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Binding Energy of the Mother Nucleus Is Lower Than That of the Daughter Nucleus

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Binding Energy of the Mother Nucleus Is Lower Than That of the Daughter Nucleus Chapter 1 Learning Objectives • Historical Recap • Understand the different length scales of nuclear physics • Know the nomenclature for isotopes and nuclear reactions • Know the different types of neutron nuclear collisions and their relationship to each other • Basic principles of nuclear reactor Learning Objectives • Neutron Sources • Basic Principles of Nuclear Reactor • Bindinggg energyy curve • Liquid drop model • Fission Reaction • ODE Review • Radioactive Decay • Decay Chains • Chart of Nuclides Historical Recap • Driscoll handout • New programs – GNEP/AFCI – Gen-IV – Nuclear Power 2010 Why nuclear? • Power density – 1000 MW electric • 10 000 tons o f coal per DAY!! • 20 tons of uranium per YEAR (of which only 1 ton is U -235) A typical pellet of uranium weighs about 7 grams (0.24ounces). It can generate as much energy as…… 3.5 barrels of oil or…… 17,000 cubic feet of natural gas, or….. 1,780 pounds of coal. Why nuclear? • Why still use coal – Capital cost – Politics – Public perception of nuclear, nuclear waster issue What do you think is the biggest barrier to constructing the next U.S. nuclear power plant? 50% 40% 30% 20% 44% 10% 16% 15% 14% 0% 10% - 2008 survey of Political Nuclear Waste Cost of Fear of Other Resistance to Disposal Nuclear Nuclear energy professionals Nuclear Energy Issues Power Plant Accident Construction Image by MIT OpenCourseWare. “Eighty-two percent of Americans living in close proximity to nuclear power plants favor nuclear energy, and 71 percent are willing to see a new reactor built near them, according to a new public opinion survey of more than 1,100 adults nationwide.”– NEI, September 2007 Basic Principles ofof Nuclear Reactor • Simple device – Fissioning fuel releases energy in the “core” – Heat isis transported away by a coolant which couples the heat source to a Rankine steam cycle – Very similar to a coal plant, with the exception of the combustion process – Main complication arises from the spent fuel, a mix of over 300 fission products Public domain image from wikipedia. Electric Main Generator Turbine Discharge Main Condenser Large Body of Water (Ocean, Lake, etc.) Intake Circulating Water Pump • Power plants will often discharge their circulating water directly back to the Image by MIT OpenCourseWare. ocean – Strict environmental protttectiion regullations – Temperature increases by 55-10 Farenheits Electric Main Generator Turbine Cooling Tower Main Condenser Circulating Water Pump Image by MIT OpenCourseWare. • If far from a water source, cooling towers are used to transfer the heat to air. – Water vapor is visible aatt the contact of the warm wet air inside the tower with the cool dry air outside ReactorsonceptsC Concepts Fuel• Fuel Coolant• Coolant – Uranium – Light water – Plutonium – Heavyy water – Thorium – Sodium – Molten salt • Moderator (optional) – Helium –CO2 – Light water –LLdead-Bismuth – Heavy water –… – Graphite – Be MitiildMacroscopic to microscopic world Cutaway of PWR pressure vessel and Internals. Fission chain reaction Public domain image from wikipedia. Public domain image from wikipedia. Neutrons Moderator (Water) F u e l R Control Rod o d in s a reactor Image Reactor Vessel Wall byMITOpenCourseWare. Shield Wall Nomenclature--Isotopes A 12 235 Z XC such as 69 or 2U Z is the atomic number A is the atomic mass N = A-Z is the number of neutrons Nuclei with the same Z and different A are called isotopes. 235 238 E.g. 92UU and 92 123 11HH and and 1H NuclearStability Nuclear Stability • AsZZ increases, the long range Coulomb repulsion between protons is balanced Image removed due to copyright restrictions. by the presence of additional neutrons to provide additional short-range attractive nuclear forces. Distribution of Stable Nuclides A Z N # nuclides Even Even Even 159 OddEvenOdd53 Odd Odd Even 50 Even Odd Odd 4 266 Nuclear Collision Reactions a + b c + d a(b, c)d 1 235 236 0 nU+→92 92U + g 235 236 92Un(,g ) 92U Fundamental Laws • Conservation of nucleons – Total “A” remains the same • Conservation of charge – Total “Z” remains the same • Conservation of momentum • Conservation of Energy – Energy, including rest mass, is conserved Rest Mass E2 _ (pc)2 = (mc2)2 Mass is a characteristic of the total energy and momentum of an object or a system of objects that is the same in all frames of reference. 2 m0 = E/c The invariant mass of the system is equal to the total system energy divided by c2. This total energy in the center of momentum frame, is the minimum energy which the system may be observed to have. Special Relativity Mass m0 m = 2 1 _ ν /c2 A body’s mass increases when it is in motion with speed v relative to an observer at rest. Q - value Exothermic reaction produces energy Endothermic reaction requires energy An exothermic reaction is defined with Q < 0 therefore it is important to understand the concept: E = mc2 _ 2 Q = [(Ma + Mb) (Mc + Md)]c Q > 0 exothermic Q < 0 endothermic 2 2 2 2 Ea + Eb + Mac + Mb c = E c + Ed + M cc+ Md c Examples of Q-value Exothermic 9 4 _ 12 _ 2 Q = [M (4Be) + M (2He) M ( 6C) mn]c Q = [9.012182u + 4.002603u _ 12.000000u _ 1.008664u]931.5MeV/u Q = 5.702MeV 9 4 12 1 4Be + 2He 6C + 0n Examples of Q-value Endothermic 16 _ 13 _ 4 2 Q = [M ( 8O) + mn M ( 6C) M(2He)]c Q = [15.994915u + 1.008664u _ 13.003354u _ 4.002603u]931.5MeV/u Q = _2.215MeV 16 1 13 4 8O + 0n 6C + 2He Examples of Q-value 16 16 8O(n,p) 7N Assumption 16 16 2 Q ⎡m M O M N mp⎤ c = ⎣ n + ( 8 ) − ( 7 ) − ⎦ Why is this incorrect? 1n 16O 16N 0e 1 p 0 + 8 → 7 + −1 + 1 This is approximately equivalent to 1 16 16 1 0 n + 8 O → 7 N + 1 H Q ⎡m M 16O M 16 N M 1 Hc⎤ 2 = ⎣ n + ( 8 ) − ( 7 ) − ( 1 )⎦ Most important Reactions An Example 235 1 129 104 1 92U + 0n 53I + 39Y + 30n Nuclear fission (n, fission) 1nX+→A A1 XX++A2 neutrons + 200MeV 0 ZZ1 Z2 Radiative Capture An Example 238 1 239 * 239 0 92U + 0n ( 92U) 92U + 0γ Radiative capture (n, γ) * 11AA++A 1 g 0 nX+→Z ()Z XX→+Z Scattering Examples 12 1 12 1 elastic 6C + 0n 6C + 0n 240 1 240 1 240 0 1 inelastic ( 94Pu + 0n 94Pu)* + 0n 94Pu + 0β + 0n Scattering (n, n) or (n, n') 1 A 1 A 0 n + Z X ν 0 n + Z X elastic scattering (n,n) * 1 A 1 A 1 A γ 0 n + Z X ν 0 n + ( Z X ) ν 0 n + Z X + inelastic scattering (n,n') Beta decay When the weak interaction converts a neutron into a proton and emits an electron and an anti-neutrino, Beta (minus) decay occurs. This happens when an atom has an excess of neutrons. A 0 A _ Z Xe→+−+1 Z 1Y++u Energy _ 137 137 0 55Cs 56Ba + -1e + υ Positron Emission Positron emission cannot occur in isolation unlike Beta decay. This happens because it requires energy (the mass of the neutron is greater than the mass of the proton). Positron emission happens inside the nuclei when the absolute value of the binding energy of the mother nucleus is lower than that of the daughter nucleus. A A 0 ZX + Energy Z-1Y + 1e + υ 22 22 0 11Na 10Ne + 1e + υ Capture of Electron A 0 A ZX + -1e + Energy Z-1Y + u In cases where ß+ decay is allowed energetically, it is accompanied by the electron capture process. 22 0 22 u 11Na + -1e 10Ne + If the energy difference between initial and final states is low 2 (less than 2mec ), then b+ decay is not energetically possible and electron capture is the sole mode decay. Alpha Decay Coulomb repulsion increases ~ Z2 Alpha decay occures only in heavy atoms (A > 100 amu ) Alpha particle has small mass relative to parent nucleus and has very high binding energy Nuclear binding force increases ~ A A A-4 ZX a + Z-2Y + Energy 238 234 92U 90Th + a Gamma decay 60 Co 27 5.26 a 0.31 MeV β γ 1.17 MeV γ 1.33 MeV 60 Ni 28 Image by MIT OpenCourseWare. • Gamma decay is the emission of a gamma ray (photon) from a nucleus • Occurs when nucleus transitions from a higher to lower energy state • Energy of photon(s) equal to the change in energy of nuclear states • Nuclear structure does not change so parent and daughter are the same Predicting type of decay 90 α 80 70 60 Line of Stability 50 + or Electron Capture β 40 − β 30 Proton Number (Z) 20 10 0 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 Neutron (N) Image by MIT OpenCourseWare. Binding Energy D = ZMp + NMn - MX The weights of these constituent masses exceeds the weight of the nucleus if we add the masses of Z protons and N neutrons that make up a nucleus. The difference is the mass defect which is positive for all nuclides. Multiplying by c2 yields the binding energy of the nucleus. When the nucleus is formed, the loss in mass is due to the conversion of mass to binding energy. It is defined as the energy that is supplied to a nucleus to completely separate its nucleons. A measure of nuclear stability is obtained when the binding energy is normalized to the number of nucleons. Calculate mass defect and binding energy ffior uranium-235 Mass of neutron 11.
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