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<ul><li><p>CHAPTER 1 Nuclear Radiation - Review</p><p>Some Nuclear Units</p><p>Nuclear energies are very high compared to atomic processes, and need larger units </p><p>However, the sizes are quite small and need smaller units:</p><p>Nuclear masses are measured in terms of atomic mass units with the carbon-12 nucleus defined as having a mass of exactly 12 amu. It is also common practice to quote the rest mass energy as if it were the mass. The conversion to amu is:</p><p>Engineering Aspects of Food Irradiation 1</p></li><li><p>Introduction</p><p>2</p><p>Relativistic Energy </p><p>The famous Einstein relationship for energy</p><p>includes both the kinetic energy and rest mass energy for a particle. The kinetic energy of a high speed particle can be calculated from</p><p>The relativistic energy of a particle can also be expressed in terms of its momentum in the expression </p><p>The relativistic energy expression is the tool used to calculate binding energies of nuclei and the energy yields of nuclear fission and fusion. </p><p>Kinetic Energy</p><p>Kinetic energy is energy of motion. The kinetic energy of an object is the energy it possesses because of its motion. The kinetic energy* of a point mass m is given by</p><p>Engineering Aspects of Food Irradiation</p></li><li><p>Introduction</p><p>Kinetic energy is an expression of the fact that a moving object can do work on anything it hits; it quantifies the amount of work the object could do as a result of its motion. The total mechanical energy of an object is the sum of its kinetic energy and potential energy.</p><p>For an object of finite size, this kinetic energy is called the translational kinetic energy of the mass to distinguish it from any rotational kinetic energy it might pos-sess - the total kinetic energy of a mass can be expressed as the sum of the transla-tional kinetic energy of its center of mass plus the kinetic energy of rotation about its center of mass. </p><p>*This assumes that the speed is much less than the speed of light. If the speed is comparable with c then the relativistic kinetic energy expression must be used.</p><p>Rest Mass Energy </p><p>The Einstein equation includes both the kinetic energy of a particle and the energy it has as a result of its mass. If the particle is at rest, then the energy is expressed as </p><p>which is sometimes called its rest mass energy. </p><p>Conservation of Energy </p><p>The relativistic energy expression is a statement about the energy an object contains as a result of its mass and is not to be construed as an exception to the principle of conservation of energy. Energy can exist in many forms, and mass energy can be considered to be one of those forms. </p><p>Engineering Aspects of Food Irradiation 3</p></li><li><p>Introduction</p><p>4</p><p>Pair Production </p><p>Every known particle has an antiparticle; if they encounter one another, they will annihilate with the production of two gamma-rays. The quantum energies of the gamma rays is equal to the sum of the mass energies of the two particles (including their kinetic energies). It is also possible for a photon to give up its quantum energy to the formation of a particle-antiparticle pair in its interaction with matter. </p><p>The rest mass energy of an electron is 0.511 MeV, so the threshold for electron-positron pair production is 1.02 MeV. For X-ray and gamma-ray energies well above 1 MeV, this pair production becomes one of the most important kinds of interactions with matter. At even higher energies, many types of particle-antiparti-cle pairs are produced. </p><p>Relativistic Kinetic Energy </p><p>The relativistic energy expression includes both rest mass energy and the kinetic energy of motion. The kinetic energy is then given by</p><p>This is essentially defining the kinetic energy of a particle as the excess of the parti-cle energy over its rest mass energy. For low velocities this expression approaches the non-relativistic kinetic energy expression.</p><p>Kinetic Energy for v/c</p></li><li><p>Introduction</p><p>and the square root expression then expanded by use of the binomial theorem</p><p>given </p><p>substituting gives</p><p>Relative scale model of an atom and the solar system</p><p>Do you perceive a gold ring to contain a larger fraction of solid matter than the solar system?</p><p>Engineering Aspects of Food Irradiation 5</p></li><li><p>Introduction</p><p>6</p><p>On this scale, the nearest star would be a little over 10,000 miles away.</p><p>Data for Scale Model of Atom</p><p>Nuclear Size and Density</p><p>Various types of scattering experiments suggest that nuclei are roughly spherical and appear to have essentially the same density. The data are summarized in the expression called the Fermi model:</p><p>Engineering Aspects of Food Irradiation</p></li><li><p>Introduction</p><p>where r is the radius of the nucleus of mass number A. The assumption of constant density leads to a nuclear density.</p><p>The most definitive information about nuclear sizes comes from electron scattering.</p><p>Nuclear Density and the Strong Force</p><p>The fact that the nuclear density seems to be independent of the details of neutron number or proton number implies that the force between the particles is essentially the same whether they are protons or neutrons. This correlates with other evidence that the strong force is the same between any pair of nucleons. </p><p>Engineering Aspects of Food Irradiation 7</p></li><li><p>Introduction</p><p>8</p><p>Nuclear Forces</p><p>Within the incredibly small nuclear size, the two strongest forces in nature are pit-ted against each other. When the balance is broken, the resultant radioactivity yields particles of enormous energy.</p><p>The electron in a hydrogen atom is attracted to the proton nucleus with a force so strong that gravity and all other forces are negligible by comparison. But two pro-tons touching each other would feel a repulsive force over 100 million times stron-ger! So how can such protons stay in such close proximity? This may give you some feeling for the enormity of the nuclear strong force which holds the nuclei together.</p><p>The Electromagnetic Force</p><p>Engineering Aspects of Food Irradiation</p></li><li><p>Introduction</p><p>One of the four fundamental forces, the electromagnetic force manifests itself through the forces between charges (Coulomb's Law) and the magnetic force, both of which are summarized in the Lorentz force law. Fundamentally, both magnetic and electric forces are manifestations of an exchange force involving the exchange of photons. The electromagnetic force is a force of infinite range which obeys the inverse square law, and is of the same form as the gravity force. </p><p>The electromagnetic force holds atoms and molecules together. In fact, the forces of electric attraction and repulsion of electric charges are so dominant over the other three fundamental forces that they can be considered to be negligible as determiners of atomic and molecular structure. Even magnetic effects are usually apparent only at high resolutions, and as small corrections. </p><p>Nuclear Particles</p><p>Nuclei are made up of protons and neutrons bound together by the strong force. Both protons and neutrons are referred to as nucleons. The number of protons is called the atomic number and determines the chemical element. Nuclei of a given element (same atomic number) may have different numbers of neutrons and are then said to be different isotopes of the element. </p><p>Proton</p><p>Along with neutrons, protons make up the nucleus, held together by the strong force. The proton is a baryon and is considered to be composed of two up quarks and one down quark. </p><p>Engineering Aspects of Food Irradiation 9</p></li><li><p>Introduction</p><p>10</p><p>It has long been considered to be a stable particle, but recent developments of grand </p><p>unification models have suggested that it might decay with a half-life of about 1031 years. Experiments are underway to see if such decays can be detected. Decay of the proton would violate the conservation of baryon number, and in doing so would be the only known process in nature which does so. </p><p>When we say that a proton is made up of two up quarks and a down, we mean that its net appearance or net set of quantum numbers match that picture. The nature of quark confinement suggests that the quarks are surrounded by a cloud of gluons, and within the tiny volume of the proton other quark-antiquark pairs can be pro-duced and then annihilated without changing the net external appearance of the pro-ton. </p><p>Neutron</p><p>Along with protons, neutrons make up the nucleus, held together by the strong force. The neutron is a baryon and is considered to be composed of two down quarks and one up quark.</p><p>A free neutron will decay with a half-life of about 10.3 minutes but it is stable if combined into a nucleus. The decay of the neutron involves the weak interaction as indicated in the Feynman diagram to the right. This fact is important in models of the early universe. The neutron is about 0.2% more massive than a proton, which translates to an energy difference of 1.29 MeV. </p><p>Engineering Aspects of Food Irradiation</p></li><li><p>Introduction</p><p>The decay of the neutron is associated with a quark transformation in which a down quark is converted to an up by the weak interaction. </p><p>The Strong Force</p><p>A force which can hold a nucleus together against the enormous forces of repulsion of the protons is strong indeed. However, it is not an inverse square force like the electromagnetic force and it has a very short range. Yukawa modeled the strong force as an exchange force in which the exchange particles are pions and other heavier particles. The range of a particle exchange force is limited by the uncer-tainty principle. It is the strongest of the four fundamental forces.</p><p>Engineering Aspects of Food Irradiation 11</p></li><li><p>Introduction</p><p>12</p><p>Nuclear Notation</p><p>Standard nuclear notation shows the chemical symbol, the mass number and the atomic number of the isotope. </p><p>Example: the isotopes of carbon. The element is determined by the atomic number 6. Carbon-12 is the common isotope, with carbon-13 as another stable isotope which makes up about 1%. Carbon 14 is radioactive and the basis for carbon dating. </p><p>Since the protons and neutrons which make up the nucleus are themselves consid-ered to be made up of quarks, and the quarks are considered to be held together by the color force, the strong force may be considered to be a residual color force. In the standard model, therefore, the basic exchange particle is the gluon which medi-ates the forces between quarks. Since the individual gluons and quarks are con-tained within the proton or neutron, the masses attributed to them cannot be used in the range relationship to predict the range of the force. When something is viewed as emerging from a proton or neutron, then it must be at least a quark-antiquark </p><p>Engineering Aspects of Food Irradiation</p></li><li><p>Introduction</p><p>pair, so it is then plausible that the pion as the lightest meson should serve as a pre-dictor of the maximum range of the strong force. </p><p>Isotopes</p><p>The different isotopes of a given element have the same atomic number but differ-ent mass numbers since they have different numbers of neutrons. The chemical properties of the different isotopes of an element are identical, but they will often have great differences in nuclear stability. For stable isotopes light elements, the number of neutrons will be almost equal to the number of protons, but a growing neutron excess is characteristic of stable heavy elements. The element tin (Sn) has the most stable isotopes with 10, the average being about 2.6 stable isotopes per element. </p><p>Information about the isotopes of each element and their abundance can be found by going to the periodic table and choosing an element. Then take the link to nuclear data. </p><p>Radioactivity</p><p>Radioactivity refers to the particles which are emitted from nuclei as a result of nuclear instability. Because the nucleus experiences the intense conflict between the two strongest forces in nature, it should not be surprising that there are many nuclear isotopes which are unstable and emit some kind of radiation. The most common types of radiation are called alpha, beta, and gamma radiation, but there are several other varieties of radioactive decay. </p><p>Radioactive decay rates are normally stated in terms of their half-lives, and the half-life of a given nuclear species is related to its radiation risk. The different types of radioactivity lead to different decay paths which transmute the nuclei into other </p><p>Engineering Aspects of Food Irradiation 13</p></li><li><p>Introduction</p><p>14</p><p>chemical elements. Examining the amounts of the decay products makes possible radioactive dating.</p><p>Radiation from nuclear sources is distributed equally in all directions, obeying the inverse square law. </p><p>Alpha Radioactivity</p><p>Composed of two protons and two neutrons, the alpha particle is a nucleus of the element helium. Because of its very large mass (more than 7000 times the mass of the beta particle) and its charge, it has a very short range. It is not suitable for radia-tion therapy since its range is less than a tenth of a millimeter inside the body. Its main radiation hazard comes when it is ingested into the body; it has great destruc-tive power within its short range. In contact with fast-growing membranes and liv-ing cells, it is positioned for maximum damage. </p><p>Engineering Aspects of Food Irradiation</p></li><li><p>Introduction</p><p>Alpha particle emission is modeled as a barrier penetration process. The alpha par-ticle is the nucleus of the helium atom and is the nucleus of highest stability.</p><p>Alpha Barrier Penetration</p><p> The energy of emitted alpha particles was a mystery to early investigators because it was evident that they did not have enough energy, according to classical physics, to escape the nucleus. Once an approximate size of the nucleus was obtained by Rutherford scattering, one could calculate the height of the Coulomb barrier at the radius of the nucleus. It was evident that this energy was several times higher than the observed alpha particle energies. There was also an incredible range of half lives for the alpha particle which could not be explained by anything in classical physics.</p><p>The resolution of this dilemma came with the realization that there was a finite probability that the alpha particle could penetrate the wall by quantum mechanical tunneling. Using tunneling, Gamow was able to calculate a dependence for the half-life as a function of alpha particle energy which was in agreement with experimen-tal observations. </p><p>Engineering Aspects of Food Irradiation 15</p></li><li><p>Introduction</p><p>16</p><p>Alpha Binding Energy</p><p>The nuclear binding energy of the alpha particle is extremely high, 28.3 MeV. It is an exceptionally stable collection of nucleons, and those heavier nuclei which can be viewed as collections of alpha particles (carbon-12, oxygen-16, etc.) are also exceptionally stable. This contrasts with a binding energy of only 8 MeV for helium-3, which forms an intermediate step in the proton-proton fusion cycle. </p><p>Alpha, Beta, and Gamma</p><p>Historically, the products of radioactivity were called alpha, beta, and gamma when it was found that they could be analyzed into three distinct species by either a mag-netic field or an electric field. </p><p>Penetration of Matter</p><p>Though the most massive and most energetic of radioactive emissions, the alpha particle is the shortest in range because of its strong in...</p></li></ul>

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