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Nuclear Binding Energy and Nuclear Stability

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Chapter 1: Radioactivity Chapter 1: Radioactivity 35 NPRE 441, Principles of Radiation Protection Chapter 1: Radioactivity Radioactivity • Radioactivity is defined as the spontaneous nuclear transformation that results in the formation of new elements. • Radioactivity and radioactive properties of nuclide are determined by nuclear considerations and independent of chemical and physical states of the radioisotope. • The probability of radioactive transformation depends primarily on two factors: ‐ Nuclear stability as related to the neutron‐to‐proton ratio. ‐ The mass‐energy relationship among the parent nucleus, daughter nucleus and the emitted particles. 36 NPRE 441, Principles of Radiation Protection Chapter 1: Radioactivity The Origin of Nuclear Radiation and a Few Related Concepts • Nuclear force and Coulomb barrier. • Nuclear binding energy and nuclear stability. • Nucleartransformationasawaytoachievegreaternuclear stability and associated energy release. 37 NPRE 441, Principles of Radiation Protection Nuclear Forces Within the incredibly small nuclear size （～10‐15m）,thetwostrongest forces in nature, Coulomb force and strong nuclear force, are pitted against each other. When the balance is broken, the resultant radioactivity yields particles of enormous energy. Coulomb potenital 1 q1 q2 VC , where 0 is the electrical permitivity http://230nsc1.phy‐astr.gsu.edu/hbase/hframe.html 40 r 38 NPRE 441, Principles of Radiation Protection Potential Energy of Nucleus • Nucleons are bounded together in nucleus by the strong force, which has a short range of ~10‐15m. • The strong force is powerful enough to overcome the Coulomb repulsion between the positively charged protons. Coulomb potenital 1 q1 q2 VC , where 0 is the electrical permitivity 40 r 39 NPRE 441, Principles of Radiation Protection Coulomb Barrier 40 NPRE 441, Principles of Radiation Protection Coulomb Barrier We can use the following equation to estimate the radiuses of the Cl nucleus and the proton, R 1.3A1/3 1015 m With A=1 and A=35 for the proton and the Cl nucleus, we have 1 q q 1 2 , V C 40 r where 0 is the electrical permitivity 41 NPRE 441, Principles of Radiation Protection A Simple Nuclear Reaction For example, thermal neutron capture by hydrogen nucleus. 42 NPRE 441, Principles of Radiation Protection Mass Defect and Nuclear Binding Energy In this case, the energy transition due to the mass defect is 43 NPRE 441, Principles of Radiation Protection Nuclear Binding Energy The nuclear binding energy In this case, the binding energy for the deuterium nucleus is given by 44 NPRE 441, Principles of Radiation Protection Nuclear Binding Energy • Nuclei are made up of protons and neutron, but the mass of a nucleus is always less than the sum of the individual masses of the protons and neutrons which constitute it. • This difference is a measure of the nuclear binding energy, which holds the nucleus together. The binding energy can be calculated from the Einstein relationship: Nuclear binding energy = Δmc2 The nuclear binding energy 45 Nuclear Binding Energy • Binding energy is always positive. • The average binding energy per nucleon peaks for A = 40 to 120, with a maximum of ~8.5MeV. • It then drops off for either higher or lower A. • There are a few nuclei, 4He, 12C and 16Oatthelowermass number end that have binding energies (per nucleon) well above that for adjacent nuclei. • In fact, these nuclei are all “multiples” of the alpha particle. •And… 46 NPRE 441, Principles of Radiation Protection Fission Reactions • A fission reaction splits up a large nucleus into smaller pieces. • A fission reaction typically happens when a neutron hits a nucleus with enough energy to make the nucleus unstable. 47 NPRE 441, Principles of Radiation Protection Average Binding Energy Per Nucleon Comparing Fusion and Fission Reactions http://230nsc1.phy‐astr.gsu.edu/hbase/hframe.html 48 NPRE 441, Principles of Radiation Protection Binding Energy of Atoms http://230nsc1.phy‐astr.gsu.edu/hbase/hframe.html 49 NPRE 441, Principles of Radiation Protection Z Chart of the Nuclides (177, 117) The nuclides are the possible nuclei of atoms. Z determines the chemistry, because the neutral atom with the nuclide as its nucleus has Zelectrons. Half‐life N Source: http://www.nndc.bnl.gov/chart/reZoom.jsp?newZoom=5 50 Chart of the Nuclides Be11 β- 11.5, 9.4 γ 2.1 51 Nuclear Stability and the Origin of Radioactivity Secondary radiations, e.g., gamma‐rays, X‐ rays, alpha‐particles, and electrons Alpha decay Parent (Z, N) Daughter (Z‐2, N‐2) 210 206 4 84 Po 82 Pb 2 He Beta decay: Parent (Z, N) Daughter (Z+1, N‐1) → ̅ Parent (Z, N) Daughter (Z‐1, N+1) Positron decay: → Electron capture: A A Z X e Z 1Y 22 22 0 11 Na10 Ne1 52 Chapter 1: Radioactivity Take‐Home Points Covered in Today’s Lecture Introduction • Major sources of radiation dose to the general population a. Medical dose b. Dose from radioactive background (ranked by importance) i. Internal ingestion of radioactivity ii. Space and cosmogenic radiation iii. Terrestrial naturally occurring radioactive materials (NORM) c. Radiation dose from indoor radon i. Inhaled radioactive Rn isotopes form the uranium (Rn‐222), thorium (Rn‐220), and actinium series (Rn219) ii. Alpha particles emitted by Rn‐222 and its daughters Chapter 1: Radioactivity • Nuclear binding energy a. What is nuclear binding energy? b. Calculation of binding energy for given radionuclides • Understanding the Chart of Nuclides a. Stable and non‐stable nuclides b. Energy release from radioactive decay 53 Chapter 1: Radioactivity Alpha Decay Key concepts • Coulomb barrier and energy release through alpha decay. • Energy spectrum of alpha particles. • Major health hazards related to alpha emission 54 NPRE 441, Principles of Radiation Protection Average Binding Energy Per Nucleon 55 NPRE 441, Principles of Radiation Protection Chapter 1: Radioactivity Alpha Emission • An alpha particle is a highly energetic helium nucleus consisting of two neutrons and 2 protons. • It is normally emitted from isotopes when the neutron‐ to‐proton ratio is too low – called the alpha decay. • Atomic number and atomic mass number are conserved in alpha decays 56 NPRE 441, Principles of Radiation Protection Chapter 1: Radioactivity Alpha Decay –An Example •Half‐life: 138.376 days; Decay mode: alpha‐decay (branching ratio: 100%); Energy release: 5.407MeV • 210Po has a neutron‐to‐proton ratio of 126 to 84 (1.5:1) and 206Pb has a neutron‐to‐proton ratio of 124 to 82 (~1.51:1) increased neutron‐to‐ proton ratio. • Alpha decay is also accompanied by the loss of two orbital electrons. 57 NPRE 441, Principles of Radiation Protection Nuclear Stability and the Origin of Radioactivity Secondary radiations, e.g., gamma‐rays, X‐ rays, alpha‐particles, and electrons Alpha decay Parent (Z, N) Daughter (Z‐2, N‐2) 210 206 4 84 Po 82 Pb 2 He Beta decay: Parent (Z, N) Daughter (Z+1, N‐1) → ̅ Parent (Z, N) Daughter (Z‐1, N+1) Positron decay: → Electron capture: A A Z X e Z 1Y 22 22 0 11 Na10 Ne1 58 Nuclear Binding Energy The nuclear binding energy In this case, the binding energy for the deuterium nucleus is given by 59 NPRE 441, Principles of Radiation Protection Potential Energy of Nucleus • Nucleons are bounded together in nucleus by the strong force, which has a short range of ~10‐15m. • The strong force is powerful enough to overcome the Coulomb repulsion between the positively charged protons. Coulomb potenital 1 q1 q2 VC , where 0 is the electrical permitivity 40 r 60 NPRE 441, Principles of Radiation Protection Chapter 1: Radioactivity Alpha Emission In heavy elements, It would require a minimum kinetic energy of ~3.8MeV for the alpha particle to “tunneling through” the potential well … 61 NPRE 441, Principles of Radiation Protection Chapter 1: Radioactivity Alpha Decay With only a few exceptions (Samarium‐147), naturally occurring alpha decay are found only among elements of atomic number greater than 82 because of the following reasons: • Electrostatic repulsive force in heavy nuclei increases much more rapidly with the increasing atomic number than the cohesive nuclear force. The magnitude of the electrostatic repulsive force may closely approach or even exceed that of the nuclear force. • Emitted alpha particles must have sufficiently high kinetic energy to overcome the potential barrier resultant from the strong nuclear force. 62 NPRE 441, Principles of Radiation Protection Chapter 1: Radioactivity Energy Release from Alpha Decay An example: Alpha decay of 226Ra The energy release can be found using the data shown in the table previously used for deriving binding energy 63 NPRE 441, Principles of Radiation Protection Understanding the Mass Defect and Nuclear Binding Energy 64 Chapter 1: Radioactivity Energy Release in Alpha Emission A more accurate version The required kinetic energy has to come from the decrease in mass following the decay process. The relationship between mass and energy associated with an alpha emission is given as 65 NPRE 441, Principles of Radiation Protection Chapter 1: Radioactivity Energy Release from Alpha Decay An example: Alpha decay of 226Ra The same example, when considering the daughter atom to have two less electrons, Note: Md, Md: masses of the parent and daughter atoms What is the energy of the alpha particle? 66 NPRE 441, Principles of Radiation Protection Chapter 1: Radioactivity Energy Spectra of Alpha Particles m is the mass of the alpha particle, and M is the mass of the recoil nucleus. Measured energy spectrum of alpha particles emitted from the decay of 238Pu. NPRE 441, Principles of Radiation Protection 67 Chapter 1: Radioactivity Energy Spectra of Alpha Particles Alpha decays are sometimes accompanied by the excited daughter products which complicates the resultant alpha particle spectra. The kinetic energy of alpha particles is given by E QA 4 / A, where A is the atomic mass number of the parent nucleus and Q is the energy release.
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