is defined as the number of ion-pairs formed per centimeter of travel in a given material. The amount of ionization produced by a charged particle per unit path length, which is a measure of its ionizing power, is roughly proportional to the particle’s mass and the square of its charge as illustrated in the equation below. where:
    I = mz2
    I is the ionizing power
    m is the mass of the particle
    z is the number of unit charges it carries
    K.E. is its kinetic energy
    Since m for an alpha particle is about 7300 times as large as m for a beta article, and z is twice as great, an alpha will produce much more ionization per unit path length than a beta particle of the same energy. This phenomenon occurs because the larger alpha particle moves slower for a given energy and thus acts on a given electron for a longer time.
    9.2  Alpha Radiation
    Alpha radiation is normally produced from the radioactive decay of heavy nuclides and from certain nuclear reactions. The alpha particle consists of 2 neutrons and 2 protons, so it is essentially the same as the nucleus of a helium atom. Because it has no electrons, the alpha particle has a charge of +2. This positive charge causes the alpha particle to strip electrons from the orbits of atoms in its vicinity. As the alpha particle passes through material, it removes electrons from the orbits of atoms it passes near. Energy is required to remove electrons and the energy of the alpha particle is reduced by each reaction. Eventually the particle will expend its kinetic energy, gain 2 electrons in orbit, and become a helium atom. Because of its strong positive charge and large mass, the alpha particle deposits a large amount of energy in a short distance of travel. This rapid, large deposition of energy limits the penetration of alpha particles. The most energetic alpha particles are stopped by a few centimeters of air or a sheet of paper.
    9.3   Beta-Minus Radiation
    A beta-minus particle is an electron that has been ejected at a high velocity from an unstable nucleus. An electron has a small mass and an electrical charge of -1. Beta particles cause ionization by displacing electrons from atom orbits. The ionization occurs from collisions with orbiting electrons. Each collision removes kinetic energy from the beta particle, causing it to slow down. Eventually the beta particle will be slowed enough to allow it to be captured as an orbiting electron in an atom. Although more penetrating than the alpha, the beta is relatively easy to stop and has a low power of penetration. Even the most energetic beta radiation can be stopped by a few millimeters of metal.
    9.4  Positron Radiation
    Positively charged electrons are called positrons. Except for the positive charge, they are identical to beta-minus particles and interact with matter in a similar manner. Positrons are very short-lived, however, and quickly are annihilated by interaction with a negatively charged electron, producing two gammas with a combined energy (calculated below) equal to the rest mass of the positive and negative electrons.
    9.5   Neutron Radiation
    Neutrons have no electrical charge. They have nearly the same mass as a proton (a hydrogen atom nucleus). A neutron has hundreds of times more mass than an electron, but 1/4 the mass of an alpha particle. The source of neutrons is primarily nuclear reactions, such as fission, but they may also be produced from the decay of radioactive nuclides. Because of its lack of charge, the neutron is difficult to stop and has a high penetrating power.
    Neutrons are attenuated (reduced in energy and numbers) by three major interactions, elastic scatter, inelastic scatter, and absorption. In elastic scatter, a neutron collides with a nucleus and bounces off. This reaction transmits some of the kinetic energy of the neutron to the nucleus of the atom, resulting in the neutron being slowed, and the atom receives some kinetic energy (motion). This process is sometimes referred to as “the billiard ball effect.”
    As the mass of the nucleus approaches the mass of the neutron, this reaction becomes more effective in slowing the neutron. Hydrogenous material attenuates neutrons most effectively. In the inelastic scatter reaction, the same neutron/nucleus collision occurs as in elastic scatter. However, in this reaction, the nucleus receives some internal energy as well as kinetic energy.  This slows the neutron, but leaves the nucleus in an excited state.
    When the nucleus decays to its original energy level, it normally emits a gamma ray. In the absorption reaction, the neutron is actually absorbed into the nucleus of an atom. The neutron is captured, but the atom is left in an excited state. If the nucleus emits one or more gamma rays to reach a stable level, the process is called radiative capture. This reaction occurs at most neutron energy levels, but is more probable at lower energy levels.
    9.6   Gamma Radiation
    Gamma radiation is electromagnetic radiation. It is commonly referred to as a gamma ray and is very similar to an x-ray. The difference is that gamma rays are emitted from the nucleus of an atom, and x-rays are produced by orbiting electrons. The x-ray is produced when orbiting electrons move to a lower energy orbit or when fast-moving electrons approaching an atom are deflected and  decelerated as they react with the atom’s electrical field (called Bremsstrahlung). The gamma ray is produced by the decay of excited nuclei and by nuclear reactions. Because the gamma ray has no mass and no charge, it is difficult to stop and has a very high penetrating power. A small fraction of the original gamma stream will pass through several feet of concrete or several meters of water.
    There are three methods of attenuating gamma rays:

    1. Photo-Electric Effect: The first method is referred to as      the photo-electric effect. When a low energy gamma strikes an atom,      the total energy of the gamma is expended in ejecting an electron from      orbit. The result is ionization of the atom and expulsion of a high energy      electron. This reaction is most predominant with low energy gammas      interacting in materials with high atomic weight and rarely occurs with      gammas having an energy above 1 MeV. Annihilation of the gamma results.      Any gamma energy in excess of the binding energy of the electron is      carried off by the electron in the form of kinetic energy.


    1.  Compton Scattering:  The second method of attenuation of      gammas is called Compton scattering. The gamma interacts with an      orbital or free electron; however, in this case, the photon loses only a      fraction of its energy. The actual energy loss depending on the scattering      angle of the gamma. The gamma continues on at lower energy, and the energy      difference is absorbed by the electron. This reaction becomes important      for gamma energies of about 0.1 MeV and higher.

    Pair Production: At higher energy      levels, a third method of attenuation is predominant. This method is pair-production.      When a high energy gamma passes close enough to a heavy nucleus, the gamma      completely disappears, and an electron and a positron are formed. For this      reaction to take place, the original gamma must have at least 1.02 MeV      energy. Any energy greater than 1.02 MeV becomes kinetic energy shared      between the electron and positron. The probability of pair production      increases significantly for higher energy