Chapter 1Chapter 1 - MIT OpenCourseWare

Chapter 1

Learning Objectives Historical Recap Understand the different length scales ofnuclear physics Know the nomenclature for isotopes andnuclear reactions Know the different types of neutronnuclear collisions and their relationship toeach other Basic principles of nuclear reactor

Learning Objectives Neutron SourcesBasic Principles of Nuclear ReactorBindingg energygy curveLiquid drop modelFission ReactionODE ReviewRadioactive DecayDecay ChainsChart of Nuclides

Historical Recap Driscoll handout New programs– GNEP/AFCI– Gen-IV– Nuclear Power 2010

Why nuclear? Power density– 1000 MW electric 10 000 ttons off coall per DAY!! 20 tons of uranium per YEAR (of which only 1 tonis UU-235)235)A typical pellet of uranium weighsabout 7 grams (0.24ounces). It cangenerate 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 nuclearnuclear, nuclear wasterissue50%What do you think is the biggest barrier to constructing thenext U.S. nuclear power plant?40%Nuclear WastePoliticalDisposalResistance toIssuesNuclear EnergyCost ofNuclearPower PlantConstructionFear age by MIT OpenCourseWare.- 2008 surveyy ofenergy professionals

“Eighty-twoEighty two percent of Americans living inclose proximity to nuclear power plantsfavor nuclear energyenergy, and 71 percent arewilling to see a new reactor built nearthem, according to a new public opinionthemsurvey of more than 1,100 adultsnationwide.nationwide ” – NEI,NEI September 2007

Basic Principles of Nuclear Reactor Simple device– Fissioning fuel releases energy in the “core”– Heat is transported away by a coolant whichcouples the heat source to a Rankine steamcycle– Very similar to a coal plant, with the exceptionof the combustion process– Main complication arises from the spent fuel,a mix of over 300 fission products

Public domain image from wikipedia.

MainTurbineElectricGeneratorDischargeMain CondenserLarge Body of Water(Ocean, Lake, etc.)IntakeCirculatingWater Pump Power plants will oftenoftendischarge their circulatingwater directly back to theocean– Strict environmentalprottectition regullatitions– Temperature increases by5-1010 FarenheitsImage by MIT OpenCourseWare.

serCirculatingWater PumpImage by MIT OpenCourseWare. If far from a water source,cooliling towers are usedd totransfer the heat to air.– Water vapor is visible at thecontact of the warm wet airinside the tower with the cooldry air outside

Reactors Concepts Fuel– Uranium– Plutonium– Thorium Moderator (optional)––––Light waterHeavy waterGraphiteBe Coolant––––––––Light waterHeavyy waterSodiumMolten saltHeliumCO2Lead-Bid Bismuthth

MMacroscopici tto microscopicii worldldCutaway of PWR pressure vessel andInternals.Fission chain reactionPublic domain image from wikipedia.Public domain image from wikipedia.

Shield WallReactor Vessel WallControl RodModerator (Water)Neutrons in a reactorFuel RodsImage by MIT OpenCourseWare.

Nomenclature IsotopesNomenclature--IsotopesAZ126X such as C or23592Z is the atomic numberA is the atomic massN A-Z is the number of neutronsNuclei with the same Z and different Aare called isotopes.238UandE.g. 23592 U9211H and 12 H and 13 HU

Nuclear StabilityImage removed due to copyright restrictions. As Z increases, thelong range Coulombrepulsion betweenprotons is balancedby the presence ofadditidditionall neuttrons toprovide additionalshort--range attractiveshortnuclear forces.

Distribution of Stable NuclidesAZN# nOddOdd4266

Nuclear Collision Reactionsa b10c dn 23592U 23592a(b, c)d23692U g23692U (n, g ) U

Fundamental Laws Conservation of nucleons– Total “A” remains the same Conservation of charge– Total “Z” remains the same Conservation of momentumgy Conservation of Energy– Energy, including rest mass, is conserved

Rest Mass22 2E (pc) (mc )2Mass is a characteristic of the total energy and momentum of an object or a systemof objects that is the same in all frames of reference.2m0 E/cThe 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 whichthe system may be observed to have.

Special Relativity Massm m02ν1/c2A body’s mass increases when it is in motion with speed vrelative to an observer at rest.

Q - valueExothermic reaction produces energyEndothermic reaction requires energyAn exothermic reaction is defined with Q 0 therefore it isimportant to understand the concept:E mc2Q [(Ma Mb) (Mc Md)]c2Q 0 exothermicQ 0 endothermicEa Eb Mac2 Mbc2 Ec Ed Mcc2 Md c2

Examples of Q-valueExothermic(Be) M(He)M(C)mn]c2Q [MQ [9.012182u 4.002603u 12.000000u1.008664u]931.5MeV/u9442126Q 5.702MeV9Be4 4He212C6 1n0

Examples of Q-valueEndothermic13Q [M ( O) mn M ( 6C) M(42He)]c2168Q [15.994915u 1.008664u 13.003354u4.002603u]931.5MeV/uQ 2.215MeV168O 1n013C6 4He2

Examples of Q-value16168O(n,p) 7NAssumptionQ mn M ( 168O ) M ( 167 N ) mp c 2Why is this incorrect?10n 168 O 167 N 10 e 11 pThis is approximately equivalent to10n O N H16816711Q mn M ( 168 O ) M ( 167 N ) M ( 11H ) c 2

Most important ReactionsAn Example235U92 10n12953I1n 104Y 3390Nuclear fission (n, fission)10n ZA X A1Z1X ZA22 X neutrons 200MeV

Radiative CaptureAn Example23892U 10n239( 92U)*Radiative capture (n, γ)10n X (AZA 1Z23992UX) *A 1Z 00γX g

ScatteringExampleselastic 126C 10n1inelastic ( 240Pu 940n121C 60n2401Pu)* 940n24001Pu β 9400nScattering (n, n) or (n, n')1010AZ10AZ10AZn X ν n Xelastic scattering (n,n)n X ν n ( X ) ν 01n ZA X γAZ*inelastic scattering (n,n')

Beta decayWhen the weak interaction converts a neutron intoa proton and emits an electron and an anti-neutrino,Beta (minus) decay occurs. This happens when anatom has an excess of neutrons.AZ0 1X e Cs13755AZ 1Y u Energy137056Ba -1e υ

Positron EmissionPositron emission cannot occur in isolation unlike Beta decay.This happens because it requires energy (the mass of the neutronis greater than the mass of the proton).Positron emission happens inside the nuclei when the absolutevalue of the binding energy of the mother nucleus is lower thanthat of the daughter nucleus.AZX Energy2211Na2210AZ-1Y01 01eNe e υ υ

Capture of ElectronAZX 0-1e EnergyAZ-1Y uIn cases where ß decay is allowed energetically, it is accompaniedby the electron capture process.22Na11 0-1e2210Ne uIf the energy difference between initial and final states is low(less than 2mec2), then b decay is not energetically possible andelectron capture is the sole mode decay.

Alpha DecayCoulomb repulsion increases Z2Alpha decay occures only in heavy atoms (A 100 amu )Alpha particle has small mass relative to parent nucleus andhas very high binding energyNuclear binding force increases AAZXa 23892UA-4Z-2Y Energy23490Th a

Gamma decay60Co27eV β1.17 MeV γ0.31 M1.33 MeV γ5.26 aNi6028Image by MIT OpenCourseWare. Gamma decay is the emission of a gamma ray (photon) from anucleus 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 thesame

Predicting type of decay90α80Proton Number (Z)7060ure50 β40ornroectElptCaLine of Stabilityβ 30201000102030405060708090100 110 120 130 140Neutron (N)Image by MIT OpenCourseWare.

Binding EnergyD ZMp NMn - MXThe weights of these constituent masses exceeds the weight of the nucleusif 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. Multiplyingby c2 yields the binding energy of the nucleus.When the nucleus is formed, the loss in mass is due to the conversion of massto binding energy. It is defined as the energy that is supplied to a nucleus tocompletely separate its nucleons.A measure of nuclear stability is obtained when the binding energy is normalizedto the number of nucleons.

Calculate mass defect and bindingf uranium-235i23energy forMass of neutron 11.008665008665 amuMass of proton 1.007826 amuMassoff one atomoff UU-235235.043924Mt235 235043924Binding energy mass defect x c2

Mass defect 11.9151791517 amu BE 11.91517931.5MeV91517 amu x 9315MV / 1 amu BE 1784 MeV1 amu 1.660541 66054 x 10-27kg 931.5931 5 MeV / c2

Binding Energy Curve Exothermic reactionsresult in reactionproducts with higherbinding energyti TTwo options– Fission of heavynuclides– Fusion of lightnuclides

First-OrderFirstOrder ODE - Review Appendix A of Lewis Handout

Radioactive Decay LewisLewis, Section 11.77

Decay chain(a) λB 5 x λA; t1 5 x t12Normalized activity1A20.750.50.250012t34(b) λB λA /5; t1 t1 /52A2(c) λB λA; t1 t1B0.750.50.250012t321Normalized activityNormalized activity1B4A2B0.750.50.250012t34AA (t)/AA (0)AB (t)/AA (0)Image by MIT OpenCourseWare.

Decay ChainsDefinition of Decay Chain: The radioactive decay of different discreteradioactive decay products as a chained series of transformations.Decay ChainsThorium series or 4nNeptunium series or 4n 1Uranium or Radium series 4n 2Actinium series or 4n 3

Chart of Nuclides3Hein t outβ outp ind inn outOriginalNucleusn ind outp outβ out α int inα, 3np, nγ, nn, 2nHeoutHe, nα, np, γd, n3He, npa, npt, n3He, pd, pTargetNucleus n, γt, npγ, npγ, pn, αn, He3α outα, 2n3t, pn, p3Image by MIT OpenCourseWare.

Chart of Nuclides Gray shaded square (stable nuclide)Symbol, mass numberPd 108Percent abundance26.71Activation cross-section in"bars" to two isomersMass (C-12 scale)σ (0.2 12)107.9030Fission product, slowneutron fission of U-235Image by MIT OpenCourseWare. White or "color" square: ( ArtificiallyProduced Radioactive Nuclide))Symbol, mass numberHalf lifeModes of decay, radiation,and energy in MeV. ( ) meansradiation from short-liveddaughter.Disintegration energy in MeV.Fe 52Fe852hB 0.80, (263), εγ 0.17, 380, (1.43)E 2.38Image by MIT OpenCourseWare.

Chart of Nuclides Black rectangles across the top of square– On gray-shaded square: Radioactive nuclide withlong half life (Considered Stable)SymbolCe 14211.07Half lifeThermal neutronabsorption cross-sectionin barnsPercent abundance5x1015yrsα, 1.5Modes of decayσ1141.9090MassImage by MIT OpenCourseWare.– On white square: Radioactive nuclide found innature with relatively short half life

Chart of Nuclides Smaller black rectangleg near topp of squareq((Nuclide is amember of a natural radioactive decay chain)Po 218SymbolRa AModes of decayand energiesα 6.00β3.05m218.0089Symbol, massnumberHalf lifeMassImage by MIT OpenCourseWare. Black triangle at bottom corner of square (nuclide isformed byy fission of U-235 or Pu-239))Pd 108Percent abundance26.71σ (0.2 12)Mass (C-12 scale)Symbol, massnumber107.9030Activation cross-sectionin "bars" to two isomersFission product, slowneutron fission of U-235Image by MIT OpenCourseWare.

Chart of Nuclides Verticallyy divided squareq– Two isomeric states, one stableSn 117SymbolPercent abundance7.61Half lifeModes of decayradiation, andenergies in Mev14 dIT 0.159γ 0.161e-Mass116.9031Radioactive upper isomer Stable lower isomerImage by MIT OpenCourseWare.– Two isomeric states, both radioactivePm 145Symbol? 16dβ 0.45Radioactiveupper isomerHalf life, ?means uncertainty18yε ,eγ 0.068, 0.073E 0.14Modes of decayradiation, andenergies in MevDisintegrationenergy in MevStable lower isomerImage by MIT OpenCourseWare.

Neutron SourcesDefinition of Spontaneous FissionSpontaneous fission (SF) is a form of radioactive decay characteristic forvery heavy isotopes. In practice, only energetically feasible for atomicmasses above 230 amu. It is theoretically possible for any atomic nucleuswith mass 100 amu.Radioisotopes for which spontaneous fission is a nonnegligibledecay mode may be used as neutron sources notably Cf-252(half-life 2.645 years, SF branch ratio 3.09%)

Intensity (ARB. UNITS)10210110012345Neutron energy (MeV)Measured neutron energy spectrum from the spontaneous fission of252Cf.Image by MIT OpenCourseWare.