{"id":60,"date":"2015-10-28T07:21:24","date_gmt":"2015-10-28T07:21:24","guid":{"rendered":"http:\/\/sitepourvtc.com\/?page_id=60"},"modified":"2024-02-10T15:58:42","modified_gmt":"2024-02-10T15:58:42","slug":"fission","status":"publish","type":"page","link":"https:\/\/sitepourvtc.com\/nuclear-power\/fission\/","title":{"rendered":"Nuclear Fission"},"content":{"rendered":"<div   id="8n9s8rpp6h"    class=\"sue-shadow-wrap sue-content-wrap sue-shadow-inline-no\"><div   id="8n9s8rpp6h"    class=\"sue-shadow sue-shadow-style-vertical\">\n<div   id="8n9s8rpp6h"    class=\"sue-panel\" data-url=\"\" data-target=\"self\" style=\"background-color:#ffffff;color:#333333;border-radius:0px;-moz-border-radius:0px;-webkit-border-radius:0px;box-shadow:none;-moz-box-shadow:none;-webkit-box-shadow:none;border:1px solid #cccccc\"><div   id="8n9s8rpp6h"    class=\"sue-panel-content sue-content-wrap\" style=\"padding:15px;text-align:left\">\n<div class=\"su-heading su-heading-style-modern-1-dark su-heading-align-left\" id=\"\" style=\"font-size:13px;margin-bottom:20px\"><div   id="8n9s8rpp6h"    class=\"su-heading-inner\">\n<h2>Article Summary &amp; FAQs<\/h2>\n<\/div><\/div>\n<h3>What is nuclear fission?<\/h3>\n<p><strong>Nuclear fission<\/strong>\u00a0is a\u00a0<a title=\"Neutron Nuclear Reactions\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/\">nuclear reaction<\/a> or a decay process in which the heavy nucleus\u00a0<strong>splits<\/strong> into smaller parts (lighter nuclei).\u00a0The fission process often produces\u00a0<a title=\"Free Neutron\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/free-neutron\/\">free neutrons,<\/a>\u00a0<a title=\"Photon \u2013 Fundamental Particle\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/photon\/\">photons<\/a>\u00a0(in the form of\u00a0<a title=\"Gamma Rays \/ Gamma Radiation\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/photon\/gamma-ray\/\">gamma rays<\/a>) and releases a <strong>large amount of energy<\/strong>.<\/p>\n<h3>Key Facts<\/h3>\n<ul>\n<li>The case of the nuclear decay process is called <a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/radioactive-decay\/spontaneous-fission\/\"><strong>spontaneous fission<\/strong><\/a>, and it is a sporadic process. <strong>Neutron-induced nuclear fission<\/strong> is the process of the most significant practical importance in\u00a0<a title=\"Reactor Physics\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/\">reactor physics<\/a>.<\/li>\n<li>Some nuclei can <strong>undergo fission<\/strong> on their own spontaneously, but only specific nuclei, like\u00a0<a title=\"Uranium 235\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-235\/\">uranium-235<\/a>,\u00a0<a title=\"Uranium 233\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-233\/\">uranium-233<\/a>,\u00a0and\u00a0<a title=\"Plutonium 239\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/plutonium\/plutonium-239\/\">plutonium-239<\/a>, can\u00a0<strong>sustain a fission chain reaction<\/strong>.<\/li>\n<li>The fission process may produce\u00a0<strong>2, 3, or more<\/strong>\u00a0<a title=\"Free Neutron\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/free-neutron\/\">free neutrons<\/a>, and these neutrons can trigger further fission, and a\u00a0<a title=\"Nuclear Fission Chain Reaction\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/\"><strong>chain reaction<\/strong><\/a> can occur.<\/li>\n<li><strong>The total energy released<\/strong>\u00a0in a reactor is\u00a0<strong>about 210 MeV<\/strong>\u00a0per\u00a0<a title=\"Uranium 235 Fission\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-235\/uranium-235-fission\/\"><sup>235<\/sup>U fission<\/a>.<\/li>\n<li><strong>About 3.1\u22c510<sup>10<\/sup>\u00a0fissions per second<\/strong>\u00a0are required to produce a power of\u00a0<strong>1 W<\/strong>.<\/li>\n<li>Since\u00a0<strong>1 gram<\/strong>\u00a0of any\u00a0<a title=\"Fissile Material\" href=\"http:\/\/sitepourvtc.com\/glossary\/fissile-material\/\">fissile material\u00a0<\/a>contains about\u00a0<strong>2.5 x 10<sup>21<\/sup>\u00a0nuclei<\/strong>, the fissioning of 1 gram of fissile material yields\u00a0<strong>about one megawatt-day (MWd)<\/strong>\u00a0of heat energy.<\/li>\n<li>In 2011 nuclear power provided 10% of the world\u2019s electricity. In 2007, the IAEA reported 439 nuclear power reactors operating globally, operating in 31 countries.<\/li>\n<\/ul>\n<div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-dotted\" style=\"margin:10px 0;border-width:2px;border-color:#999999\"><\/div>\n<div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\">\n<div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-modern-light su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>How does nuclear fission work?<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><strong>How does nuclear fission work?<\/strong><\/p>\n<ul>\n<li>In principle,\u00a0<strong>any nucleus<\/strong>, if brought into a sufficiently <strong>high excited state<\/strong>,\u00a0<strong>can be split<\/strong>.<\/li>\n<li>The excitation energy must be <strong>above <\/strong><a title=\"Critical Energy \u2013 Threshold Energy for Fission\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/critical-energy-threshold-energy-for-fission\/\"><strong>the critical energy (E<sub>crit<\/sub>)<\/strong>\u00a0or\u00a0<strong>threshold energy<\/strong><\/a> for fission to occur.<\/li>\n<li>For heavier nuclei with Z &gt; 90, the critical energy is about\u00a0<strong>4 to 6 MeV<\/strong> for A-even nuclei and generally is<strong>\u00a0much lower for A-odd nuclei<\/strong>.<\/li>\n<li>Thermal neutrons can bring about 5 MeV (binding energy) to such nuclei, thus inducing fission.<\/li>\n<\/ul>\n<\/div><\/div>\n<div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-modern-light su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>What is nuclear fission example?<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">\n<strong>What is nuclear fission example?<\/strong><\/p>\n<p>A\u00a0<strong>typical fission reaction<\/strong> is below.\u00a0About 15% of all absorption reactions result in radiative capture of neutrons. About 85% of all absorption reactions result in fission.<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/06\/uranium_absorption_reaction.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-12159\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/06\/uranium_absorption_reaction.png\" sizes=\"(max-width: 775px) 100vw, 775px\" srcset=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/06\/uranium_absorption_reaction.png 775w, http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/06\/uranium_absorption_reaction-300x57.png 300w\" alt=\"Uranium absorption reaction\" width=\"775\" height=\"148\" \/><\/a><\/p>\n<\/div><\/div>\n<div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-modern-light su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>What is nuclear fission and nuclear fusion?<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">\n<strong>What are nuclear fission and nuclear fusion?<\/strong><\/p>\n<p><strong>Nuclear fission<\/strong> is a nuclear reaction in which the nucleus of an atom splits into smaller parts (lighter nuclei). The fission process often produces\u00a0<a title=\"Free Neutron\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/free-neutron\/\">free neutrons<\/a> and photons (in the form of gamma rays) and releases a large amount of energy.<\/p>\n<p><strong>Nuclear fusion<\/strong> occurs when two or more atomic nuclei collide at a very high speed and join to form a new type of atomic nucleus. The fusion reaction of deuterium and tritium is fascinating because of its potential of providing energy for the future.<\/p>\n<\/div><\/div>\n<\/div>\n<\/div><\/div>\n<\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-dotted\" style=\"margin:10px 0;border-width:2px;border-color:#999999\"><\/div>\n<div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-100 lgc-tablet-grid-100 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\"><strong>Nuclear fission<\/strong> is a <a title=\"Neutron Nuclear Reactions\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/\">nuclear reaction<\/a> in which the nucleus of an atom <strong>splits<\/strong> into smaller parts (lighter nuclei). The fission process often produces <a title=\"Free Neutron\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/free-neutron\/\">free neutrons<\/a> and <a title=\"Photon \u2013 Fundamental Particle\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/photon\/\">photons<\/a> (in the form of <a title=\"Gamma Rays \/ Gamma Radiation\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/photon\/gamma-ray\/\">gamma rays<\/a>) and releases a <strong>large amount of energy<\/strong>. In nuclear physics, nuclear fission is <strong>either a nuclear reaction<\/strong> <strong>or a radioactive decay process<\/strong>. The case of the decay process is called <strong>spontaneous fission,<\/strong> and it is a sporadic process. In this section, <strong>neutron-induced nuclear fission<\/strong>, the process of the greatest practical importance in <a title=\"Reactor Physics\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/\">reactor physics<\/a>, will be discussed.\n<p>See also: <a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/ternary-fission\/\">Ternary Fission<\/a><\/p>\n<p><a href=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2021\/10\/nuclear-fission-characteristics-min.png\"><img loading=\"lazy\" class=\"aligncenter wp-image-33684 size-large\" src=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2021\/10\/nuclear-fission-characteristics-min-926x1024.png\" alt=\"nuclear fission - characteristics\" width=\"926\" height=\"1024\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2021\/10\/nuclear-fission-characteristics-min-926x1024.png 926w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2021\/10\/nuclear-fission-characteristics-min-271x300.png 271w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2021\/10\/nuclear-fission-characteristics-min-768x849.png 768w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2021\/10\/nuclear-fission-characteristics-min-1389x1536.png 1389w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2021\/10\/nuclear-fission-characteristics-min.png 1440w\" sizes=\"(max-width: 926px) 100vw, 926px\" \/><\/a><\/p>\n<div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-dotted\" style=\"margin:15px 0;border-width:2px;border-color:#999999\"><\/div>\n<div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>A Brief History of Nuclear Fission<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">\n<p>Nuclear fission of heavy elements was discovered on December 17, 1938, by Otto Hahn and his assistant Fritz Strassmann. They attempted to create transuranic elements by bombarding uranium with neutrons. Rather than the heavy elements they expected, they got several unidentified products. When they finally identified one of the products as Barium-141, they were circumspective of publishing the finding because it was unexpected.<\/p>\n<p>When they finally published the results in 1939, they came to the attention of Lise Meitner, an Austrian-born physicist who had worked with Hahn on his nuclear experiments. She was the first to realize that Hahn\u2019s barium and other lighter products from the neutron bombardment experiments were coming from the fission of U-235. Meitner and Frisch carried out further experiments, which showed that the U-235 fission could release large amounts of energy both as electromagnetic radiation and as kinetic energy of the fragments (heating the bulk material where fission takes place). They realized that this made possible a chain reaction with an unprecedented energy yield.<\/p><\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-dotted\" style=\"margin:15px 0;border-width:2px;border-color:#999999\"><\/div><\/div><\/div>\n<div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-100 lgc-tablet-grid-100 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\">\n<h2>Key Characteristics of Nuclear Fission<\/h2>\n<ul>\n<li><strong>Nuclear fission<\/strong> is the primary process of generating nuclear energy.<\/li>\n<li>Most of the energy (~85%) is released in the form of the kinetic energy of the split parts.<\/li>\n<li><strong>Neutrons<\/strong> trigger <strong>nuclear fission<\/strong>.<\/li>\n<li>The fission process produces free neutrons (2 or 3).<\/li>\n<li>The chain reaction means if the reaction induces <b>one or more<\/b> reactions.<\/li>\n<li>The probability that fission will occur depends on incident <a title=\"Neutron Energy\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/neutron-energy\/\" target=\"_blank\" rel=\"noopener\">neutron energy<\/a>.<\/li>\n<li>Therefore the <a title=\"Neutron moderator\" href=\"http:\/\/sitepourvtc.com\/neutron-moderator\/\" target=\"_blank\" rel=\"noopener\">moderator<\/a> is used to slow down neutrons (to increase the probability of fission)<\/li>\n<li>For reactors using light water as moderators, enriched uranium fuel is required.<\/li>\n<li>Control rods contain material that absorbs neutrons (<a title=\"Boron 10\" href=\"http:\/\/sitepourvtc.com\/glossary\/boron-10\/\">boron<\/a>, <a title=\"Cadmium\" href=\"http:\/\/sitepourvtc.com\/glossary\/cadmium\/\">cadmium<\/a>, &#8230;)<\/li>\n<li>Withdrawal of the rods increases the parameter <b>one or more<\/b> (multiplication factor), thus increase the power.<\/li>\n<li>Insertion of the rods decreases the parameter <b>one or more<\/b> (multiplication factor), thus decrease the power.<\/li>\n<li>The multiplication factor is also influenced by other parameters such as temperature, fuel burnup, and reactor poisoning.<\/li>\n<li>The fission takes place\u00a0in the <a title=\"Reactor Core\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor-core\/\"><strong>nuclear reactor core<\/strong><\/a>.<\/li>\n<li>The reactor core consists of <a title=\"Nuclear Fuel\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/\">nuclear fuel<\/a>, <a title=\"Control Rods\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/control-rods\/\">control rods<\/a>, <a title=\"Neutron moderator\" href=\"http:\/\/sitepourvtc.com\/neutron-moderator\/\" target=\"_blank\" rel=\"noopener\">moderator<\/a> (coolant), and neutron reflector.<\/li>\n<\/ul>\n<h2>Nuclear Fission and Chain Reaction<\/h2>\n<p>Some nuclei can <strong>undergo fission<\/strong> on their own spontaneously, but only specific nuclei, like <a title=\"Uranium 235\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-235\/\">uranium-235<\/a>, <a title=\"Uranium 233\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-233\/\">uranium-233<\/a>, and <a title=\"Plutonium 239\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/plutonium\/plutonium-239\/\">plutonium-239<\/a>, can <strong>sustain a fission chain reaction<\/strong>. This is because these nuclei release <a title=\"Neutron\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/\" target=\"_blank\" rel=\"noopener\">neutrons<\/a> when they break apart, which can induce fission of other nuclei. Free neutrons released by each fission play a critical role as a trigger of the reaction.<\/p>\n<figure id=\"attachment_64\" aria-describedby=\"caption-attachment-64\" style=\"width: 695px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2014\/10\/nuclear_fission.jpg\"><img loading=\"lazy\" class=\"wp-image-64 size-large\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2014\/10\/nuclear_fission-1024x439.jpg\" alt=\"Nuclear fission\" width=\"705\" height=\"302\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2014\/10\/nuclear_fission-1024x439.jpg 1024w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2014\/10\/nuclear_fission-300x128.jpg 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2014\/10\/nuclear_fission.jpg 1681w\" sizes=\"(max-width: 705px) 100vw, 705px\" \/><\/a><figcaption id=\"caption-attachment-64\" class=\"wp-caption-text\">Nuclear fission is a nuclear reaction in which the nucleus of an atom splits into smaller parts (lighter nuclei). The neutron triggers this nuclear reaction. Source: chemwiki.ucdavis.edu<\/figcaption><\/figure>\n<h3>Chain reaction<\/h3>\n<p><strong>A nuclear chain reaction<\/strong> occurs when one single nuclear reaction causes an average of <b>one or more<\/b> subsequent nuclear reactions, thus leading to the possibility of a self-propagating series of these reactions. The \u201c<b>one or more<\/b>\u201d is the key parameter of reactor physics. The amount of reactions must be changed (using the control rods) to raise or lower the power so that the number of neutrons present (hence the power generation rate) is either reduced or increased.<\/p>\n<figure id=\"attachment_68\" aria-describedby=\"caption-attachment-68\" style=\"width: 471px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2014\/10\/chain-reaction.jpg\"><img loading=\"lazy\" class=\"wp-image-68\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2014\/10\/chain-reaction.jpg\" alt=\"Nuclear chain reaction\" width=\"481\" height=\"453\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2014\/10\/chain-reaction.jpg 550w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2014\/10\/chain-reaction-300x282.jpg 300w\" sizes=\"(max-width: 481px) 100vw, 481px\" \/><\/a><figcaption id=\"caption-attachment-68\" class=\"wp-caption-text\">A nuclear chain reaction occurs when one single nuclear reaction causes an average of one or more subsequent nuclear reactions.<\/figcaption><\/figure>\n<div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-dotted\" style=\"margin:15px 0;border-width:2px;border-color:#999999\"><\/div><\/div><\/div>\n<div   id="8n9s8rpp6h"    class=\"collapsible-container\">\n<h2>Physics of Nuclear Fission<\/h2>\n<p style=\"text-align: left;\">In general,<strong> the neutron-induced fission reaction<\/strong> is the reaction in which the <a title=\"Neutron\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/\">incident neutron<\/a> enters the heavy target nucleus (<a title=\"Fissionable Material\" href=\"http:\/\/sitepourvtc.com\/glossary\/fissionable-material\/\">fissionable nucleus<\/a>), forming a<a title=\"Compound Nucleus Reactions\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/compound-nucleus-reactions\/\"> compound nucleus<\/a> that is <strong>excited<\/strong> to such a <strong>high energy level<\/strong> (<strong>E<sub>excitation<\/sub> &gt; E<sub>critical<\/sub><\/strong>) that the nucleus <strong>splits<\/strong> into two large <a title=\"Fission Fragments\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/fission-fragments\/\">fission fragments<\/a>. A large amount of energy is released in the form of <a title=\"Forms of Ionizing Radiation\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/radiation\/forms-ionizing-radiation\/\">radiation<\/a> and fragment kinetic energy. Moreover, and what is crucial, the fission process may produce <strong>2, 3, or more<\/strong> <a title=\"Free Neutron\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/free-neutron\/\">free neutrons<\/a>, and these neutrons can trigger further fission, and a <a title=\"Nuclear Fission Chain Reaction\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/\"><strong>chain reaction<\/strong><\/a> can occur. To understand the process of fission, we must understand processes that occur inside the nucleus to be fissioned. At first, the <strong>nuclear binding energy<\/strong> must be defined.<\/p>\n<div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\"><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Uranium - 235 Fission Reaction<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">\n<figure id=\"attachment_12060\" aria-describedby=\"caption-attachment-12060\" style=\"width: 290px\" class=\"wp-caption alignright\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/Uranium_235.png\"><img loading=\"lazy\" class=\"size-medium wp-image-12060\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/Uranium_235-300x212.png\" alt=\"Fissile \/ Fertile Material Cross-sections\" width=\"300\" height=\"212\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/Uranium_235-300x212.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/Uranium_235.png 574w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-12060\" class=\"wp-caption-text\">Source: JANIS (Java-based nuclear information software)<br \/>http:\/\/www.oecd-nea.org\/janis\/<\/figcaption><\/figure>\n<p><a title=\"Uranium 235\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-235\/\">Uranium 235<\/a> is a <a title=\"Fissile Material\" href=\"http:\/\/sitepourvtc.com\/glossary\/fissile-material\/\">fissile isotope<\/a>, and its <a title=\"Cross-sections of Uranium\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/cross-sections-of-uranium\/\">fission cross-section<\/a> for thermal neutrons is about <strong>585 barns<\/strong> (for 0.0253 eV neutron). For fast neutrons, its fission cross-section is <strong>on the order of barns<\/strong>. Most absorption reactions result in fission reaction, but a minority results in <a title=\"Neutron Capture \u2013 Radiative Capture\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/neutron-capture-radiative-capture\/\">radiative capture<\/a> forming <sup>236<\/sup>U. The cross-section for radiative capture for thermal neutrons is about <strong>99 barns<\/strong> (for 0.0253 eV neutron). Therefore about 15% of all absorption reactions result in radiative capture of neutrons. About 85% of all absorption reactions result in fission.<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/06\/uranium_absorption_reaction.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-12159\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/06\/uranium_absorption_reaction.png\" alt=\"Uranium absorption reaction\" width=\"775\" height=\"148\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/06\/uranium_absorption_reaction.png 775w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/06\/uranium_absorption_reaction-300x57.png 300w\" sizes=\"(max-width: 775px) 100vw, 775px\" \/><\/a><\/p>\n<h2><\/h2>\n<\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Uranium - 233 Fission Reaction<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">\n<figure id=\"attachment_12061\" aria-describedby=\"caption-attachment-12061\" style=\"width: 290px\" class=\"wp-caption alignright\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/Uranium_233.png\"><img loading=\"lazy\" class=\"size-medium wp-image-12061\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/Uranium_233-300x209.png\" alt=\"Fissile \/ Fertile Material Cross-sections\" width=\"300\" height=\"209\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/Uranium_233-300x209.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/Uranium_233.png 580w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-12061\" class=\"wp-caption-text\">Source: JANIS (Java-based nuclear information software)<br \/>http:\/\/www.oecd-nea.org\/janis\/<\/figcaption><\/figure>\n<p><a title=\"Uranium 233\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-233\/\">Uranium 233<\/a> is a very good <a title=\"Fissile Material\" href=\"http:\/\/sitepourvtc.com\/glossary\/fissile-material\/\">fissile isotope<\/a>, and its fission <a title=\"Neutron cross-section\" href=\"http:\/\/sitepourvtc.com\/neutron-cross-section\/\">cross-<\/a>section for\u00a0thermal neutrons is about <strong>531 barns<\/strong> (for 0.0253 eV neutron). For fast neutrons, its fission cross-section is on the order of barns. Most absorption reactions result in <a title=\"Nuclear Fission\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/\">fission reaction<\/a>, but a minority results in <a title=\"Neutron Capture \u2013 Radiative Capture\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/neutron-capture-radiative-capture\/\">radiative capture<\/a> forming <sup>234<\/sup>U. The cross-section for radiative capture for thermal neutrons is about <strong>45 barns<\/strong> (for 0.0253 eV neutron). Therefore about 6% of all absorption reactions result in radiative capture of neutrons. About 94% of all absorption reactions result in fission. The capture-to-fission ratio is much smaller than the other two major fissile fuels <sup>235<\/sup>U\u00a0and <sup>239<\/sup>U.<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/11\/uranium_233_absorption_reaction_2.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-15961\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/11\/uranium_233_absorption_reaction_2.png\" alt=\"Uranium 233 absorption reaction\" width=\"731\" height=\"147\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/11\/uranium_233_absorption_reaction_2.png 731w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/11\/uranium_233_absorption_reaction_2-300x60.png 300w\" sizes=\"(max-width: 731px) 100vw, 731px\" \/><\/a><\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Plutonium - 239 Fission Reaction<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">\n<figure id=\"attachment_12064\" aria-describedby=\"caption-attachment-12064\" style=\"width: 290px\" class=\"wp-caption alignright\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/plutonium_239.png\"><img loading=\"lazy\" class=\"size-medium wp-image-12064\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/plutonium_239-300x207.png\" alt=\"Fissile \/ Fertile Material Cross-sections\" width=\"300\" height=\"207\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/plutonium_239-300x207.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/plutonium_239.png 583w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-12064\" class=\"wp-caption-text\">Source: JANIS (Java-based nuclear information software)<br \/>http:\/\/www.oecd-nea.org\/janis\/<\/figcaption><\/figure>\n<p><a title=\"Plutonium 239\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/plutonium\/plutonium-239\/\">Plutonium 239<\/a> is a<a title=\"Fissile Material\" href=\"http:\/\/sitepourvtc.com\/glossary\/fissile-material\/\"> fissile isotope<\/a>, and its fission cross-section for thermal<a title=\"Neutron Energy\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/neutron-energy\/\">\u00a0neutrons<\/a> is about <strong>750 barns<\/strong> (for 0.025 eV neutron). <strong>For fast neutrons,<\/strong> its fission cross-section is <strong>on the order of barns<\/strong>. Most absorption reactions result in <a title=\"Nuclear Fission\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/\">fission reaction<\/a>, but a part of reactions result in <a title=\"Neutron Capture \u2013 Radiative Capture\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/neutron-capture-radiative-capture\/\">radiative capture<\/a> forming <sup>240<\/sup>Pu. The cross-section for radiative capture for thermal neutrons is about <strong>270 barns<\/strong> (for 0.025 eV neutron). Therefore about <strong>27%<\/strong> of all absorption reactions result in radiative capture of incident neutron. About<strong> 73%<\/strong> of all absorption reactions result in fission.<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/07\/plutonium-fission.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-12392\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/07\/plutonium-fission.png\" alt=\"Plutonium fission vs. radiative capture\" width=\"753\" height=\"132\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/07\/plutonium-fission.png 753w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/07\/plutonium-fission-300x53.png 300w\" sizes=\"(max-width: 753px) 100vw, 753px\" \/><\/a><\/div><\/div><\/div>\n<h2>Nuclear Binding Energy<\/h2>\n<div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\"><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Binding Energy<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><strong>A <a title=\"Binding Energy\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/binding-energy\/\">binding energy<\/a><\/strong> is generally the energy required to <strong>disassemble<\/strong> a whole system into separate parts. It is known the sum of separate parts typically has higher potential energy than a bound system. Therefore the <strong>bound system is more stable<\/strong>. The creation of a bound system is often accompanied by subsequent energy release. We usually distinguish the binding energy according to these levels:<\/p>\n<ul>\n<li>Atomic-level<\/li>\n<li>Molecular\u00a0level<\/li>\n<li>Nuclear\u00a0level<\/li>\n<\/ul>\n<\/div><\/div>\n<\/div>\n<p>At the nuclear level, the <a title=\"Nuclear Binding Energy\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/binding-energy\/nuclear-binding-energy\/\"><strong>nuclear binding energy<\/strong><\/a> is required to <strong>disassemble<\/strong> (to overcome <strong>the strong nuclear force<\/strong>) <strong>a nucleus of an atom into its component parts<\/strong> (protons and <a title=\"Neutron\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/\">neutrons<\/a>). The protons and neutrons in an atomic nucleus are held together by the nuclear forces (strong force). The mass of a nucleus is always less than the sum of masses of the constituent protons and neutrons when separated. The difference is a measure of the <strong>nuclear binding energy (E<sub>b<\/sub>)<\/strong> which holds the nucleus together. According to the Einstein relationship (<a title=\"E=mc2 Meaning\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/nuclear-energy\/emc2-meaning\/\">E=m.c<sup>2<\/sup><\/a>) this binding energy is proportional to this mass difference, known as <strong>the mass defect<\/strong>.<\/p>\n<figure id=\"attachment_237\" aria-describedby=\"caption-attachment-237\" style=\"width: 374px\" class=\"wp-caption alignright\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2014\/11\/nuclear_binding_energy.gif\"><img loading=\"lazy\" class=\" wp-image-237\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2014\/11\/nuclear_binding_energy.gif\" alt=\"Nuclear binding energy curve.\" width=\"384\" height=\"250\" \/><\/a><figcaption id=\"caption-attachment-237\" class=\"wp-caption-text\">Nuclear binding energy curve.<br \/>Source: hyperphysics.phy-astr.gsu.edu<\/figcaption><\/figure>\n<p>During the <strong>nuclear splitting<\/strong> or <a title=\"Nuclear Fusion\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/nuclear-fusion\/\">nuclear fusion<\/a>, some of the mass of the nucleus gets <strong>converted<\/strong> into vast amounts of energy. Thus this mass is removed from the total mass of the original particles, and the mass is missing in the resulting nucleus. <strong>The nuclear binding energies are enormous<\/strong>, and they\u00a0are on the order of a million times greater than the electron binding energies of atoms.<\/p>\n<p>For a nucleus with A (mass number) nucleons, the binding energy per nucleon <strong>E<sub>b<\/sub>\/A<\/strong> can be calculated. This calculated fraction is shown in the chart as a function of the mass number A. As can be seen, for low mass numbers, <strong>E<sub>b<\/sub>\/A<\/strong>\u00a0increases rapidly and reaches a maximum of <strong>8.8 MeV<\/strong> at approximately <strong>A=60<\/strong>. The nuclei with the highest binding energies that are most tightly bound belong to the <strong>\u201ciron group\u201d<\/strong> of isotopes (<sup>56<\/sup>Fe, <sup>58<\/sup>Fe, <sup>62<\/sup>Ni). <strong>After that, the binding energy per nucleon decreases<\/strong>. A more stable configuration is obtained in the heavy nuclei (A&gt;60) region when a <strong>heavy nucleus splits into two lighter nuclei<\/strong>. This is the origin of the fission process. It may seem that all the heavy nuclei may undergo <strong>fission<\/strong> or even <strong>spontaneous fission<\/strong>. In fact, for all nuclei with atomic number greater than about 60, fission occurs very rarely. For the fission process to take place, a <strong>sufficient amount of energy must be added to the nucleus<\/strong>, no matter how. The energetics and binding energies of a specific nucleus are well described by <strong>the Liquid Drop Model<\/strong>, which examines the global properties of nuclei.<div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\"><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Example: Mass defect of a reactor core<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">Calculate the <a title=\"Mass Defect\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/nuclear-energy\/mass-defect\/\"><strong>mass defect<\/strong><\/a> of the <strong>3000MW<sub>th<\/sub><\/strong> <a title=\"Reactor Core\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor-core\/\">reactor core<\/a> after one year of operation.<\/p>\n<p>The average <a title=\"Energy Release from Fission\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/energy-release-from-fission\/\">recoverable energy per fission<\/a> is about <strong>200 MeV<\/strong>, being the total energy minus the energy of <a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/antineutrino\/\">antineutrinos<\/a> radiated away.<\/p>\n<p>The <a title=\"Reaction Rate\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/reaction-rate\/\"><strong>reaction rate<\/strong><\/a> per entire <strong>3000MW<sub>th<\/sub><\/strong>\u00a0reactor core is about \u00a0<strong>9.33\u00d710<sup>19<\/sup> fissions\/second<\/strong>.<\/p>\n<p><strong>The overall energy release<\/strong> in the units of joules is:<\/p>\n<p>200\u00d710<sup>6<\/sup> (eV) x 1.602\u00d710<sup>-19<\/sup> (J\/eV) x 9.33\u00d710<sup>19<\/sup> (s<sup>-1<\/sup>) x 31.5\u00d710<sup>6<\/sup> (seconds in year) = <strong>9.4\u00d710<sup>16<\/sup> J\/year<\/strong><\/p>\n<p>The mass defect is calculated as:<\/p>\n<p>\u0394m = \u0394E\/c<sup>2<\/sup><\/p>\n<p><strong>\u0394m<\/strong> = 9.4\u00d710<sup>16<\/sup> \/ (2.9979 x 10<sup>8<\/sup>)<sup>2<\/sup> = <strong>1.046 kg<\/strong><\/p>\n<p>That means in a typical <strong>3000MWth<\/strong> reactor core, about 1 kilogram of the matter is <strong>converted<\/strong> into pure energy.<\/p>\n<p>Note that a typical annual <a title=\"Uranium\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/\">uranium<\/a> load for a <strong>3000MWth <\/strong>reactor core is about <strong>20 tonnes<\/strong> of <strong><a title=\"Enriched Uranium\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/enriched-uranium\/\">enriched uranium<\/a> <\/strong>(i.e., about<strong>22.7 tonnes of UO<sub>2<\/sub><\/strong>). The entire reactor core may contain about 80 tonnes of enriched uranium.<\/p>\n<h2>Mass defect directly from E=mc<sup>2<\/sup><\/h2>\n<p>The mass defect can be calculated directly from\u00a0the Einstein relationship (<strong><a title=\"E=mc2 Meaning\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/nuclear-energy\/emc2-meaning\/\">E = mc<sup>2<\/sup><\/a><\/strong>) as:<\/p>\n<p>\u0394m = \u0394E\/c<sup>2<\/sup><\/p>\n<p>\u0394m = 3000\u00d710<sup>6<\/sup>\u00a0(W = J\/s) x\u00a031.5\u00d710<sup>6<\/sup> (seconds in year) \/ (2.9979 x 10<sup>8<\/sup>)<sup>2\u00a0<\/sup>= <strong>1,051 kg<\/strong><\/div><\/div><\/div>\n<h2>Liquid Drop Model<\/h2>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/liquid-drop-model-min.png\"><img loading=\"lazy\" class=\"alignright wp-image-13259\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/liquid-drop-model-min-1024x1024.png\" alt=\"Liquid Drop Model\" width=\"450\" height=\"450\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/liquid-drop-model-min-1024x1024.png 1024w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/liquid-drop-model-min-150x150.png 150w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/liquid-drop-model-min-300x300.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/liquid-drop-model-min-66x66.png 66w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/liquid-drop-model-min.png 1080w\" sizes=\"(max-width: 450px) 100vw, 450px\" \/><\/a>One of the first models that could describe the behavior of the nuclear binding energies. Therefore nuclear masses were the mass formula of <strong>von Weizsaecker<\/strong> (also called <strong>the semi-empirical mass formula &#8211; SEMF)<\/strong> published in 1935 by German physicist <strong>Carl Friedrich von Weizs\u00e4cker<\/strong>. This theory is based on <a title=\"Liquid Drop Model\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/liquid-drop-model\/\"><strong>the liquid drop model<\/strong><\/a> proposed by <strong>George Gamow<\/strong>.<\/p>\n<p>According to this model, the atomic nucleus behaves <strong>like the molecules in a drop<\/strong> of liquid. But in this nuclear scale, the fluid is made of nucleons (protons and <a title=\"Neutron\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/\">neutrons<\/a>), held together by <strong>the strong nuclear force<\/strong>. The liquid drop model of the nucleus considers that the nuclear forces on the nucleons on the surface are different from those on nucleons in the interior of the nucleus. Other attracting nucleons completely surround the interior nucleons. Here is the analogy with the forces that form a drop of liquid.<\/p>\n<p>In the ground state, the nucleus is <strong>spherical<\/strong>. If sufficient kinetic or binding energy is added, this spherical nucleus may be distorted into a <strong>dumbbell shape<\/strong> and then maybe split into <strong>two fragments<\/strong>. Since these fragments are more stable, the splitting of such heavy nuclei must be accompanied by <strong>energy release<\/strong>. This model does not explain all the properties of the atomic nucleus but does explain the predicted nuclear binding energies.<\/p>\n<p>The nuclear binding energy, as a function of the mass number A and the number of<br \/>\nprotons Z, is based on <strong>the liquid drop model<\/strong>. Its formula can be written as:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/Weizsaecker-formula-general.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-13261\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/Weizsaecker-formula-general.png\" alt=\"Weizsaecker formula - semi-empirical mass formula\" width=\"648\" height=\"212\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/Weizsaecker-formula-general.png 648w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/Weizsaecker-formula-general-300x98.png 300w\" sizes=\"(max-width: 648px) 100vw, 648px\" \/><\/a><\/p>\n<p>This formula is called <strong>the Weizsaecker Formula<\/strong> (or <strong>the semi-empirical mass formula<\/strong>). The physical meaning of this equation can be discussed term by term.<\/p>\n<div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\">\n<div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Volume term<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><strong>Volume term &#8211; a<sub>V<\/sub>.A.<\/strong> The first two terms describe a spherical liquid drop of an incompressible fluid that contributes to the volume scaling with A and the surface, scaling with A<sup>2\/3<\/sup>. The first positive term <strong>a<sub>V<\/sub>.A<\/strong> is known as the volume term, which is caused by attracting strong forces between the nucleons. The <strong>strong force<\/strong> has a <strong>very limited range,<\/strong> and a given nucleon may only interact with its <strong>direct neighbors<\/strong>. Therefore this term is proportional to A instead of A<sup>2<\/sup>. The coefficient <strong>a<sub>V<\/sub><\/strong>\u00a0is usually about ~ 16 MeV.<\/p>\n<\/div><\/div>\n<div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Surface term<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><strong>Surface term &#8211; a<sub>sf<\/sub>.A<sup>2\/3<\/sup>.<\/strong> The surface term is also based on the strong force. It is, in fact, a <strong>correction to the volume term<\/strong>. The point is that other particles do not completely surround particles at the surface of the nucleus. In the volume term, it is suggested that each nucleon interacts with a constant number of nucleons, independent of A. This assumption is nearly true for nucleons deep within the nucleus but <strong>causes an overestimation<\/strong> of the binding energy on the surface. By analogy with a liquid drop, this effect is indicated as <strong>the surface tension effect<\/strong>. If the volume of the nucleus is proportional to A, then the geometrical radius should be proportional to A<sup>1\/3<\/sup>. Therefore the surface term must be proportional to the surface area, i.e., proportional to A<sup>2\/3<\/sup>.<\/p>\n<\/div><\/div>\n<div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Coulomb term<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><strong>Coulomb term &#8211; a<sub>C<\/sub>.Z<sup>2<\/sup>.A<sup>-\u2153<\/sup>.<\/strong> This term describes the Coulomb repulsion between the uniformly distributed protons and is proportional to the number of proton pairs <strong>Z<sup>2<\/sup>\/R<\/strong>, whereby R is proportional to A<sup>1\/3<\/sup>. <strong>This effect lowers the binding energy<\/strong> because of the repulsion between charges of the equal sign.<\/p>\n<\/div><\/div>\n<div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Asymmetry term<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><strong>Asymmetry term &#8211; a<sub>A<\/sub>.(A-2Z)<sup>2<\/sup>\/A.<\/strong> This term cannot be described as \u2018classically\u2019 as the first three. This effect is not based on any of the fundamental forces, and this effect is based only on <strong>the Pauli exclusion principle<\/strong> (no two fermions can occupy the same quantum state in an atom). The heavier nuclei contain more neutrons than protons. These extra neutrons are necessary for the stability of the heavier nuclei. They provide (via the attractive forces between the neutrons and protons) some compensation for the repulsion between the protons. On the other hand, if there are significantly more neutrons than protons in a nucleus, some of the neutrons will be higher in energy level in the nucleus. This is the basis for a correction factor, the so-called symmetry term.<\/p>\n<\/div><\/div>\n<div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Pairing term<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><strong>Pairing term &#8211; \u03b4(A,Z).<\/strong> The last term is the pairing term \u03b4(A, Z). This term captures the effect of spin-coupling. Nuclei with an even number of protons and an even number of neutrons are (due to the Pauli exclusion principle) very stable thanks to the occurrence of \u201cpaired spin\u201d. On the other hand, nuclei with an odd number of protons and neutrons are mostly unstable.<\/p>\n<\/div><\/div>\n<div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Table of Calculated Binding Energies<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">\n<figure id=\"attachment_13246\" aria-describedby=\"caption-attachment-13246\" style=\"width: 683px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/Table-semi-empirical-mass-formula-weizsaecker.png\"><img loading=\"lazy\" class=\"size-full wp-image-13246\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/Table-semi-empirical-mass-formula-weizsaecker.png\" alt=\"the semi-empirical mass formula - weizsaecker formula\" width=\"693\" height=\"350\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/Table-semi-empirical-mass-formula-weizsaecker.png 693w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/Table-semi-empirical-mass-formula-weizsaecker-300x152.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/Table-semi-empirical-mass-formula-weizsaecker-540x272.png 540w\" sizes=\"(max-width: 693px) 100vw, 693px\" \/><\/a><figcaption id=\"caption-attachment-13246\" class=\"wp-caption-text\">Table of binding energies for some nuclides. Calculated according to the semi-empirical mass formula.<\/figcaption><\/figure>\n<p>&nbsp;<\/p>\n<\/div><\/div>\n<\/div>\n<p>With the aid of <strong>the Weizsaecker formula,<\/strong> the binding energy can be calculated very well for nearly all isotopes. This formula provides a good fit for heavier nuclei. For light nuclei, especially for <sup>4<\/sup>He, it provides a poor fit. The main reason is the formula does not consider the internal shell structure of the nucleus.<\/p>\n<p>The coefficients a<sub>V<\/sub>, a<sub>S<\/sub>, a<sub>C<\/sub>, a<sub>A<\/sub>, and a<sub>P<\/sub> must be known to calculate the binding energy. The coefficients have units of <strong>megaelectronvolts (MeV)<\/strong> and are calculated <strong>by fitting<\/strong> to <strong>experimentally measured masses of nuclei<\/strong>. They usually vary depending on the fitting methodology. According to ROHLF, J. W., Modern Physics from \u03b1 to Z0, Wiley, 1994., the coefficients in the equation are following:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/Weizsaecker-formula.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-13260\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/Weizsaecker-formula.png\" alt=\"Weizsaecker formula - semi-empirical mass formula\" width=\"817\" height=\"100\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/Weizsaecker-formula.png 817w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/Weizsaecker-formula-300x37.png 300w\" sizes=\"(max-width: 817px) 100vw, 817px\" \/><\/a><\/p>\n<p>Using <strong>the Weizsaecker formula<\/strong>, also the mass of an atomic nucleus can be derived and is given by:<\/p>\n<p><strong>m = Z.m<sub>p<\/sub> + N.m<sub>n<\/sub> &#8211; E<sub>b<\/sub>\/c<sup>2<\/sup><\/strong><\/p>\n<p>where <strong>m<sub>p<\/sub><\/strong>\u00a0and <strong>m<sub>n<\/sub><\/strong>\u00a0are the rest mass of a proton and a neutron, respectively, and <strong>E<sub>b<\/sub><\/strong>\u00a0is the nuclear binding energy of the nucleus.<\/p>\n<p>From the nuclear binding energy curve and from the table, it can be seen that, in the case of splitting a <a title=\"Uranium 235\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-235\/\"><sup>235<\/sup>U<\/a> nucleus into two parts, the binding energy of the fragments (A \u2248 120) together is more significant than that of the original <sup>235<\/sup>U nucleus.<br \/>\nAccording to the Weizsaecker formula, the total energy released for such a reaction will be approximately <strong>235 x (8.5 \u2013 7.6) \u2248 200 MeV.<\/strong><\/p>\n<p>See also: <a title=\"Liquid Drop Model\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/liquid-drop-model\/\">Liquid Drop Model<\/a><\/p>\n<h2>Critical Energy &#8211; Threshold Energy for Fission<\/h2>\n<p>In principle, <strong>any nucleus<\/strong>, if brought into a sufficiently <strong>high excited state<\/strong>, <strong>can be split<\/strong>. For fission to occur, the excitation energy must be <strong>above a particular value<\/strong> for a certain nuclide. The minimum excitation energy required for fission to occur is known as <a title=\"Critical Energy \u2013 Threshold Energy for Fission\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/critical-energy-threshold-energy-for-fission\/\"><strong>the critical energy (E<sub>crit<\/sub>)<\/strong> or <strong>threshold energy<\/strong><\/a>.<\/p>\n<p>The critical energy depends on the nuclear structure and is significant for light nuclei with Z &lt; 90. For heavier nuclei with Z &gt; 90, the critical energy is about <strong>4 to 6 MeV<\/strong> for A-even nuclei and generally is<strong> much lower for A-odd nuclei<\/strong>. It must be noted, some heavy nuclei (<strong>e.g.,,<a title=\"Plutonium 240\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/plutonium\/plutonium-240\/\"> <sup>240<\/sup>Pu<\/a> or <sup>252<\/sup>Cf<\/strong>) exhibit fission even <strong>in the ground state<\/strong> (without externally added excitation energy). This phenomenon is known as <strong>spontaneous fission<\/strong>. This process occurs without adding the critical energy by the quantum-mechanical process of <strong>quantum tunneling<\/strong> through the Coulomb barrier (similarly to <a title=\"Alpha Particle\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/alpha-particle\/\">alpha particles<\/a> in the alpha decay). <strong>Spontaneous fission<\/strong> ensures sufficient neutron flux on source range detectors when the reactor is <strong>subcritical<\/strong> in long-term shutdown.<\/p>\n<p>See also: <a title=\"Critical Energy \u2013 Threshold Energy for Fission\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/critical-energy-threshold-energy-for-fission\/\">Critical Energy &#8211; Threshold Energy for Fission<\/a>.<br \/>\n<a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/Critical-Energy-Threshold-Energy.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-13250\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/Critical-Energy-Threshold-Energy.png\" alt=\"Critical Energy - Threshold Energy\" width=\"886\" height=\"592\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/Critical-Energy-Threshold-Energy.png 886w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/Critical-Energy-Threshold-Energy-300x200.png 300w\" sizes=\"(max-width: 886px) 100vw, 886px\" \/><\/a><br \/>\nThe minimum excitation energy required for fission to occur is known as the <strong>critical energy (E<sub>crit<\/sub>)<\/strong> or <strong>threshold energy<\/strong>.<br \/>\n<a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/Critical-Energy-to-Binding-Energy.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-13251\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/Critical-Energy-to-Binding-Energy.png\" alt=\"Critical Energy to Binding Energy\" width=\"938\" height=\"402\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/Critical-Energy-to-Binding-Energy.png 938w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/Critical-Energy-to-Binding-Energy-300x129.png 300w\" sizes=\"(max-width: 938px) 100vw, 938px\" \/><\/a><br \/>\nThis table shows critical energies compared to binding energies of the last neutron of a number of nuclei.<\/p>\n<h2>Energy Release from Fission<\/h2>\n<p>In general, <strong>nuclear fission<\/strong> results in the release of <strong>enormous quantities of energy<\/strong>. The amount of energy <strong>depends strongly on<\/strong> the nucleus fissioned and depends strongly on an incident neutron\u2019s kinetic energy. To calculate the reactor\u2019s power, it is necessary to accurately identify the individual components of this energy. At first, it is important to distinguish between<strong> the total energy released<\/strong> and <strong>the energy that can be recovered in a<a title=\"Nuclear Reactor\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor\/\"> reactor<\/a><\/strong>.<\/p>\n<p><a title=\"Energy Release from Fission\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/energy-release-from-fission\/\"><strong>The total energy released<\/strong><\/a> in fission can be calculated from binding energies of the initial target nucleus to be fissioned and binding energies of <a title=\"Fission Fragments\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/fission-fragments\/\">fission products<\/a>. But not all the total energy can be recovered in a reactor. For example, <strong>about 10 MeV<\/strong>\u00a0is released in the form of <a title=\"Neutrino\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutrino\/\">neutrinos<\/a>\u00a0(in fact <a title=\"Antineutrino\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/antineutrino\/\">antineutrinos<\/a>). Since the neutrinos are weakly interacting (with extremely low cross-section of any interaction), they do not contribute to the energy that can be recovered in a reactor.<\/p>\n<p>To understand this issue, we have first to investigate a <strong>typical fission reaction<\/strong> such as the one listed below.<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/06\/uranium_absorption_reaction.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-12159\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/06\/uranium_absorption_reaction.png\" alt=\"Uranium absorption reaction\" width=\"775\" height=\"148\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/06\/uranium_absorption_reaction.png 775w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/06\/uranium_absorption_reaction-300x57.png 300w\" sizes=\"(max-width: 775px) 100vw, 775px\" \/><\/a><\/p>\n<p>Using this picture, we can identify and describe almost <strong>all the individual components<\/strong> of the total energy released during the fission reaction.<\/p>\n<div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\">\n<div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span> Kinetic energy of fission fragments<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">As can be seen when the <a title=\"Compound Nucleus Reactions\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/compound-nucleus-reactions\/\">compound nucleus<\/a> splits, it breaks into two <a title=\"Fission Fragments\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/fission-fragments\/\">fission fragments<\/a>. In most cases, the resultant fission fragments have masses that vary widely, but the most probable pair of fission fragments for the <a title=\"Thermal Neutron\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/thermal-neutron\/\">thermal neutron<\/a>-induced fission of the <a title=\"Uranium 235\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-235\/\"><sup>235<\/sup>U<\/a> have masses of about 94 and 139.<\/p>\n<p><strong>The largest part of the energy<\/strong> produced during fission (about 80 % or about 170 MeV or about 27 picojoules) appears as <strong>kinetic energy of the fission fragments<\/strong>. The initial velocity of these fission fragments is of the order of <strong>10 000 km per second<\/strong>. The<a title=\"Interaction of Heavy Charged Particles with Matter\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/interaction-radiation-matter\/interaction-heavy-charged-particles\/\"> fission fragments interact strongly <\/a>(intensely) with the surrounding atoms or molecules traveling at high speed, <strong>causing them to ionize<\/strong>. Creation of ion pairs requires energy, which is lost from the kinetic energy of the charged fission fragment causing it to decelerate. The positive ions and free electrons created by the passage of the charged fission fragment will then reunite, releasing energy<strong> in the form of heat<\/strong> (e.g.,, vibrational energy or rotational energy of atoms).<\/p>\n<p>The range of these massive, highly charged particles in the fuel is <strong>of the order of micrometers<\/strong>, so that the recoil energy is effectively deposited as heat at the point of fission. This is the principle how fission fragments heat <a title=\"Nuclear Fuel\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/\">fuel<\/a> in <a title=\"Reactor Core\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor-core\/\">the reactor core<\/a>.<\/p>\n<p>See also: <a title=\"Interaction of Heavy Charged Particles with Matter\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/interaction-radiation-matter\/interaction-heavy-charged-particles\/\">Interaction of Heavy Charged Particles with Matter<\/a><\/p>\n<\/div><\/div>\n<div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Spoiler title<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><strong><a title=\"Prompt Neutrons\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/prompt-neutrons\/\">Prompt neutrons<\/a><\/strong> are emitted directly from fission, and they are emitted within a very short time of <strong>about 10<sup>-14<\/sup> seconds<\/strong>. Usually, more than <strong>99%<\/strong> of the fission neutrons are\u00a0<strong>prompt neutrons. <\/strong>Still, the\u00a0exact fraction is dependent on the nuclide to be fissioned and is also dependent on an incident neutron energy (usually increases with energy).<\/p>\n<p>For example, fission of <a title=\"Uranium 235\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-235\/\"><sup>235<\/sup>U<\/a> by <a title=\"Thermal Neutron\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/thermal-neutron\/\">thermal neutron<\/a> yields <strong>2.43 neutrons<\/strong>, of which <strong>2.42 neutrons are the prompt neutrons,<\/strong> and 0.01585 neutrons (<strong>0.01585\/2.43=0.0065=\u00df<\/strong>) are <a title=\"Delayed Neutrons\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/delayed-neutrons\/\">the delayed neutrons<\/a>. Almost all prompt fission neutrons have energies between <strong>0.1 MeV and 10 MeV<\/strong>. The mean neutron energy is <strong>about 2 MeV<\/strong>. The most probable neutron energy is <strong>about 0.7 MeV<\/strong>.<\/p>\n<p>Most of this energy is deposited in the coolant (<a title=\"Neutron Moderator\" href=\"http:\/\/sitepourvtc.com\/neutron-moderator\/\">moderator<\/a>) because the water has the highest <a title=\"Macroscopic Slowing Down Power \u2013 MSDP\" href=\"http:\/\/sitepourvtc.com\/glossary\/macroscopic-slowing-down-power-msdp\/\">macroscopic slowing down power (MSDP)<\/a> of the materials that are in a <a title=\"Reactor Core\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor-core\/\">reactor core<\/a> (<a title=\"PWR \u2013 Pressurized water reactor\" href=\"http:\/\/sitepourvtc.com\/pwr-pressurized-water-reactor\/\">PWR<\/a>).\u00a0<span style=\"line-height: 1.5;\">The range of neutrons in a reactor depends strongly on a specific reactor type. In the case of PWRs, it is usually of the order of centimeters.<\/span><\/p>\n<\/div><\/div>\n<div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Energy carried by prompt \u03b3-rays<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">With the <a title=\"Prompt Neutrons\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/prompt-neutrons\/\">prompt neutrons<\/a>, <strong><a title=\"Prompt Gamma Rays\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/prompt-neutrons\/prompt-gamma-rays\/\">prompt gamma rays<\/a><\/strong> are associated. <strong>Most prompt gamma rays are emitted after prompt neutrons.<\/strong> The fission reaction releases approximately <strong>~7 MeV<\/strong> in prompt gamma rays.<\/p>\n<p>The <a title=\"Gamma Rays \/ Gamma Radiation\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/photon\/gamma-ray\/\">gamma rays<\/a> are well attenuated by<strong> high-density<\/strong> and <strong>high Z materials<\/strong>. In <a title=\"Reactor Core\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor-core\/\">a reactor core, <\/a>the largest share of the energy will be deposited <strong>in the<a title=\"Nuclear Fuel\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/\"> fuel<\/a> <\/strong>containing uranium dioxide. Still, a significant share of the energy will also be deposited in the fuel cladding and the coolant (<a title=\"Neutron Moderator\" href=\"http:\/\/sitepourvtc.com\/neutron-moderator\/\">moderator<\/a>).<\/p>\n<p>The range of gamma rays in a reactor varies according to the initial energy of the gamma-ray. It can be stated the most gammas in a reactor have ranged from 10cm-1m.<\/p>\n<\/div><\/div>\n<div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Energy of \u03b2\u2212 decay<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><strong>About 6 MeV<\/strong> of fission energy is in the form of the <strong>kinetic energy of electrons<\/strong> (<a title=\"Beta Particle\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/beta-particle\/\">beta particles<\/a>). The fission fragments are <strong>neutron-rich nuclei,<\/strong> and therefore they usually undergo <strong>beta decay<\/strong> to stabilize themselves. Beta particles deposit their energy essentially<strong> in the fuel element<\/strong>, within about 1 mm of the fission fragment.<\/p>\n<\/div><\/div>\n<p>The existence of emission of antineutrinos and their extremely low cross-section for any interaction leads to a fascinating phenomenon. <div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Energy of antineutrinos<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><a title=\"Antineutrino\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/antineutrino\/\">Antineutrinos <\/a>are produced in <strong>negative beta decay<\/strong>. A <a title=\"Nuclear Reactor\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor\/\">nuclear reactor<\/a> occurs especially the \u03b2\u2212 decay because the common feature of the <a title=\"Fission Fragments\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/fission-fragments\/\">fission fragments<\/a> is an <strong>excess of neutrons<\/strong>. Roughly <strong>about 5% of released energy<\/strong> per one fission is <strong>radiated away<\/strong> from a reactor in the form of antineutrinos.<\/p>\n<p>For a typical nuclear reactor with thermal power of <strong>3000 MWth<\/strong> (~1000MWe of electrical power), the total power produced is higher, approximately <strong>3150 MW<\/strong>, of which 150 MW is radiated away into space antineutrino radiation. This amount of energy is <strong>forever lost<\/strong>\u00a0because antineutrinos can penetrate all reactor materials without any interaction.<\/p>\n<p>A common statement in physics texts is that <strong>the mean free path<\/strong> of a neutrino is approximately <strong>a light-year of lead<\/strong>. Moreover, a neutrino of moderate energy can easily penetrate <strong>a thousand light-years of lead<\/strong> (according to J. B. Griffiths).<\/p>\n<\/div><\/div>\n<div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Spoiler title<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">The fission fragments are <strong>neutron-rich<\/strong> and <strong>very unstable nuclei.<\/strong> These nuclei undergo <strong>many beta decays<\/strong> to stabilize themselves. <a title=\"Gamma Rays \/ Gamma Radiation\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/photon\/gamma-ray\/\">Gamma rays<\/a> usually <strong>accompany<\/strong> beta decay. Their energy is transferred as heat to the surrounding material, similarly to the energy carried by <strong>prompt \u03b3-rays<\/strong>.<\/p>\n<\/div><\/div>\n<div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Spoiler title<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">A fraction of the <a title=\"Neutron Absorption\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/neutron-absorption\/\">neutron absorption reactions<\/a> result in <strong><a title=\"Neutron Capture \u2013 Radiative Capture\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/neutron-capture-radiative-capture\/\">radiative capture<\/a> <\/strong>followed by <strong>gamma-ray emission<\/strong>, producing on average <strong>about 7 MeV per fission<\/strong> in the form of energetic <a title=\"Gamma Rays \/ Gamma Radiation\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/photon\/gamma-ray\/\">gamma rays<\/a>. Their energy is transferred as heat to the surrounding material, similarly to the energy carried by prompt \u03b3-rays.<\/p>\n<\/div><\/div>\n<\/div>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/energy_release_per_fission.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-13272\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/energy_release_per_fission.png\" alt=\"Energy release per fission\" width=\"826\" height=\"651\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/energy_release_per_fission.png 826w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/energy_release_per_fission-300x236.png 300w\" sizes=\"(max-width: 826px) 100vw, 826px\" \/><\/a><br \/>\n<strong>The total energy released<\/strong> in a reactor is <strong>about 210 MeV<\/strong> per <a title=\"Uranium 235 Fission\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-235\/uranium-235-fission\/\"><sup>235<\/sup>U fission<\/a>, distributed as shown in the table. The<strong>\u00a0average recoverable energy<\/strong> per fission in a reactor is <strong>about 200 MeV <\/strong>(the total energy minus the energy of <a title=\"Antineutrino\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/antineutrino\/\">antineutrinos<\/a> radiated away). This means that <strong>about 3.1\u22c510<sup>10<\/sup> fissions per second<\/strong> are required to produce a power of <strong>1 W<\/strong>. Since <strong>1 gram<\/strong> of any <a title=\"Fissile Material\" href=\"http:\/\/sitepourvtc.com\/glossary\/fissile-material\/\">fissile material <\/a>contains about <strong>2.5 x 10<sup>21<\/sup> nuclei<\/strong>, the fissioning of 1 gram of fissile material yields <strong>about one megawatt-day (MWd)<\/strong> of heat energy.<\/p>\n<p>As can be seen from the description of the individual components of the total energy released during the fission reaction, there is a <strong>significant amount of energy generated outside the <a title=\"Nuclear Fuel\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/\">nuclear fuel<\/a><\/strong> (outside fuel rods). Especially the kinetic energy of <a title=\"Prompt Neutrons\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/prompt-neutrons\/\">prompt neutrons<\/a> is primarily generated<strong>\u00a0in the coolant (<a title=\"Neutron Moderator\" href=\"http:\/\/sitepourvtc.com\/neutron-moderator\/\">moderator<\/a>)<\/strong>. This phenomenon needs to be included in the nuclear calculations.<\/p>\n<p>For LWR, it is generally accepted that <strong>about 2.5%<\/strong> of total energy is recovered <strong>in the moderator<\/strong>. This fraction of energy depends on the materials, their arrangement within the reactor, and thus on the reactor type.<\/p>\n<h2>Fission Fragments &#8211; Products of Nuclear Fission<\/h2>\n<figure id=\"attachment_11611\" aria-describedby=\"caption-attachment-11611\" style=\"width: 340px\" class=\"wp-caption alignright\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/02\/fission_fragments_yield.png\"><img loading=\"lazy\" class=\"size-full wp-image-11611\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/02\/fission_fragments_yield.png\" alt=\"Fission fragment yields\" width=\"350\" height=\"280\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/02\/fission_fragments_yield.png 350w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/02\/fission_fragments_yield-300x240.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/02\/fission_fragments_yield-177x142.png 177w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/02\/fission_fragments_yield-147x118.png 147w\" sizes=\"(max-width: 350px) 100vw, 350px\" \/><\/a><figcaption id=\"caption-attachment-11611\" class=\"wp-caption-text\">Fission fragment yield for different nuclei. The most probable fragment masses are around mass 95 (Krypton) and 137 (Barium).<\/figcaption><\/figure>\n<p>Nuclear <strong>fission fragments<\/strong>\u00a0are the fragments left after a <a title=\"Nuclear Fission\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/\">nucleus fissions<\/a>. Typically, when the uranium 235 nucleus undergoes fission, the nucleus splits into <strong>two smaller nuclei<\/strong>, along with a few neutrons and release of energy in the form of heat (<strong>kinetic energy of these fission fragments<\/strong>) and gamma rays.\u00a0The average of the fragment mass is about 118, but very few fragments near that average are found. It is much more probable to break up into unequal fragments, and the most probable fragment masses are around mass 95 (Krypton) and 137 (Barium).<\/p>\n<p>Most of these fission fragments are <strong>highly unstable<\/strong> (radioactive) and\u00a0undergo further <a title=\"Radioactive Decay\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/radioactive-decay\/\">radioactive decays<\/a> to <a title=\"Nuclear Stability\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/nuclear-stability\/\">stabilize themselves<\/a>.\u00a0Fission fragments\u00a0interact strongly with the surrounding atoms or molecules traveling\u00a0at high speed, causing them to ionize.<\/p>\n<p>See also: <a title=\"Interaction of Heavy Charged Particles with Matter\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/interaction-radiation-matter\/interaction-heavy-charged-particles\/\">Interaction of Heavy Charged Particles with Matter<\/a><\/p>\n<h2>Prompt and Delayed Neutrons<\/h2>\n<p>It is known the fission neutrons are of importance in any chain-reacting system. <a title=\"Neutron\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/\">Neutrons<\/a> trigger the <a title=\"Nuclear Fission\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/\">nuclear fission<\/a> of some nuclei (<a title=\"Uranium 235\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-235\/\"><sup>235<\/sup>U<\/a>, <a title=\"Uranium 238\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-238\/\"><sup>238<\/sup>U<\/a>, or even <a title=\"Thorium 232\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/thorium\/thorium-232\/\"><sup>232<\/sup>Th<\/a>). What is crucial the fission of such nuclei produces <strong>2, 3, or more<\/strong> <a title=\"Free Neutron\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/free-neutron\/\">free neutrons<\/a>.<\/p>\n<p>But not all neutrons are released <strong>at the same time following fission<\/strong>. Even the nature of the creation of these neutrons is different. From this point of view, we usually divide the fission neutrons into two following groups:<\/p>\n<ul>\n<li><strong><a title=\"Prompt Neutrons\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/prompt-neutrons\/\">Prompt Neutrons<\/a>.<\/strong> Prompt neutrons are emitted <strong>directly from fission,<\/strong> and they are emitted within a <strong>very short time of about 10<sup>-14<\/sup> seconds<\/strong>.<\/li>\n<li><strong><a title=\"Delayed Neutrons\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/delayed-neutrons\/\">Delayed Neutrons<\/a>.<\/strong> Delayed neutrons are emitted by <strong>neutron-rich <a title=\"Fission Fragments\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/fission-fragments\/\">fission fragments<\/a><\/strong> that are called<strong> delayed neutron precursors<\/strong>. These precursors usually undergo <a title=\"Beta Particle\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/beta-particle\/\">beta decay<\/a>, but a small fraction of them are excited enough to undergo <strong>neutron emission<\/strong>. The neutron is produced via this type of decay, which happens <strong>orders of magnitude later<\/strong> than the emission of the prompt neutrons, which plays a crucial role in the control of the reactor.<\/li>\n<\/ul>\n<p>See also: <a title=\"Prompt Neutrons\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/prompt-neutrons\/\">Prompt Neutrons<\/a><\/p>\n<p>See also: <a title=\"Delayed Neutrons\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/delayed-neutrons\/\">Delayed Neutrons<\/a><\/p>\n<p>See also: <a title=\"Infinite Multiplying System Without Source and with Delayed Neutrons\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/delayed-neutrons\/infinite-multiplying-system-without-source-and-with-delayed-neutrons\/\">Reactor control with and without delayed neutrons &#8211; Interactive chart<\/a>.<\/p>\n<figure id=\"attachment_12807\" aria-describedby=\"caption-attachment-12807\" style=\"width: 290px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/10\/Neutron-production-Prompt-Delayed.png\"><img loading=\"lazy\" class=\"size-medium wp-image-12807\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/10\/Neutron-production-Prompt-Delayed-300x242.png\" alt=\"Neutron Production - Prompt Neutrons\" width=\"300\" height=\"242\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/10\/Neutron-production-Prompt-Delayed-300x242.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/10\/Neutron-production-Prompt-Delayed-177x142.png 177w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/10\/Neutron-production-Prompt-Delayed-147x118.png 147w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/10\/Neutron-production-Prompt-Delayed.png 815w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-12807\" class=\"wp-caption-text\">Most of the neutrons produced in fission are prompt neutrons. Usually, more than 99 percent of the fission neutrons are prompt neutrons. Still, the exact fraction is dependent on specific nuclides to be fissioned and is also dependent on an incident neutron energy (usually increases with energy).<\/figcaption><\/figure>\n<p>Source: JANIS (Java-based Nuclear Data Information Software); The JEFF-3.1.1 Nuclear Data Library<\/p>\n<figure id=\"attachment_12818\" aria-describedby=\"caption-attachment-12818\" style=\"width: 290px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/10\/Prompt-and-Delayed-Neutrons-Characteristics-Table.png\"><img loading=\"lazy\" class=\"size-medium wp-image-12818\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/10\/Prompt-and-Delayed-Neutrons-Characteristics-Table-300x109.png\" alt=\"Table of key prompt and delayed neutrons characteristics\" width=\"300\" height=\"109\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/10\/Prompt-and-Delayed-Neutrons-Characteristics-Table-300x109.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/10\/Prompt-and-Delayed-Neutrons-Characteristics-Table.png 647w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-12818\" class=\"wp-caption-text\">Table of key prompt and delayed neutrons characteristics. Thermal vs. Fast Fission<\/figcaption><\/figure>\n<h3>Key Characteristics of Prompt Neutrons<\/h3>\n<ul>\n<li>Prompt neutrons are emitted <strong>directly from fission,<\/strong> and they are emitted within a very short time of about <strong>10<sup>-14<\/sup> seconds<\/strong>.<\/li>\n<\/ul>\n<ul>\n<li>Most of the neutrons produced in fission are prompt neutrons &#8211; <strong>about 99.9%<\/strong>.<\/li>\n<\/ul>\n<ul>\n<li>For example, fission of <a title=\"Uranium 235\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-235\/\"><sup>235<\/sup>U<\/a> by thermal neutron yields <strong>2.43 neutrons<\/strong>, of which 2.42 neutrons are prompt neutrons, and 0.01585 neutrons are <a title=\"Delayed Neutrons\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/delayed-neutrons\/\">the delayed neutrons<\/a>.<\/li>\n<\/ul>\n<ul>\n<li>The production of prompt neutrons slightly increases with incident <a title=\"Neutron Energy\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/neutron-energy\/\">neutron energy<\/a>.<\/li>\n<\/ul>\n<ul>\n<li>Almost all prompt fission neutrons have <strong>energies between 0.1 MeV and 10 MeV<\/strong>.<\/li>\n<\/ul>\n<ul>\n<li>The mean neutron energy is about<strong> 2 MeV<\/strong>. The most probable neutron energy is about<strong> 0.7 MeV<\/strong>.<\/li>\n<\/ul>\n<ul>\n<li>In reactor design,<strong> the prompt neutron lifetime<\/strong> (PNL) belongs to key neutron-physical characteristics of the reactor core.<\/li>\n<\/ul>\n<ul>\n<li>Its value depends primarily on the type of the <a title=\"Neutron moderator\" href=\"http:\/\/sitepourvtc.com\/neutron-moderator\/\">moderator<\/a> and the energy of the neutrons causing fission.<\/li>\n<\/ul>\n<ul>\n<li>In an infinite reactor (without escape), prompt neutron lifetime is the sum of the <strong>slowing downtime and the diffusion time<\/strong>.<\/li>\n<\/ul>\n<ul>\n<li>In <a title=\"Types of Reactors\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/reactor-types\/\">LWRs<\/a>, the <strong>PNL increases with the fuel burnup<\/strong>.<\/li>\n<\/ul>\n<ul>\n<li>The typical prompt neutron lifetime in thermal reactors is on the order of <strong>10<sup>-4<\/sup><\/strong> seconds.<\/li>\n<\/ul>\n<ul>\n<li>The typical prompt neutron lifetime in <a title=\"Fast Neutron Reactor\" href=\"http:\/\/sitepourvtc.com\/fast-neutron-reactor\/\">fast reactors<\/a> is on the order of <strong>10<sup>-7<\/sup><\/strong> seconds.<\/li>\n<\/ul>\n<h3>Key Characteristics of Delayed Neutrons<\/h3>\n<ul>\n<li>The presence of delayed neutrons is perhaps <strong>the<\/strong> <strong>most important aspect of the fission process<\/strong> from reactor control.<\/li>\n<\/ul>\n<ul>\n<li>Delayed neutrons are emitted by neutron-rich <a title=\"Fission Fragments\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/fission-fragments\/\">fission fragments<\/a> that are called <strong>delayed neutron precursors<\/strong>.<\/li>\n<\/ul>\n<ul>\n<li>These precursors usually undergo <a title=\"Beta Particle\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/beta-particle\/\">beta decay<\/a>, but a small fraction of them are excited enough <strong>to undergo neutron emission.<\/strong><\/li>\n<\/ul>\n<ul>\n<li>The emission of neutrons happens orders <strong>of magnitude later<\/strong> compared to the emission of the prompt neutrons.<\/li>\n<\/ul>\n<ul>\n<li>About <strong>240 n-emitters<\/strong> are known between <sup>8<\/sup>He and <sup>210<\/sup>Tl. About 75 of them are in the non-fission region.<\/li>\n<\/ul>\n<ul>\n<li>The grouping of precursors based on their half-lives is designed to simplify the kinetic calculations of the reactor.<\/li>\n<\/ul>\n<ul>\n<li>Therefore delayed neutrons are traditionally represented by <strong>six delayed neutron groups<\/strong>.<\/li>\n<\/ul>\n<ul>\n<li>Neutrons can also be produced in <strong>(\u03b3, n) reactions<\/strong> (especially in reactors with <a title=\"CANDU \u2013 Heavy Water Reactor\" href=\"http:\/\/sitepourvtc.com\/candu-heavy-water-reactor\/\">heavy water moderator<\/a>), and therefore, they are usually referred to as <strong>photoneutrons<\/strong>. <strong>Photoneutrons<\/strong> are usually treated no differently than regularly delayed neutrons in the kinetic calculations.<\/li>\n<\/ul>\n<ul>\n<li>The total yield of delayed neutrons per fission, v<sub>d<\/sub>, depends on:\n<ul>\n<li>An isotope that is fissioned.<\/li>\n<li>The energy of a neutron induces fission.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<ul>\n<li>Variation among individual group yields is much more significant than variation among group periods.<\/li>\n<\/ul>\n<ul>\n<li>In reactor kinetic calculations, it is convenient to use relative units usually referred to as <strong>delayed neutron fraction (DNF)<\/strong>.<\/li>\n<\/ul>\n<ul>\n<li>At the steady-state condition of criticality, with k<sub>eff<\/sub> = 1, the delayed neutron fraction is equal to the precursor yield fraction \u03b2.<\/li>\n<\/ul>\n<ul>\n<li>In LWRs, the <strong>\u03b2 decreases with fuel burnup<\/strong>. This is due to isotopic changes in the fuel.<\/li>\n<\/ul>\n<ul>\n<li>Delayed neutrons have<strong> initial energy between 0.3 and 0.9 MeV<\/strong> with an <strong>average energy of 0.4 MeV<\/strong>.<\/li>\n<\/ul>\n<ul>\n<li>Depending on the <strong>type of the reactor<\/strong>, and their <strong>spectrum<\/strong>, the delayed neutrons may be more (in thermal reactors) or less effective than prompt neutrons (in <a title=\"Fast Neutron Reactor\" href=\"http:\/\/sitepourvtc.com\/fast-neutron-reactor\/\">fast reactors<\/a>). To include this effect into the reactor kinetic calculations,<strong> the effectively delayed neutron fraction &#8211; \u03b2<sub>eff<\/sub><\/strong>\u00a0must be defined.<\/li>\n<\/ul>\n<ul>\n<li>The effectively delayed neutron fraction is the product of the average delayed neutron fraction and the importance factor <strong>\u03b2<sub>eff<\/sub>\u00a0= \u03b2 . I.<\/strong><\/li>\n<\/ul>\n<ul>\n<li>The weighted delayed generation time is given by <strong>\u03c4 = \u2211<sub>i<\/sub>\u03c4<sub>i<\/sub> . \u03b2<sub>i<\/sub> \/ \u03b2 = 13.05 s<\/strong>, therefore the weighted decay constant <strong>\u03bb = 1 \/ \u03c4 \u2248 0.08 s<sup>-1<\/sup><\/strong>.<\/li>\n<\/ul>\n<ul>\n<li>The mean generation time with delayed neutrons is about <strong>~0.1 s<\/strong>, rather than <strong>~10<sup>-5<\/sup><\/strong> as in section Prompt Neutron Lifetime, where the delayed neutrons were omitted.<\/li>\n<\/ul>\n<ul>\n<li>Their presence completely changes the dynamic time response of a reactor to some reactivity change, <strong>making it controllable by control systems<\/strong> such as <a title=\"Control Rods\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/control-rods\/\">the control rods<\/a>.<\/li>\n<\/ul>\n<h2>Capture-to-Fission Ratio<\/h2>\n<p>The probability that a <a title=\"Neutron\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/\">neutron<\/a> absorbed in a <a title=\"Fissile Material\" href=\"http:\/\/sitepourvtc.com\/glossary\/fissile-material\/\">fissile nuclide <\/a>causes a<br \/>\nfission is an important parameter of each fissile isotope. In terms of cross-sections, this probability is defined as:<\/p>\n<p><strong>\u03c3<sub>f<\/sub> \/ (\u03c3<sub>f<\/sub> + \u03c3<sub>\u03b3<\/sub>) = 1 \/ (1 + \u03c3<sub>\u03b3<\/sub>\/\u03c3<sub>f<\/sub>) = 1 \/ (1 + \u03b1),<\/strong><\/p>\n<p>where <strong>\u03b1 = \u03c3<sub>\u03b3<\/sub>\/\u03c3<sub>f<\/sub><\/strong>\u00a0is referred to as <strong>the capture-to-fission ratio<\/strong>. The capture-to-fission ratio may be used as an indicator of the \u201cquality\u201d of fissile isotopes. The lower <strong>C\/F ratio<\/strong> simply means that an <a title=\"Neutron Absorption\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/neutron-absorption\/\">absorption reaction<\/a> will result in fission rather than <a title=\"Neutron Capture \u2013 Radiative Capture\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/neutron-capture-radiative-capture\/\">radiative capture<\/a>. The ratio depends strongly on the incident <a title=\"Neutron Energy\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/neutron-energy\/\">neutron energy<\/a>. In\u00a0the fast neutron region, the C\/F ratio decreases. It is determined by the steeper decrease in<a title=\"Neutron Capture Cross-section\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/neutron-capture-radiative-capture\/neutron-capture-cross-section\/\"> radiative capture cross-section<\/a> (see chart).<\/p>\n<p>For <a title=\"Uranium 235\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-235\/\"><sup>235<\/sup>U<\/a> and <a title=\"Uranium 233\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-233\/\"><sup>233<\/sup>U<\/a>, the <a title=\"Thermal Neutron\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/thermal-neutron\/\">thermal neutron<\/a> <strong>capture-to-fission ratios<\/strong> are typically lower than fast neutrons (for mean energy of about 100 keV). It must be noted, the neutron flux of most fast reactors tends to peak around 200 keV, but the mean energy is between 100-200 keV depending on specific reactor design.<\/p>\n<p>Further increase in neutron energy causes a decrease in the C\/F ratio conversely. This is not the case with <a title=\"Plutonium 239\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/plutonium\/plutonium-239\/\"><sup>239<\/sup>Pu<\/a>. For 100 keV neutrons, the C\/F ratio is lower than for thermal neutrons. A small capture-to-fission ratio is advantageous for the fissile isotopes (<a title=\"Uranium 233\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-233\/\"><sup>233<\/sup>U<\/a>, <a title=\"Uranium 235\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-235\/\"><sup>235<\/sup>U<\/a>,\u00a0and <a title=\"Plutonium 239\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/plutonium\/plutonium-239\/\"><sup>239<\/sup>Pu<\/a>) because neutrons captured onto them are lost.<\/p>\n<figure id=\"attachment_13302\" aria-describedby=\"caption-attachment-13302\" style=\"width: 290px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/capture-to-fission-ratio.png\"><img loading=\"lazy\" class=\"size-medium wp-image-13302\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/capture-to-fission-ratio-300x152.png\" alt=\"The capture-to-fission ratio\" width=\"300\" height=\"152\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/capture-to-fission-ratio-300x152.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/capture-to-fission-ratio-1024x519.png 1024w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/capture-to-fission-ratio-540x272.png 540w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/capture-to-fission-ratio.png 1264w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-13302\" class=\"wp-caption-text\">Source: JANIS (Java-based Nuclear Data Information Software); The JEFF-3.1.1 Nuclear Data Library<\/figcaption><\/figure>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/table_capture-to-fission-ratio.png\"><img loading=\"lazy\" class=\"size-medium wp-image-13303 aligncenter\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/table_capture-to-fission-ratio-300x243.png\" alt=\"capture-to-fission ratio\" width=\"300\" height=\"243\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/table_capture-to-fission-ratio-300x243.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/table_capture-to-fission-ratio-177x142.png 177w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/table_capture-to-fission-ratio-147x118.png 147w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/table_capture-to-fission-ratio.png 625w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p>Source: JANIS (Java-based Nuclear Data Information Software); The JEFF-3.1.1 Nuclear Data Library<\/p>\n<h2>Nuclear Fission Chain Reaction<\/h2>\n<p><strong><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/Six-Factor-Formula-Four-Factor-Formula.png\"><img loading=\"lazy\" class=\"alignright size-medium wp-image-13834\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/Six-Factor-Formula-Four-Factor-Formula-300x282.png\" alt=\"Six Factor Formula - Four Factor Formula\" width=\"300\" height=\"282\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/Six-Factor-Formula-Four-Factor-Formula-300x282.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/Six-Factor-Formula-Four-Factor-Formula-52x50.png 52w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/Six-Factor-Formula-Four-Factor-Formula.png 839w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a>The chain reaction<\/strong> can take place only in the\u00a0<strong>proper<\/strong> <strong>multiplication environment<\/strong> and only under <strong>proper conditions<\/strong>. Obviously, suppose one neutron causes two further fissions. In that case, the number of neutrons in the multiplication system will increase in time, and the reactor power (<a title=\"Reaction Rate\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/reaction-rate\/\">reaction rate<\/a>) will also increase in time. Moreover, this multiplication environment (nuclear reactor) behaves like an exponential system, which means the power increase is not linear but exponential. The non-fission <a title=\"Neutron Absorption\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/neutron-absorption\/\">neutron absorption<\/a> in the system (e.g.,, insert<strong>\u00a0<a title=\"Control Rods\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/control-rods\/\">control rods<\/a><\/strong>) must increase to stabilize such a multiplication environment.<\/p>\n<p>On the other hand, if one neutron causes<strong> less than one<\/strong> further fission, the number of neutrons in the multiplication system will decrease in time, and the reactor power (reaction rate) will also decrease in time. \u00a0The non-fission neutron absorption in the system (e.g.,, to <strong>withdraw control rods<\/strong>) must be decreased to\u00a0<strong>sustain the chain reaction.<\/strong><\/p>\n<p>There is always a<strong> competition<\/strong> for the fission neutrons in the multiplication environment. Some neutrons will cause further <strong>fission reaction<\/strong>, fuel materials or non-fuel materials will capture some, and some will<strong> leak out<\/strong> of the system.<\/p>\n<p>The <strong><a title=\"Four Factor Formula \u2013 Infinite Multiplication Factor\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/four-factor-formula-infinite-multiplication-factor\/\">infinite<\/a> and <a title=\"Six Factor Formula \u2013 Effective Multiplication Factor\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/six-factor-formula-effective-multiplication-factor\/\">finite multiplication factors<\/a><\/strong> of a reactor must be defined to describe a multiplication system. The method of calculations of multiplication factors was developed <strong>in the early years<\/strong> of nuclear energy. It is only applicable to <strong>thermal reactors<\/strong>, where the bulk of fission reactions occurs at thermal energies. This method puts into context all the processes associated with the thermal reactors (e.g.,, <strong>neutron thermalization<\/strong>, <strong>neutron diffusion,<\/strong> or <strong>fast fission<\/strong>) because the most critical neutron-physical processes occur in energy <strong>regions that can be clearly separated from each other<\/strong>. In short, the calculation of the multiplication factor gives a good insight into the processes that occur in each thermal multiplying system.<\/p>\n<h2>The distinction between Fissionable, Fissile, and Fertile<\/h2>\n<p>In nuclear engineering, <strong>fissionable material<\/strong> (nuclide) is material that is capable of undergoing <a title=\"Nuclear Fission\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/\">fission reaction<\/a>\u00a0after absorbing either thermal (<a title=\"Neutron Energy\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/neutron-energy\/\">slow or low energy<\/a>) <a title=\"Neutron\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/\">neutron<\/a>\u00a0or fast (high energy) neutron. Fissionable materials are a superset of fissile materials. Fissionable materials also include an isotope <strong><sup>238<\/sup>U<\/strong> that can be fissioned only with high energy (&gt;1MeV) neutron. These materials are used to fuel thermal nuclear reactors because they can sustain a nuclear fission chain reaction.<\/p>\n<p>Fissile materials undergo a fission reaction after absorption of the <a title=\"Nuclear Binding Energy\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/binding-energy\/nuclear-binding-energy\/\">binding energy<\/a> of the thermal neutron. They do not require additional kinetic energy for fission. If the neutron has higher kinetic energy, this energy will be transformed into the additional excitation energy of the compound nucleus. On the other hand, the binding energy released by the compound nucleus of <strong>(<sup>238<\/sup>U + n)<\/strong> after thermal neutron absorption is less than the critical energy, so the fission reaction <strong>cannot occur<\/strong>. The distinction is described in the\u00a0following points.<\/p>\n<ul>\n<li><strong>Fissile materials are a subset of fissionable materials<\/strong>.<\/li>\n<li><a title=\"Fissionable Material\" href=\"http:\/\/sitepourvtc.com\/glossary\/fissionable-material\/\"><strong>Fissionable material <\/strong><\/a>consists of isotopes that are capable of undergoing nuclear fission after capturing <strong>either fast neutron<\/strong> (<a title=\"Neutron Energy\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/neutron-energy\/\">high energy neutron<\/a> &#8211; let say &gt;1 MeV) <strong>or thermal neutron<\/strong> (low energy neutron &#8211; let say 0.025 eV). \u00a0 Typical fissionable materials: <a title=\"Uranium 238\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-238\/\"><strong><sup>238<\/sup>U<\/strong><\/a>, <a title=\"Plutonium 240\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/plutonium\/plutonium-240\/\"><strong><sup>240<\/sup>Pu<\/strong><\/a>, but also\u00a0<a title=\"Uranium 235\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-235\/\"><strong><sup>235<\/sup>U<\/strong><\/a>, <a title=\"Uranium 233\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-233\/\"><strong><sup>233<\/sup>U<\/strong><\/a>, <a title=\"Plutonium 239\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/plutonium\/plutonium-239\/\"><strong><sup>239<\/sup>Pu<\/strong><\/a>, <a title=\"Plutonium 241\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/plutonium\/plutonium-241\/\"><strong><sup>241<\/sup>Pu<\/strong><\/a><\/li>\n<li><strong><a title=\"Fissile Material\" href=\"http:\/\/sitepourvtc.com\/glossary\/fissile-material\/\">Fissile material<\/a> consists of fissionable isotopes<\/strong>\u00a0capable of undergoing nuclear fission <strong>only after capturing a thermal neutron<\/strong>. Typical fissile materials: <strong>235U, 233U, 239Pu, 241Pu<\/strong>. <strong><sup>238<\/sup>U\u00a0<\/strong>is not a fissile isotope because <span style=\"font-size: 13.3333px;\"><b>a thermal neutron cannot fission 238U<\/b><\/span>. <strong><sup>238<\/sup>U\u00a0<\/strong>does not also meet alternative requirements to fissile materials. <strong><sup>238<\/sup>U<\/strong> cannot sustain a nuclear fission chain reaction because neutrons produced by the fission of <strong><sup>238<\/sup>U<\/strong> have lower energies than the original neutron (usually below the threshold energy of 1 MeV).<\/li>\n<li><a title=\"Fertile Material\" href=\"http:\/\/sitepourvtc.com\/glossary\/fertile-material\/\"><strong>Fertile material<\/strong><\/a> consists of isotopes that are not fissionable by thermal neutrons but <strong>can be converted into fissile isotopes<\/strong>\u00a0(after neutron absorption and subsequent nuclear decay). Typical fertile materials: <strong><sup>238<\/sup>U<\/strong>, <a title=\"Thorium 232\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/thorium\/thorium-232\/\"><strong><sup>232<\/sup>Th<\/strong><\/a>.<\/li>\n<\/ul>\n<p>Fissile materials undergo a fission reaction after absorption of the <a title=\"Nuclear Binding Energy\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/binding-energy\/nuclear-binding-energy\/\">binding energy<\/a> of the thermal neutron. They do not require additional kinetic energy for fission. If the neutron has higher kinetic energy, this energy will be transformed into the additional excitation energy of the compound nucleus. On the other hand, the binding energy released by the compound nucleus of <strong>(<sup>238<\/sup>U + n)<\/strong> after absorption of the thermal neutron is less than the critical energy, so the fission reaction <strong>cannot occur<\/strong>. The distinction is described in the\u00a0following points.<\/p>\n<ul>\n<li><strong>Fissile materials are a subset of fissionable materials<\/strong>.<\/li>\n<li><strong>Fissionable material <\/strong>consists of isotopes that are capable of undergoing nuclear fission after capturing <strong>either fast neutron<\/strong> (<a title=\"Neutron Energy\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/neutron-energy\/\">high energy neutron<\/a> &#8211; let say &gt;1 MeV) <strong>or thermal neutron<\/strong> (low energy neutron &#8211; let say 0.025 eV). \u00a0 Typical fissionable materials: <a title=\"Uranium 238\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-238\/\"><strong><sup>238<\/sup>U<\/strong><\/a>, <strong><sup>240<\/sup>Pu<\/strong>, but also\u00a0<a title=\"Uranium 235\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-235\/\"><strong><sup>235<\/sup>U<\/strong><\/a>, <a title=\"Uranium 233\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-233\/\"><strong><sup>233<\/sup>U<\/strong><\/a>, <strong><sup>239<\/sup>Pu<\/strong>, <strong><sup>241<\/sup>Pu<\/strong><\/li>\n<li><strong><a title=\"Fissile Material\" href=\"http:\/\/sitepourvtc.com\/glossary\/fissile-material\/\">Fissile material<\/a>\u00a0<\/strong>consists of fissionable isotopes capable of undergoing nuclear fission <strong>only after capturing a thermal neutron<\/strong>. Typical fissile materials:<strong> 235U, 233U, 239Pu, 241Pu<\/strong>. <strong><sup>238<\/sup>U\u00a0<\/strong>is not a fissile isotope because <span style=\"font-size: 13.3333px;\"><b>a thermal neutron cannot fission 238U<\/b><\/span>. <strong><sup>238<\/sup>U\u00a0<\/strong>does not also meet the alternative requirement to fissile materials. <strong><sup>238<\/sup>U<\/strong> cannot sustain a nuclear fission chain reaction because neutrons produced by the fission of <strong><sup>238<\/sup>U<\/strong> have lower energies than the original neutron (usually below the threshold energy of 1 MeV).<\/li>\n<li><a title=\"Fertile Material\" href=\"http:\/\/sitepourvtc.com\/glossary\/fertile-material\/\"><strong>Fertile material<\/strong><\/a> consists of isotopes that are not fissionable by thermal neutrons but <strong>can be converted into fissile isotopes<\/strong>\u00a0(after neutron absorption and subsequent nuclear decay). Typical fertile materials: <strong><sup>238<\/sup>U<\/strong>, <strong><sup>232<\/sup>Th<\/strong>.<\/li>\n<\/ul>\n<p>See also: <a title=\"Neutron cross-section\" href=\"http:\/\/sitepourvtc.com\/neutron-cross-section\/\">Neutron cross-section<\/a>.<\/p>\n<p style=\"text-align: left;\"><strong>Comparison of cross-sections<\/strong><\/p>\n<p style=\"text-align: left;\"><strong>Source: JANIS (Java-based nuclear information software) \u00a0<a href=\"http:\/\/www.oecd-nea.org\/janis\/\">http:\/\/www.oecd-nea.org\/janis\/<\/a><\/strong><\/p>\n<figure id=\"attachment_12102\" aria-describedby=\"caption-attachment-12102\" style=\"width: 290px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/fissile_fertile.png\"><img loading=\"lazy\" class=\"size-medium wp-image-12102\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/fissile_fertile-300x144.png\" alt=\"Fissile \/ Fertile Material Cross-sections\" width=\"300\" height=\"144\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/fissile_fertile-300x144.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/fissile_fertile-1024x492.png 1024w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/fissile_fertile.png 1307w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-12102\" class=\"wp-caption-text\">Source: JANIS (Java-based Nuclear Data Information Software)<br \/>http:\/\/www.oecd-nea.org\/janis\/<\/figcaption><\/figure>\n<p style=\"text-align: left;\">Fissile \/ Fertile Material Cross-sections. Comparison of total fission cross-sections.<br \/>\n<a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/Uranium_235.png\"><img loading=\"lazy\" class=\"aligncenter size-medium wp-image-12060\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/Uranium_235-300x212.png\" alt=\"Fissile \/ Fertile Material Cross-sections\" width=\"300\" height=\"212\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/Uranium_235-300x212.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/Uranium_235.png 574w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a>Uranium 235. Comparison of total fission cross-section and cross-section for radiative capture.<\/p>\n<figure id=\"attachment_12062\" aria-describedby=\"caption-attachment-12062\" style=\"width: 290px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/Uranium_238.png\"><img loading=\"lazy\" class=\"size-medium wp-image-12062\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/Uranium_238-300x205.png\" alt=\"Fissile \/ Fertile Material Cross-sections\" width=\"300\" height=\"205\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/Uranium_238-300x205.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/Uranium_238.png 588w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-12062\" class=\"wp-caption-text\">Source: JANIS (Java-based nuclear information software)<br \/>http:\/\/www.oecd-nea.org\/janis\/<\/figcaption><\/figure>\n<p style=\"text-align: left;\">Uranium 238. Comparison of total fission cross-section and cross-section for radiative capture.<\/p>\n<\/div>\n<div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-33 lgc-tablet-grid-33 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\">\n<\/div><\/div><div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-33 lgc-tablet-grid-33 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\">\n<h2>See above:<\/h2>\n<p>Neutron Nuclear Reactions<a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/\" class=\"su-button su-button-style-flat\" style=\"color:#606060;background-color:#ffffff;border-color:#cccccc;border-radius:10px;-moz-border-radius:10px;-webkit-border-radius:10px\" target=\"_self\"><span style=\"color:#606060;padding:7px 20px;font-size:16px;line-height:24px;border-color:#ffffff;border-radius:10px;-moz-border-radius:10px;-webkit-border-radius:10px;text-shadow:0px 0px 0px #000000;-moz-text-shadow:0px 0px 0px #000000;-webkit-text-shadow:0px 0px 0px #000000\"><i class=\"sui sui-link\" style=\"font-size:16px;color:#5d5d5d\"><\/i> <\/span><\/a><\/p><\/div><\/div><div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-33 lgc-tablet-grid-33 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\">\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Physics of Nuclear Fission In general, the neutron-induced fission reaction is the reaction in which the incident neutron enters the heavy target nucleus (fissionable nucleus), forming a compound nucleus that is excited to such a high energy level (Eexcitation &gt; Ecritical) that the nucleus splits into two large fission fragments. A large amount of energy &#8230; <a title=\"Nuclear Fission\" class=\"read-more\" href=\"https:\/\/sitepourvtc.com\/nuclear-power\/fission\/\" aria-label=\"More on Nuclear Fission\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":52,"menu_order":4,"comment_status":"closed","ping_status":"closed","template":"","meta":{"generate_page_header":""},"_links":{"self":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/60"}],"collection":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/comments?post=60"}],"version-history":[{"count":17,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/60\/revisions"}],"predecessor-version":[{"id":40106,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/60\/revisions\/40106"}],"up":[{"embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/52"}],"wp:attachment":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/media?parent=60"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}