{"id":3657,"date":"2015-05-06T03:51:00","date_gmt":"2015-05-06T03:51:00","guid":{"rendered":"https:\/\/courses.candelalearning.com\/oschemtemp\/?post_type=chapter&#038;p=3657"},"modified":"2016-10-25T19:09:46","modified_gmt":"2016-10-25T19:09:46","slug":"nuclear-equations-2","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-fmcc-chem-atoms-first\/chapter\/nuclear-equations-2\/","title":{"raw":"Nuclear Equations","rendered":"Nuclear Equations"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\nBy the end of this module, you will be able to:\r\n<ul>\r\n \t<li>Identify common particles and energies involved in nuclear reactions<\/li>\r\n \t<li>Write and balance nuclear equations<\/li>\r\n<\/ul>\r\n<\/div>\r\nChanges of nuclei that result in changes in their atomic numbers, mass numbers, or energy states are <strong>nuclear reactions<\/strong>. To describe a nuclear reaction, we use an equation that identifies the nuclides involved in the reaction, their mass numbers and atomic numbers, and the other particles involved in the reaction.\r\n<h2>Types of Particles in Nuclear Reactions<\/h2>\r\nMany entities can be involved in nuclear reactions. The most common are protons, neutrons, alpha particles, beta particles, positrons, and gamma rays, as shown in Table\u00a01. Protons [latex]\\left({}_{1}^{1}\\text{p}\\text{, also represented by the symbol }{}_{1}^{1}\\text{H}\\right)[\/latex] and neutrons [latex]\\left({}_{0}^{1}\\text{n}\\right)[\/latex] are the constituents of atomic nuclei, and have been described previously. <strong>Alpha particles<\/strong> [latex]\\left({}_{2}^{4}\\text{He}\\text{, also represented by the symbol }_{2}^{4}\\alpha\\right)[\/latex] are high-energy helium nuclei. <strong>Beta particles<\/strong> [latex]\\left({}_{-1}^{0}\\beta\\text{, also represented by the symbol }_{-1}^{0}\\text{e}\\right)[\/latex] are high-energy electrons, and gamma rays are photons of very high-energy electromagnetic radiation. <strong>Positrons<\/strong> [latex]\\left({}_{+1}^{0}\\beta\\text{, also represented by the symbol }_{+1}^{0}\\beta\\right)[\/latex] are positively charged electrons (\u201canti-electrons\u201d). The subscripts and superscripts are necessary for balancing nuclear equations, but are usually optional in other circumstances. For example, an alpha particle is a helium nucleus (He) with a charge of +2 and a mass number of 4, so it is symbolized [latex]{}_{2}^{4}\\text{He}[\/latex]. This works because, in general, the ion charge is not important in the balancing of nuclear equations.\r\n\r\nAlthough many species are encountered in nuclear reactions, Table\u00a01\u00a0summarizes the names, symbols, representations, and descriptions of the most common of these.\r\n<table>\r\n<thead>\r\n<tr>\r\n<th colspan=\"4\">Table 1. Nuclear Particles<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<th style=\"width: 15%;\">Name<\/th>\r\n<th style=\"width: 20%;\">Symbol(s)<\/th>\r\n<th style=\"width: 20%;\">Representation<\/th>\r\n<th style=\"width: 45%;\">Description<\/th>\r\n<\/tr>\r\n<tr>\r\n<td>Alpha particle<\/td>\r\n<td>[latex]{}_{2}^{4}\\text{He}[\/latex] \u00a0or \u00a0[latex]{}_{2}^{4}\\alpha[\/latex]<\/td>\r\n<td><img class=\"size-full wp-image-5944 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/218\/2016\/10\/25183458\/alpha.png\" alt=\"two blank white sphere attached to two blue spheres of about the same size with positive signs in them\" width=\"91\" height=\"87\" \/><\/td>\r\n<td>(High-energy) helium nuclei consisting of two protons and two neutrons<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Beta particle<\/td>\r\n<td>[latex]{}_{-1}^{0}\\text{e}[\/latex] \u00a0or \u00a0[latex]{}_{-1}^{0}\\beta[\/latex]<\/td>\r\n<td><img class=\"size-full wp-image-5945 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/218\/2016\/10\/25183518\/beta.png\" alt=\"a small red sphere with a negative sign in it\" width=\"59\" height=\"54\" \/><\/td>\r\n<td>(High-energy) electrons<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Positron<\/td>\r\n<td>[latex]{}_{+1}^{0}\\text{e}[\/latex] \u00a0or \u00a0[latex]{}_{+1}^{0}\\beta[\/latex]<\/td>\r\n<td><img class=\"aligncenter size-full wp-image-5946\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/218\/2016\/10\/25183540\/positron.png\" alt=\"a small red sphere with a positive sign in it\" width=\"53\" height=\"48\" \/><\/td>\r\n<td>Particles with the same mass as an electron but with 1 unit of positive charge<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Proton<\/td>\r\n<td>\u00a0[latex]{}_{1}^{1}\\text{H}[\/latex] \u00a0or \u00a0[latex]{}_{1}^{1}\\text{p}[\/latex]<\/td>\r\n<td><img class=\"aligncenter size-full wp-image-5947\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/218\/2016\/10\/25183559\/proton.png\" alt=\"a blue sphere with a positive sign in it\" width=\"70\" height=\"53\" \/><\/td>\r\n<td>Nuclei of hydrogen atoms<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Neutron<\/td>\r\n<td>\u00a0[latex]{}_{0}^{1}\\text{n}[\/latex]<\/td>\r\n<td>\u00a0<img class=\"aligncenter size-full wp-image-5948\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/218\/2016\/10\/25183615\/neutron.png\" alt=\"a blank white sphere\" width=\"66\" height=\"63\" \/><\/td>\r\n<td>Particles with a mass approximately equal to that of a proton but with no charge<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Gamma ray<\/td>\r\n<td>\u00a0[latex]\\gamma[\/latex]<\/td>\r\n<td><img class=\"aligncenter size-full wp-image-5949\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/218\/2016\/10\/25183632\/gammaray.png\" alt=\"and a purple squiggle ling with an arrow pointing right to a lowercase gamma.\" width=\"191\" height=\"47\" \/><\/td>\r\n<td>Very high-energy electromagnetic radiation<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nNote that positrons are exactly like electrons, except they have the opposite charge. They are the most common example of <strong>antimatter<\/strong>, particles with the same mass but the opposite state of another property (for example, charge) than ordinary matter. When antimatter encounters ordinary matter, both are annihilated and their mass is converted into energy in the form of <strong>gamma rays (\u03b3)<\/strong>\u2014and other much smaller subnuclear particles, which are beyond the scope of this chapter\u2014according to the mass-energy equivalence equation <em>E<\/em> = <em>mc<\/em><sup>2<\/sup>, seen in the preceding section. For example, when a positron and an electron collide, both are annihilated and two gamma ray photons are created:\r\n<p style=\"text-align: center;\">[latex]{}_{-1}^{0}\\text{e}+{}_{+1}^{0}\\text{e}\\longrightarrow \\gamma+\\gamma[\/latex]<\/p>\r\nAs seen in the chapter discussing light and electromagnetic radiation, gamma rays compose short wavelength, high-energy electromagnetic radiation and are (much) more energetic than better-known X-rays that can behave as particles in the wave-particle duality sense. Gamma rays are produced when a nucleus undergoes a transition from a higher to a lower energy state, similar to how a photon is produced by an electronic transition from a higher to a lower energy level. Due to the much larger energy differences between nuclear energy shells, gamma rays emanating from a nucleus have energies that are typically millions of times larger than electromagnetic radiation emanating from electronic transitions.\r\n<h2>Balancing Nuclear Reactions<\/h2>\r\nA balanced chemical reaction equation reflects the fact that during a chemical reaction, bonds break and form, and atoms are rearranged, but the total numbers of atoms of each element are conserved and do not change. A balanced nuclear reaction equation indicates that there is a rearrangement during a nuclear reaction, but of subatomic particles rather than atoms. Nuclear reactions also follow conservation laws, and they are balanced in two ways:\r\n<ol id=\"fs-idp258853168\" data-number-style=\"arabic\">\r\n \t<li>The sum of the mass numbers of the reactants equals the sum of the mass numbers of the products.<\/li>\r\n \t<li>The sum of the charges of the reactants equals the sum of the charges of the products.<\/li>\r\n<\/ol>\r\nIf the atomic number and the mass number of all but one of the particles in a nuclear reaction are known, we can identify the particle by balancing the reaction. For instance, we could determine that [latex]{}_{8}^{17}\\text{O}[\/latex] is a product of the nuclear reaction of [latex]{}_{7}^{14}\\text{N}[\/latex] and [latex]{}_{2}^{4}\\text{He}[\/latex] if we knew that a proton, [latex]{}_{1}^{1}\\text{H}[\/latex], was one of the two products. Example 1\u00a0shows how we can identify a nuclide by balancing the nuclear reaction.\r\n<div class=\"textbox examples\">\r\n<h3>Example 1:\u00a0Balancing Equations for Nuclear Reactions<\/h3>\r\nThe reaction of an \u03b1 particle with magnesium-25 [latex]\\left({}_{12}^{25}\\text{Mg}\\right)[\/latex] produces a proton and a nuclide of another element. Identify the new nuclide produced.\r\n[reveal-answer q=\"369341\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"369341\"]\r\n\r\nThe nuclear reaction can be written as:\r\n<p style=\"text-align: center;\">[latex]{}_{12}^{25}\\text{Mg}+{}_{2}^{4}\\text{He}\\longrightarrow {}_{1}^{1}\\text{H}+{}_{\\text{Z}}^{\\text{A}}\\text{X}[\/latex]<\/p>\r\nwhere A is the mass number and Z is the atomic number of the new nuclide, X. Because the sum of the mass numbers of the reactants must equal the sum of the mass numbers of the products:\r\n<p style=\"text-align: center;\">[latex]25+4=\\text{A}+1,\\text{or A}=28[\/latex]<\/p>\r\nSimilarly, the charges must balance, so:\r\n<p style=\"text-align: center;\">[latex]12+2=\\text{Z}+1,\\text{and Z}=13[\/latex]<\/p>\r\nCheck the periodic table: The element with nuclear charge = +13 is aluminum. Thus, the product is [latex]{}_{13}^{28}\\text{Al}[\/latex].\r\n\r\n[\/hidden-answer]\r\n<h4>Check Your Learning<\/h4>\r\nThe nuclide [latex]{}_{53}^{125}\\text{I}[\/latex] combines with an electron and produces a new nucleus and no other massive particles. What is the equation for this reaction?\r\n[reveal-answer q=\"372850\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"372850\"][latex]{}_{53}^{125}\\text{I}+{}_{-1}^{0}\\text{e}\\longrightarrow {}_{52}^{125}\\text{Te}[\/latex][\/hidden-answer]\r\n\r\n<\/div>\r\nFollowing are the equations of several nuclear reactions that have important roles in the history of nuclear chemistry:\r\n<ul id=\"fs-idp95347744\" data-bullet-style=\"bullet\">\r\n \t<li>The first naturally occurring unstable element that was isolated, polonium, was discovered by the Polish scientist Marie <strong>Curie<\/strong> and her husband Pierre in 1898. It decays, emitting \u03b1 particles:\r\n<ul>\r\n \t<li>[latex]{}_{84}^{212}\\text{Po}\\longrightarrow {}_{82}^{208}\\text{Pb}+{}_{2}^{4}\\text{He}[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>The first nuclide to be prepared by artificial means was an isotope of oxygen, <sup>17<\/sup>O. It was made by Ernest <strong>Rutherford<\/strong> in 1919 by bombarding nitrogen atoms with \u03b1 particles:\r\n<ul>\r\n \t<li>[latex]{}_{7}^{14}\\text{N}+{}_{2}^{4}\\alpha\\longrightarrow {}_{8}^{17}\\text{O}+{}_{1}^{1}\\text{H}[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>James <strong>Chadwick<\/strong> discovered the neutron in 1932, as a previously unknown neutral particle produced along with <sup>12<\/sup>C by the nuclear reaction between <sup>9<\/sup>Be and <sup>4<\/sup>He:\r\n<ul>\r\n \t<li>[latex]{}_{4}^{9}\\text{Be}+{}_{2}^{4}\\text{He}\\longrightarrow {}_{6}^{12}\\text{C}+{}_{0}^{1}\\text{n}[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>The first element to be prepared that does not occur naturally on the earth, technetium, was created by bombardment of molybdenum by deuterons (heavy hydrogen, [latex]{}_{1}^{2}\\text{H}\\)[\/latex] , by Emilio <strong>Segre<\/strong> and Carlo <strong>Perrier<\/strong> in 1937:\r\n<ul>\r\n \t<li>[latex]{}_{1}^{2}\\text{H}+{}_{42}^{97}\\text{Mo}\\longrightarrow 2{}_{0}^{1}\\text{n}+{}_{43}^{97}\\text{Tc}[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>The first controlled nuclear chain reaction was carried out in a reactor at the University of Chicago in 1942. One of the many reactions involved was:\r\n<ul>\r\n \t<li>[latex]{}_{92}^{235}\\text{U}+{}_{0}^{1}\\text{n}\\longrightarrow {}_{35}^{87}\\text{Br}+{}_{57}^{146}\\text{La}+3{}_{0}^{1}\\text{n}[\/latex].<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Key Concepts and Summary<\/h3>\r\nNuclei can undergo reactions that change their number of protons, number of neutrons, or energy state. Many different particles can be involved in nuclear reactions. The most common are protons, neutrons, positrons (which are positively charged electrons), alpha (\u03b1) particles (which are high-energy helium nuclei), beta (\u03b2) particles (which are high-energy electrons), and gamma (\u03b3) rays (which compose high-energy electromagnetic radiation). As with chemical reactions, nuclear reactions are always balanced. When a nuclear reaction occurs, the total mass (number) and the total charge remain unchanged.\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Exercises<\/h3>\r\nWrite a brief description or definition of each of the following:\r\n<ol>\r\n \t<li>nucleon<\/li>\r\n \t<li>\u03b1 particle<\/li>\r\n \t<li>\u03b2 particle<\/li>\r\n \t<li>positron<\/li>\r\n \t<li>\u03b3 ray<\/li>\r\n \t<li>nuclide<\/li>\r\n \t<li>mass number<\/li>\r\n \t<li>atomic number<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"386825\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"386825\"]\r\n<ol>\r\n \t<li>A nucleon is any particle contained in the nucleus of the atom, so it can refer to protons and neutrons.<\/li>\r\n \t<li>An \u03b1 particle is one product of natural radioactivity and is the nucleus of a helium atom.<\/li>\r\n \t<li>A \u03b2 particle is a product of natural radioactivity and is a high-speed electron.<\/li>\r\n \t<li>A positron is a particle with the same mass as an electron but with a positive charge.<\/li>\r\n \t<li>Gamma rays compose electromagnetic radiation of high energy and short wavelength.<\/li>\r\n \t<li>Nuclide is a term used when referring to a single type of nucleus.<\/li>\r\n \t<li>The mass number is the sum of the number of protons and the number of neutrons in an element.<\/li>\r\n \t<li>The atomic number is the number of protons in the nucleus of an element.<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Exercises<\/h3>\r\n<ol>\r\n \t<li>Which of the various particles (\u03b1 particles, \u03b2 particles, and so on) that may be produced in a nuclear reaction are actually nuclei.<\/li>\r\n \t<li>Complete each of the following equations by adding the missing species:\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]{}_{13}^{27}\\text{Al}+{}_{2}^{4}\\text{He}\\longrightarrow ?+{}_{0}^{1}\\text{n}[\/latex]<\/li>\r\n \t<li>[latex]{}_{94}^{239}\\text{Pu}+?\\longrightarrow {}_{96}^{242}\\text{Cm}+{}_{0}^{1}\\text{n}[\/latex]<\/li>\r\n \t<li>[latex]{}_{7}^{14}\\text{N}+{}_{2}^{4}\\text{He}\\longrightarrow \\text{?}+{}_{1}^{1}\\text{H}[\/latex]<\/li>\r\n \t<li>[latex]{}_{92}^{235}\\text{U}\\longrightarrow \\text{?}+{}_{55}^{135}\\text{Cs}+4{}_{0}^{1}\\text{n}[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Complete each of the following equations:\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]{}_{3}^{7}\\text{Li}+\\text{?}\\longrightarrow 2{}_{2}^{4}\\text{He}[\/latex]<\/li>\r\n \t<li>[latex]{}_{6}^{14}\\text{C}\\longrightarrow {}_{7}^{14}\\text{N}+\\text{?}[\/latex]<\/li>\r\n \t<li>[latex]{}_{13}^{27}\\text{Al}+{}_{2}^{4}\\text{He}\\longrightarrow \\text{?}+{}_{0}^{1}\\text{n}[\/latex]<\/li>\r\n \t<li>[latex]{}_{96}^{250}\\text{Cm}\\longrightarrow \\text{?}+{}_{38}^{98}\\text{Sr}+4{}_{0}^{1}\\text{n}[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Write a balanced equation for each of the following nuclear reactions:\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>the production of <sup>17<\/sup>O from <sup>14<\/sup>N by \u03b1 particle bombardment<\/li>\r\n \t<li>the production of <sup>14<\/sup>C from <sup>14<\/sup>N by neutron bombardment<\/li>\r\n \t<li>the production of <sup>233<\/sup>Th from <sup>232<\/sup>Th by neutron bombardment<\/li>\r\n \t<li>the production of <sup>239<\/sup>U from <sup>238<\/sup>U by [latex]{}_{1}^{2}\\text{H}[\/latex] bombardment<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Technetium-99 is prepared from <sup>98<\/sup>Mo. Molybdenum-98 combines with a neutron to give molybdenum-99, an unstable isotope that emits a \u03b2 particle to yield an excited form of technetium-99, represented as <sup>99<\/sup>Tc<sup>*<\/sup>. This excited nucleus relaxes to the ground state, represented as <sup>99<\/sup>Tc, by emitting a \u03b3 ray. The ground state of <sup>99<\/sup>Tc then emits a \u03b2 particle. Write the equations for each of these nuclear reactions.<\/li>\r\n \t<li>The mass of the atom [latex]{}_{9}^{19}\\text{F}[\/latex] is 18.99840 amu.\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>Calculate its binding energy per atom in millions of electron volts.<\/li>\r\n \t<li>Calculate its binding energy per nucleon.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>For the reaction [latex]{}_{6}^{14}\\text{C}\\longrightarrow {}_{7}^{14}\\text{N}+\\text{?}[\/latex], if 100.0 g of carbon reacts, what volume of nitrogen gas (N<sub>2<\/sub>) is produced at 273K and 1 atm?<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"699603\"]Show Selected Answers[\/reveal-answer]\r\n[hidden-answer a=\"699603\"]\r\n\r\n2. The completed equations are as follows:\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]{}_{13}^{27}\\text{Al}+{}_{2}^{4}\\text{He}\\longrightarrow {}_{15}^{30}\\text{P}+{}_{0}^{1}\\text{n}[\/latex]<\/li>\r\n \t<li>[latex]{}_{94}^{239}\\text{Pu}+{}_{2}^{4}\\text{He}\\longrightarrow {}_{96}^{242}\\text{Cm}+{}_{0}^{1}\\text{n}[\/latex]<\/li>\r\n \t<li>[latex]{}_{7}^{14}\\text{N}+{}_{2}^{4}\\text{He}\\longrightarrow {}_{8}^{17}\\text{O}+{}_{1}^{1}\\text{H}[\/latex]<\/li>\r\n \t<li>[latex]{}_{92}^{235}\\text{U}\\longrightarrow {}_{37}^{96}\\text{Rb}+{}_{55}^{135}\\text{Cs}+4_{0}^{1}\\text{n}[\/latex]<\/li>\r\n<\/ol>\r\n4.\u00a0The balanced\u00a0equations are as follows:\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]{}_{7}^{14}\\text{N}+{}_{2}^{4}\\text{He}\\longrightarrow {}_{8}^{17}\\text{O}+{}_{1}^{1}\\text{H}[\/latex]<\/li>\r\n \t<li>[latex]{}_{7}^{14}\\text{N}+{}_{0}^{1}\\text{n}\\longrightarrow {}_{6}^{14}\\text{N}+{}_{1}^{1}\\text{H}[\/latex]<\/li>\r\n \t<li>[latex]{}_{90}^{232}\\text{Th}+{}_{0}^{1}\\text{n}\\longrightarrow {}_{90}^{233}\\text{Th}[\/latex]<\/li>\r\n \t<li>[latex]{}_{92}^{238}\\text{U}+{}_{1}^{2}\\text{H}\\longrightarrow {}_{92}^{239}\\text{U}+{}_{1}^{1}\\text{H}[\/latex]<\/li>\r\n<\/ol>\r\n6. The answers are as follows:\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>Determine the mass defect of the nuclide, which is the difference between the mass of 9 protons, 10 neutrons, and 9 electrons, and the observed mass of a [latex]{}_{9}^{19}\\text{F}[\/latex] atom:\r\n[latex]\\begin{array}{rcl}\\\\ \\text{mass defect}&amp;=&amp;\\left[\\left(9\\times1.0073\\text{ amu}\\right)+\\left(10\\times1.0087\\text{ amu}\\right)+\\left(9\\times0.00055\\text{ amu}\\right)\\right]-18.99840\\text{ amu}\\\\{}&amp;=&amp;19.15765\\text{ amu}-18.99840\\text{ amu}\\\\{}&amp;=&amp;0.15925\\text{ amu}\\end{array}[\/latex]\r\n[latex]\\begin{array}{rcl}\\\\ E=m{c}^{2}&amp;=&amp;\\text{0.15925 amu}\\times \\frac{1.6605\\times {10}^{-27}\\text{kg}}{\\text{1 amu}}\\times {\\left(2.998\\times {10}^{8}\\frac{m}{s}\\right)}^{2}\\\\{}&amp;=&amp;2.377\\times10^{-11}\\text{ kg m\/s}^2\\\\{}&amp;=&amp;2.377\\times10^{-11}\\text{ J}\\\\ {}\\end{array}[\/latex]\r\n[latex]2.337\\times {10}^{-11}\\text{J}\\times \\frac{\\text{1 MeV}}{1.602\\times {10}^{-13}\\text{J}}=\\text{148.8 MeV per atom}[\/latex]<\/li>\r\n \t<li>Binding energy per nucleon = [latex]\\frac{\\text{148.4 MeV}}{19}=\\text{7.808 MeV\/nucleon}[\/latex]<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<h2>Glossary<\/h2>\r\n<strong>alpha particle: <\/strong>(<strong>\u03b1<\/strong> or [latex]{}_{\\mathbf{2}}^{\\mathbf{4}}\\mathbf{\\text{He}}[\/latex] or [latex]{}_{\\mathbf{2}}^{\\mathbf{4}}\\mathbf{\\alpha})[\/latex] high-energy helium nucleus; a helium atom that has lost two electrons and contains two protons and two neutrons\r\n\r\n<strong>antimatter: <\/strong>particles with the same mass but opposite properties (such as charge) of ordinary particles\r\n\r\n<strong>beta particle: <\/strong>[latex]\\mathbf\\beta[\/latex] or [latex]{}_{\\mathbf{-1}}^{\\mathbf{0}}\\mathbf{\\text{e}}[\/latex] or [latex]{}_{\\mathbf{-1}}^{\\mathbf{0}}\\mathbf{\\beta}\\mathbf{\\text{)}}[\/latex] high-energy electron\r\n\r\n<strong>gamma ray: <\/strong>(<strong>\u03b3<\/strong> or [latex]{}_{\\mathbf{0}}^{\\mathbf{0}}\\mathbf{\\gamma}\\mathbf{\\text{)}}[\/latex] short wavelength, high-energy electromagnetic radiation that exhibits wave-particle duality\r\n\r\n<strong>nuclear reaction: <\/strong>change to a nucleus resulting in changes in the atomic number, mass number, or energy state\r\n\r\n<strong>positron [latex]\\text{(}{}_{+1}^{0}\\beta_{\\phantom{}}^{\\phantom{}}[\/latex] or [latex]{}_{+1}^{0}\\text{e}\\text{)}[\/latex] : <\/strong>antiparticle to the electron; it has identical properties to an electron, except for having the opposite (positive) charge","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<p>By the end of this module, you will be able to:<\/p>\n<ul>\n<li>Identify common particles and energies involved in nuclear reactions<\/li>\n<li>Write and balance nuclear equations<\/li>\n<\/ul>\n<\/div>\n<p>Changes of nuclei that result in changes in their atomic numbers, mass numbers, or energy states are <strong>nuclear reactions<\/strong>. To describe a nuclear reaction, we use an equation that identifies the nuclides involved in the reaction, their mass numbers and atomic numbers, and the other particles involved in the reaction.<\/p>\n<h2>Types of Particles in Nuclear Reactions<\/h2>\n<p>Many entities can be involved in nuclear reactions. The most common are protons, neutrons, alpha particles, beta particles, positrons, and gamma rays, as shown in Table\u00a01. Protons [latex]\\left({}_{1}^{1}\\text{p}\\text{, also represented by the symbol }{}_{1}^{1}\\text{H}\\right)[\/latex] and neutrons [latex]\\left({}_{0}^{1}\\text{n}\\right)[\/latex] are the constituents of atomic nuclei, and have been described previously. <strong>Alpha particles<\/strong> [latex]\\left({}_{2}^{4}\\text{He}\\text{, also represented by the symbol }_{2}^{4}\\alpha\\right)[\/latex] are high-energy helium nuclei. <strong>Beta particles<\/strong> [latex]\\left({}_{-1}^{0}\\beta\\text{, also represented by the symbol }_{-1}^{0}\\text{e}\\right)[\/latex] are high-energy electrons, and gamma rays are photons of very high-energy electromagnetic radiation. <strong>Positrons<\/strong> [latex]\\left({}_{+1}^{0}\\beta\\text{, also represented by the symbol }_{+1}^{0}\\beta\\right)[\/latex] are positively charged electrons (\u201canti-electrons\u201d). The subscripts and superscripts are necessary for balancing nuclear equations, but are usually optional in other circumstances. For example, an alpha particle is a helium nucleus (He) with a charge of +2 and a mass number of 4, so it is symbolized [latex]{}_{2}^{4}\\text{He}[\/latex]. This works because, in general, the ion charge is not important in the balancing of nuclear equations.<\/p>\n<p>Although many species are encountered in nuclear reactions, Table\u00a01\u00a0summarizes the names, symbols, representations, and descriptions of the most common of these.<\/p>\n<table>\n<thead>\n<tr>\n<th colspan=\"4\">Table 1. Nuclear Particles<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<th style=\"width: 15%;\">Name<\/th>\n<th style=\"width: 20%;\">Symbol(s)<\/th>\n<th style=\"width: 20%;\">Representation<\/th>\n<th style=\"width: 45%;\">Description<\/th>\n<\/tr>\n<tr>\n<td>Alpha particle<\/td>\n<td>[latex]{}_{2}^{4}\\text{He}[\/latex] \u00a0or \u00a0[latex]{}_{2}^{4}\\alpha[\/latex]<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-5944 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/218\/2016\/10\/25183458\/alpha.png\" alt=\"two blank white sphere attached to two blue spheres of about the same size with positive signs in them\" width=\"91\" height=\"87\" \/><\/td>\n<td>(High-energy) helium nuclei consisting of two protons and two neutrons<\/td>\n<\/tr>\n<tr>\n<td>Beta particle<\/td>\n<td>[latex]{}_{-1}^{0}\\text{e}[\/latex] \u00a0or \u00a0[latex]{}_{-1}^{0}\\beta[\/latex]<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-5945 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/218\/2016\/10\/25183518\/beta.png\" alt=\"a small red sphere with a negative sign in it\" width=\"59\" height=\"54\" \/><\/td>\n<td>(High-energy) electrons<\/td>\n<\/tr>\n<tr>\n<td>Positron<\/td>\n<td>[latex]{}_{+1}^{0}\\text{e}[\/latex] \u00a0or \u00a0[latex]{}_{+1}^{0}\\beta[\/latex]<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-5946\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/218\/2016\/10\/25183540\/positron.png\" alt=\"a small red sphere with a positive sign in it\" width=\"53\" height=\"48\" \/><\/td>\n<td>Particles with the same mass as an electron but with 1 unit of positive charge<\/td>\n<\/tr>\n<tr>\n<td>Proton<\/td>\n<td>\u00a0[latex]{}_{1}^{1}\\text{H}[\/latex] \u00a0or \u00a0[latex]{}_{1}^{1}\\text{p}[\/latex]<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-5947\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/218\/2016\/10\/25183559\/proton.png\" alt=\"a blue sphere with a positive sign in it\" width=\"70\" height=\"53\" \/><\/td>\n<td>Nuclei of hydrogen atoms<\/td>\n<\/tr>\n<tr>\n<td>Neutron<\/td>\n<td>\u00a0[latex]{}_{0}^{1}\\text{n}[\/latex]<\/td>\n<td>\u00a0<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-5948\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/218\/2016\/10\/25183615\/neutron.png\" alt=\"a blank white sphere\" width=\"66\" height=\"63\" \/><\/td>\n<td>Particles with a mass approximately equal to that of a proton but with no charge<\/td>\n<\/tr>\n<tr>\n<td>Gamma ray<\/td>\n<td>\u00a0[latex]\\gamma[\/latex]<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-5949\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/218\/2016\/10\/25183632\/gammaray.png\" alt=\"and a purple squiggle ling with an arrow pointing right to a lowercase gamma.\" width=\"191\" height=\"47\" \/><\/td>\n<td>Very high-energy electromagnetic radiation<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Note that positrons are exactly like electrons, except they have the opposite charge. They are the most common example of <strong>antimatter<\/strong>, particles with the same mass but the opposite state of another property (for example, charge) than ordinary matter. When antimatter encounters ordinary matter, both are annihilated and their mass is converted into energy in the form of <strong>gamma rays (\u03b3)<\/strong>\u2014and other much smaller subnuclear particles, which are beyond the scope of this chapter\u2014according to the mass-energy equivalence equation <em>E<\/em> = <em>mc<\/em><sup>2<\/sup>, seen in the preceding section. For example, when a positron and an electron collide, both are annihilated and two gamma ray photons are created:<\/p>\n<p style=\"text-align: center;\">[latex]{}_{-1}^{0}\\text{e}+{}_{+1}^{0}\\text{e}\\longrightarrow \\gamma+\\gamma[\/latex]<\/p>\n<p>As seen in the chapter discussing light and electromagnetic radiation, gamma rays compose short wavelength, high-energy electromagnetic radiation and are (much) more energetic than better-known X-rays that can behave as particles in the wave-particle duality sense. Gamma rays are produced when a nucleus undergoes a transition from a higher to a lower energy state, similar to how a photon is produced by an electronic transition from a higher to a lower energy level. Due to the much larger energy differences between nuclear energy shells, gamma rays emanating from a nucleus have energies that are typically millions of times larger than electromagnetic radiation emanating from electronic transitions.<\/p>\n<h2>Balancing Nuclear Reactions<\/h2>\n<p>A balanced chemical reaction equation reflects the fact that during a chemical reaction, bonds break and form, and atoms are rearranged, but the total numbers of atoms of each element are conserved and do not change. A balanced nuclear reaction equation indicates that there is a rearrangement during a nuclear reaction, but of subatomic particles rather than atoms. Nuclear reactions also follow conservation laws, and they are balanced in two ways:<\/p>\n<ol id=\"fs-idp258853168\" data-number-style=\"arabic\">\n<li>The sum of the mass numbers of the reactants equals the sum of the mass numbers of the products.<\/li>\n<li>The sum of the charges of the reactants equals the sum of the charges of the products.<\/li>\n<\/ol>\n<p>If the atomic number and the mass number of all but one of the particles in a nuclear reaction are known, we can identify the particle by balancing the reaction. For instance, we could determine that [latex]{}_{8}^{17}\\text{O}[\/latex] is a product of the nuclear reaction of [latex]{}_{7}^{14}\\text{N}[\/latex] and [latex]{}_{2}^{4}\\text{He}[\/latex] if we knew that a proton, [latex]{}_{1}^{1}\\text{H}[\/latex], was one of the two products. Example 1\u00a0shows how we can identify a nuclide by balancing the nuclear reaction.<\/p>\n<div class=\"textbox examples\">\n<h3>Example 1:\u00a0Balancing Equations for Nuclear Reactions<\/h3>\n<p>The reaction of an \u03b1 particle with magnesium-25 [latex]\\left({}_{12}^{25}\\text{Mg}\\right)[\/latex] produces a proton and a nuclide of another element. Identify the new nuclide produced.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q369341\">Show Answer<\/span><\/p>\n<div id=\"q369341\" class=\"hidden-answer\" style=\"display: none\">\n<p>The nuclear reaction can be written as:<\/p>\n<p style=\"text-align: center;\">[latex]{}_{12}^{25}\\text{Mg}+{}_{2}^{4}\\text{He}\\longrightarrow {}_{1}^{1}\\text{H}+{}_{\\text{Z}}^{\\text{A}}\\text{X}[\/latex]<\/p>\n<p>where A is the mass number and Z is the atomic number of the new nuclide, X. Because the sum of the mass numbers of the reactants must equal the sum of the mass numbers of the products:<\/p>\n<p style=\"text-align: center;\">[latex]25+4=\\text{A}+1,\\text{or A}=28[\/latex]<\/p>\n<p>Similarly, the charges must balance, so:<\/p>\n<p style=\"text-align: center;\">[latex]12+2=\\text{Z}+1,\\text{and Z}=13[\/latex]<\/p>\n<p>Check the periodic table: The element with nuclear charge = +13 is aluminum. Thus, the product is [latex]{}_{13}^{28}\\text{Al}[\/latex].<\/p>\n<\/div>\n<\/div>\n<h4>Check Your Learning<\/h4>\n<p>The nuclide [latex]{}_{53}^{125}\\text{I}[\/latex] combines with an electron and produces a new nucleus and no other massive particles. What is the equation for this reaction?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q372850\">Show Answer<\/span><\/p>\n<div id=\"q372850\" class=\"hidden-answer\" style=\"display: none\">[latex]{}_{53}^{125}\\text{I}+{}_{-1}^{0}\\text{e}\\longrightarrow {}_{52}^{125}\\text{Te}[\/latex]<\/div>\n<\/div>\n<\/div>\n<p>Following are the equations of several nuclear reactions that have important roles in the history of nuclear chemistry:<\/p>\n<ul id=\"fs-idp95347744\" data-bullet-style=\"bullet\">\n<li>The first naturally occurring unstable element that was isolated, polonium, was discovered by the Polish scientist Marie <strong>Curie<\/strong> and her husband Pierre in 1898. It decays, emitting \u03b1 particles:\n<ul>\n<li>[latex]{}_{84}^{212}\\text{Po}\\longrightarrow {}_{82}^{208}\\text{Pb}+{}_{2}^{4}\\text{He}[\/latex]<\/li>\n<\/ul>\n<\/li>\n<li>The first nuclide to be prepared by artificial means was an isotope of oxygen, <sup>17<\/sup>O. It was made by Ernest <strong>Rutherford<\/strong> in 1919 by bombarding nitrogen atoms with \u03b1 particles:\n<ul>\n<li>[latex]{}_{7}^{14}\\text{N}+{}_{2}^{4}\\alpha\\longrightarrow {}_{8}^{17}\\text{O}+{}_{1}^{1}\\text{H}[\/latex]<\/li>\n<\/ul>\n<\/li>\n<li>James <strong>Chadwick<\/strong> discovered the neutron in 1932, as a previously unknown neutral particle produced along with <sup>12<\/sup>C by the nuclear reaction between <sup>9<\/sup>Be and <sup>4<\/sup>He:\n<ul>\n<li>[latex]{}_{4}^{9}\\text{Be}+{}_{2}^{4}\\text{He}\\longrightarrow {}_{6}^{12}\\text{C}+{}_{0}^{1}\\text{n}[\/latex]<\/li>\n<\/ul>\n<\/li>\n<li>The first element to be prepared that does not occur naturally on the earth, technetium, was created by bombardment of molybdenum by deuterons (heavy hydrogen, [latex]{}_{1}^{2}\\text{H}\\)[\/latex] , by Emilio <strong>Segre<\/strong> and Carlo <strong>Perrier<\/strong> in 1937:\n<ul>\n<li>[latex]{}_{1}^{2}\\text{H}+{}_{42}^{97}\\text{Mo}\\longrightarrow 2{}_{0}^{1}\\text{n}+{}_{43}^{97}\\text{Tc}[\/latex]<\/li>\n<\/ul>\n<\/li>\n<li>The first controlled nuclear chain reaction was carried out in a reactor at the University of Chicago in 1942. One of the many reactions involved was:\n<ul>\n<li>[latex]{}_{92}^{235}\\text{U}+{}_{0}^{1}\\text{n}\\longrightarrow {}_{35}^{87}\\text{Br}+{}_{57}^{146}\\text{La}+3{}_{0}^{1}\\text{n}[\/latex].<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<div class=\"textbox key-takeaways\">\n<h3>Key Concepts and Summary<\/h3>\n<p>Nuclei can undergo reactions that change their number of protons, number of neutrons, or energy state. Many different particles can be involved in nuclear reactions. The most common are protons, neutrons, positrons (which are positively charged electrons), alpha (\u03b1) particles (which are high-energy helium nuclei), beta (\u03b2) particles (which are high-energy electrons), and gamma (\u03b3) rays (which compose high-energy electromagnetic radiation). As with chemical reactions, nuclear reactions are always balanced. When a nuclear reaction occurs, the total mass (number) and the total charge remain unchanged.<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Exercises<\/h3>\n<p>Write a brief description or definition of each of the following:<\/p>\n<ol>\n<li>nucleon<\/li>\n<li>\u03b1 particle<\/li>\n<li>\u03b2 particle<\/li>\n<li>positron<\/li>\n<li>\u03b3 ray<\/li>\n<li>nuclide<\/li>\n<li>mass number<\/li>\n<li>atomic number<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q386825\">Show Answer<\/span><\/p>\n<div id=\"q386825\" class=\"hidden-answer\" style=\"display: none\">\n<ol>\n<li>A nucleon is any particle contained in the nucleus of the atom, so it can refer to protons and neutrons.<\/li>\n<li>An \u03b1 particle is one product of natural radioactivity and is the nucleus of a helium atom.<\/li>\n<li>A \u03b2 particle is a product of natural radioactivity and is a high-speed electron.<\/li>\n<li>A positron is a particle with the same mass as an electron but with a positive charge.<\/li>\n<li>Gamma rays compose electromagnetic radiation of high energy and short wavelength.<\/li>\n<li>Nuclide is a term used when referring to a single type of nucleus.<\/li>\n<li>The mass number is the sum of the number of protons and the number of neutrons in an element.<\/li>\n<li>The atomic number is the number of protons in the nucleus of an element.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Exercises<\/h3>\n<ol>\n<li>Which of the various particles (\u03b1 particles, \u03b2 particles, and so on) that may be produced in a nuclear reaction are actually nuclei.<\/li>\n<li>Complete each of the following equations by adding the missing species:\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]{}_{13}^{27}\\text{Al}+{}_{2}^{4}\\text{He}\\longrightarrow ?+{}_{0}^{1}\\text{n}[\/latex]<\/li>\n<li>[latex]{}_{94}^{239}\\text{Pu}+?\\longrightarrow {}_{96}^{242}\\text{Cm}+{}_{0}^{1}\\text{n}[\/latex]<\/li>\n<li>[latex]{}_{7}^{14}\\text{N}+{}_{2}^{4}\\text{He}\\longrightarrow \\text{?}+{}_{1}^{1}\\text{H}[\/latex]<\/li>\n<li>[latex]{}_{92}^{235}\\text{U}\\longrightarrow \\text{?}+{}_{55}^{135}\\text{Cs}+4{}_{0}^{1}\\text{n}[\/latex]<\/li>\n<\/ol>\n<\/li>\n<li>Complete each of the following equations:\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]{}_{3}^{7}\\text{Li}+\\text{?}\\longrightarrow 2{}_{2}^{4}\\text{He}[\/latex]<\/li>\n<li>[latex]{}_{6}^{14}\\text{C}\\longrightarrow {}_{7}^{14}\\text{N}+\\text{?}[\/latex]<\/li>\n<li>[latex]{}_{13}^{27}\\text{Al}+{}_{2}^{4}\\text{He}\\longrightarrow \\text{?}+{}_{0}^{1}\\text{n}[\/latex]<\/li>\n<li>[latex]{}_{96}^{250}\\text{Cm}\\longrightarrow \\text{?}+{}_{38}^{98}\\text{Sr}+4{}_{0}^{1}\\text{n}[\/latex]<\/li>\n<\/ol>\n<\/li>\n<li>Write a balanced equation for each of the following nuclear reactions:\n<ol style=\"list-style-type: lower-alpha;\">\n<li>the production of <sup>17<\/sup>O from <sup>14<\/sup>N by \u03b1 particle bombardment<\/li>\n<li>the production of <sup>14<\/sup>C from <sup>14<\/sup>N by neutron bombardment<\/li>\n<li>the production of <sup>233<\/sup>Th from <sup>232<\/sup>Th by neutron bombardment<\/li>\n<li>the production of <sup>239<\/sup>U from <sup>238<\/sup>U by [latex]{}_{1}^{2}\\text{H}[\/latex] bombardment<\/li>\n<\/ol>\n<\/li>\n<li>Technetium-99 is prepared from <sup>98<\/sup>Mo. Molybdenum-98 combines with a neutron to give molybdenum-99, an unstable isotope that emits a \u03b2 particle to yield an excited form of technetium-99, represented as <sup>99<\/sup>Tc<sup>*<\/sup>. This excited nucleus relaxes to the ground state, represented as <sup>99<\/sup>Tc, by emitting a \u03b3 ray. The ground state of <sup>99<\/sup>Tc then emits a \u03b2 particle. Write the equations for each of these nuclear reactions.<\/li>\n<li>The mass of the atom [latex]{}_{9}^{19}\\text{F}[\/latex] is 18.99840 amu.\n<ol style=\"list-style-type: lower-alpha;\">\n<li>Calculate its binding energy per atom in millions of electron volts.<\/li>\n<li>Calculate its binding energy per nucleon.<\/li>\n<\/ol>\n<\/li>\n<li>For the reaction [latex]{}_{6}^{14}\\text{C}\\longrightarrow {}_{7}^{14}\\text{N}+\\text{?}[\/latex], if 100.0 g of carbon reacts, what volume of nitrogen gas (N<sub>2<\/sub>) is produced at 273K and 1 atm?<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q699603\">Show Selected Answers<\/span><\/p>\n<div id=\"q699603\" class=\"hidden-answer\" style=\"display: none\">\n<p>2. The completed equations are as follows:<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]{}_{13}^{27}\\text{Al}+{}_{2}^{4}\\text{He}\\longrightarrow {}_{15}^{30}\\text{P}+{}_{0}^{1}\\text{n}[\/latex]<\/li>\n<li>[latex]{}_{94}^{239}\\text{Pu}+{}_{2}^{4}\\text{He}\\longrightarrow {}_{96}^{242}\\text{Cm}+{}_{0}^{1}\\text{n}[\/latex]<\/li>\n<li>[latex]{}_{7}^{14}\\text{N}+{}_{2}^{4}\\text{He}\\longrightarrow {}_{8}^{17}\\text{O}+{}_{1}^{1}\\text{H}[\/latex]<\/li>\n<li>[latex]{}_{92}^{235}\\text{U}\\longrightarrow {}_{37}^{96}\\text{Rb}+{}_{55}^{135}\\text{Cs}+4_{0}^{1}\\text{n}[\/latex]<\/li>\n<\/ol>\n<p>4.\u00a0The balanced\u00a0equations are as follows:<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]{}_{7}^{14}\\text{N}+{}_{2}^{4}\\text{He}\\longrightarrow {}_{8}^{17}\\text{O}+{}_{1}^{1}\\text{H}[\/latex]<\/li>\n<li>[latex]{}_{7}^{14}\\text{N}+{}_{0}^{1}\\text{n}\\longrightarrow {}_{6}^{14}\\text{N}+{}_{1}^{1}\\text{H}[\/latex]<\/li>\n<li>[latex]{}_{90}^{232}\\text{Th}+{}_{0}^{1}\\text{n}\\longrightarrow {}_{90}^{233}\\text{Th}[\/latex]<\/li>\n<li>[latex]{}_{92}^{238}\\text{U}+{}_{1}^{2}\\text{H}\\longrightarrow {}_{92}^{239}\\text{U}+{}_{1}^{1}\\text{H}[\/latex]<\/li>\n<\/ol>\n<p>6. The answers are as follows:<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>Determine the mass defect of the nuclide, which is the difference between the mass of 9 protons, 10 neutrons, and 9 electrons, and the observed mass of a [latex]{}_{9}^{19}\\text{F}[\/latex] atom:<br \/>\n[latex]\\begin{array}{rcl}\\\\ \\text{mass defect}&=&\\left[\\left(9\\times1.0073\\text{ amu}\\right)+\\left(10\\times1.0087\\text{ amu}\\right)+\\left(9\\times0.00055\\text{ amu}\\right)\\right]-18.99840\\text{ amu}\\\\{}&=&19.15765\\text{ amu}-18.99840\\text{ amu}\\\\{}&=&0.15925\\text{ amu}\\end{array}[\/latex]<br \/>\n[latex]\\begin{array}{rcl}\\\\ E=m{c}^{2}&=&\\text{0.15925 amu}\\times \\frac{1.6605\\times {10}^{-27}\\text{kg}}{\\text{1 amu}}\\times {\\left(2.998\\times {10}^{8}\\frac{m}{s}\\right)}^{2}\\\\{}&=&2.377\\times10^{-11}\\text{ kg m\/s}^2\\\\{}&=&2.377\\times10^{-11}\\text{ J}\\\\ {}\\end{array}[\/latex]<br \/>\n[latex]2.337\\times {10}^{-11}\\text{J}\\times \\frac{\\text{1 MeV}}{1.602\\times {10}^{-13}\\text{J}}=\\text{148.8 MeV per atom}[\/latex]<\/li>\n<li>Binding energy per nucleon = [latex]\\frac{\\text{148.4 MeV}}{19}=\\text{7.808 MeV\/nucleon}[\/latex]<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<h2>Glossary<\/h2>\n<p><strong>alpha particle: <\/strong>(<strong>\u03b1<\/strong> or [latex]{}_{\\mathbf{2}}^{\\mathbf{4}}\\mathbf{\\text{He}}[\/latex] or [latex]{}_{\\mathbf{2}}^{\\mathbf{4}}\\mathbf{\\alpha})[\/latex] high-energy helium nucleus; a helium atom that has lost two electrons and contains two protons and two neutrons<\/p>\n<p><strong>antimatter: <\/strong>particles with the same mass but opposite properties (such as charge) of ordinary particles<\/p>\n<p><strong>beta particle: <\/strong>[latex]\\mathbf\\beta[\/latex] or [latex]{}_{\\mathbf{-1}}^{\\mathbf{0}}\\mathbf{\\text{e}}[\/latex] or [latex]{}_{\\mathbf{-1}}^{\\mathbf{0}}\\mathbf{\\beta}\\mathbf{\\text{)}}[\/latex] high-energy electron<\/p>\n<p><strong>gamma ray: <\/strong>(<strong>\u03b3<\/strong> or [latex]{}_{\\mathbf{0}}^{\\mathbf{0}}\\mathbf{\\gamma}\\mathbf{\\text{)}}[\/latex] short wavelength, high-energy electromagnetic radiation that exhibits wave-particle duality<\/p>\n<p><strong>nuclear reaction: <\/strong>change to a nucleus resulting in changes in the atomic number, mass number, or energy state<\/p>\n<p><strong>positron [latex]\\text{(}{}_{+1}^{0}\\beta_{\\phantom{}}^{\\phantom{}}[\/latex] or [latex]{}_{+1}^{0}\\text{e}\\text{)}[\/latex] : <\/strong>antiparticle to the electron; it has identical properties to an electron, except for having the opposite (positive) charge<\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-3657\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Chemistry. <strong>Provided by<\/strong>: OpenStax College. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/openstaxcollege.org\">http:\/\/openstaxcollege.org<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at https:\/\/openstaxcollege.org\/textbooks\/chemistry\/get<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":17,"menu_order":3,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Chemistry\",\"author\":\"\",\"organization\":\"OpenStax College\",\"url\":\"http:\/\/openstaxcollege.org\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at https:\/\/openstaxcollege.org\/textbooks\/chemistry\/get\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-3657","chapter","type-chapter","status-publish","hentry"],"part":2950,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/suny-fmcc-chem-atoms-first\/wp-json\/pressbooks\/v2\/chapters\/3657","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/suny-fmcc-chem-atoms-first\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/suny-fmcc-chem-atoms-first\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-fmcc-chem-atoms-first\/wp-json\/wp\/v2\/users\/17"}],"version-history":[{"count":9,"href":"https:\/\/courses.lumenlearning.com\/suny-fmcc-chem-atoms-first\/wp-json\/pressbooks\/v2\/chapters\/3657\/revisions"}],"predecessor-version":[{"id":5950,"href":"https:\/\/courses.lumenlearning.com\/suny-fmcc-chem-atoms-first\/wp-json\/pressbooks\/v2\/chapters\/3657\/revisions\/5950"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/suny-fmcc-chem-atoms-first\/wp-json\/pressbooks\/v2\/parts\/2950"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/suny-fmcc-chem-atoms-first\/wp-json\/pressbooks\/v2\/chapters\/3657\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/suny-fmcc-chem-atoms-first\/wp-json\/wp\/v2\/media?parent=3657"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-fmcc-chem-atoms-first\/wp-json\/pressbooks\/v2\/chapter-type?post=3657"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-fmcc-chem-atoms-first\/wp-json\/wp\/v2\/contributor?post=3657"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-fmcc-chem-atoms-first\/wp-json\/wp\/v2\/license?post=3657"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}