放射化学第4讲(放射性衰变)

选课名单*C.L.Liu 学号 姓名 学号 姓名 学号 姓名 610044 梅洁 710043 付赫 710103 孙佳俊 610045 赵明哲 710044 金文最 710112 杨阳 610053 赵文博 710046 殷昊霖 710113 巩昊 610065 程晓亮 710049 吴东锴 710118 陈焕发 610151 蔡李超 710050 王典 710121 王家锐 610180 光洁 710053 孙轶伦 710122 艾达尔·木合塔尔 710002 石莹 710056 相锟 710123 刘茜 710006 杨穗嘉 710058 王雨辰 710125 钟梦绮 710007 胡墨 710061 海洋 710126 徐瑶 710010 吕宏品 710062 邓先河 710129 张一苇 710011 张桐 710066 周昕 710132 冯鹏 710018 楼宇 710079 杨扬 710133 张伟 710019 汪韬 710082 高琛 710135 刘一帆 710021 李跃星 710084 李力一 710151 陈铖 710023 蔡元博 710086 蔡康 710152 李昆霖 710024 席雨濛 710088 陈戈敦 710153 信跃龙 710029 马开 710092 张欣亮 710158 史怡 710030 卓峻峭 710095 周凡 746099 李亚伟 710031 张行 710098 贺蓓 746129 叶萌 710032 马佳辰 710101 赵晓堃 710102 桑金钊 746172 杨博衍C.L.Liu*C.L.Liu一些核素和粒子的质量MassesofsomenuclidesadotherparticlesC.L.Liu*C.L.Liu复习与回顾 核衰变？特点？ 不稳定原子核自发地放出粒子或电磁辐射变成另一种原子核的过程称为核衰变 核衰变是放射性核素的特征核性质，一般情况下不受外界条件，诸如温度、压力、电磁场、化学形态、物理状态等的影响； 核衰变总是伴随着能量的释放（放热过程）C.L.Liu*C.L.Liu复习与回顾 核衰变的主要类型？Alphadecay(adecay)Betadecay(bdecay)(+,-,EC)Gammadecay(gdecay)SpontaneousfissionDelayedneutronandprotonemissionTwo-protondecayCompositeparticleemissionDoublebetadecayC.L.Liu*C.L.Liu复习与回顾 填空210Po()；()234Th；()231Th210Po()206Pb；238U()234Th；235U()231ThC.L.Liu*C.L.Liu复习与回顾 能谱与能谱区别？C.L.Liu*C.L.Liu复习与回顾 Augerelectrons(俄歇电子)？K俘获过程的另一种伴随粒子是俄歇电子：当一个L层电子跳到K层来填充空位时，可以不发射X射线，而把能量交给另一个L电子，于是这个L电子就会克服结合能而飞出。这种电子叫俄歇电子。C.L.Liu*C.L.Liu复习与回顾 GammaDecay？ Indecay,electromagneticradiationisemittedasanucleusundergoestransitionsfromitshigherexcitedstate(s*)tolowerexcitedstate(s1*),oritsgroundstate(sg)C.L.Liu放射性衰变RadioactiveDecayC.L.Liu*C.L.Liu习题45C.L.Liu*C.L.Liu67习题C.L.Liu*C.L.Liu第四讲：放射性衰变 放射性衰变的基本规律衰变常数（）半衰期（t1/2)平均寿命()活度（A)比活度（As) 放射性平衡长期平衡暂时平衡不成平衡C.L.Liu*C.L.LiuRadioactiveDecayC.L.Liu*C.L.LiuRadioactiveDecayC.L.Liu*C.L.LiuLawofRadioactiveDecay ThelawofradioactivedecaydescribesthekineticsofthereactionC.L.Liu*C.L.LiuLawofRadioactiveDecay:decayconstant(衰变常数） Time(t) numberofatomsofacertainradionuclide 0 N0 t N tt+dt -dN/dtN-dN=NdtC.L.Liu*C.L.LiuThedecayconstant（衰变常数）:单位时间内大量原子核的自发衰变率，单个原子核在单位时间内的自发衰变几率在一般情况下，衰变常数与外界条件（诸如温度、压力、外部电磁场等）无关，C.L.Liu*C.L.LiuLawofRadioactiveDecay Half-life(t1/2,半衰期):thetimeneededforhalfofastatisticallylargenumberofradioactiveatomsinasampletodecay.C.L.Liu*C.L.LiuTheaveragelifetime（平均寿命） Averagelife(t,平均寿命):theaveragetimeneededforanatomtodecay; ThetimespendforanumberofradioactiveatomsthathasbeendecreasedfromN0toN0/eC.L.Liu*C.L.LiuUnitsofRadioactiveDecay（活度） Theexpressionsofactivityarealwaysbasedonthedisappearanceoftheparent,ratherthanontheappearanceofaproduct. 单位时间内母体衰变掉多少的量度，decays/s(dps) TheSIunitofradioactivity(放射性活度)isthebecquerel(Bq,贝克).Itisequalto1dps. Anolderactivityunitthatisstillwidelyusedisthecurie(Ci，居里).Thecurieisdefinedtobeexactly3.71010dps(themeasuredactivityof1gof226Ra).C.L.Liu*C.L.LiuConceptsoftherelativelevelsofactivitydesignatedbytheCurieunit CurieLevel(居里级)，radioactivesamplespossessingactivityattheCilevelareconsideredtobevery“hot”;thatis,highlyradioactive. MillicurieLevel(毫居级)，AfairlycommonworkinglevelofradioactivityfortracerstudieswouldbeatmCilevel(3.7x107dps). MicrocurieLevel(微居级)，atthe1.0-mCilevel(3.7x104dps)exposureriskstopersonnelareconsideredtobeminimalformostcommonlyusedradioactivetracers.Heavymetala-particleemitterssuchasplutonium(Pu)areanexception.C.L.Liu*C.L.Liu放射性活度和比活度C.L.Liu*C.L.Liu放射性活度和比活度（As) A=λN，dps,dpm,Ci, As=A/m As的单位固体样品：kBq/g;MBq/g;mCi/g;Ci/g液体样品：kBq/g;MBq/g;mCi/g;Ci/g液体（气体）样品：kBq/dm3;mCi/dm3.C.L.Liu*C.L.Liu放射性活度与质量的关系C.L.Liu*C.L.Liu放射性活度与质量的关系1mCi的短寿命放射性核素的质量是很小的，而1mCi长寿命放射性核素的质量是可观的。32P(t1/2=14.282d),1mCi3.510-9g;238U(t1/2=4.4681010a),1mCi3kgC.L.Liu*C.L.LiuExamples Example:99mTc是核医学中常用的放射性核素。其衰变的半衰期是6.01小时。衰变常数为0.115小时-1。计算经过多长时间注射到病人体内的放射性活度减少为开始注射时的0.1%？随堂作业A/A0=0.1%=0.001，0.001=e-(0.115/h)(t)ln(0.001)=-(0.115/h)t，t=60.1hC.L.Liu*C.L.Liu长期平衡暂时平衡不成平衡放射性平衡C.L.Liu*C.L.LiuRadioactiveEquilibriums Aparentwillproduceoneormoreradioactivedaughters,whichwillthemselvesdecayintostableoractive“granddaughters.” Aparentradionuclidewithonlyoneradioactivedaughter; Aparentradionuclideproducingmultipleradioactivedaughters.C.L.Liu*C.L.Liu衰变规律C.L.Liu*C.L.LiuC.L.Liu*C.L.Liu t1/2(1)>>t1/2(2) (SecularRadioactiveEquilibrium) t1/2(1)>t1/2(2) (TransientRadioactiveEquilibrium) t1/2(1)<t1/2(2)(non-equilibrium)C.L.Liu*C.L.LiuSecularRadioactiveEquilibrium(长期平衡）A1A2C.L.Liu*C.L.Liu Thehalf-lifeoftheparentisatleast10timesgreaterthanthatofthedaughterandthereisessentiallynochangeintheactivityoftheparentduringtheexperimentalobservation. Fordecaytimesthatarelongwithrespecttothehalf-lifeofthedaughter;5timesthehalflife Inaddition,thedecayconstantofthelong-livedparentwillbeverysmallcomparedtothatofthedaughter.SecularRadioactiveEquilibriumC.L.Liu*C.L.LiuSecularRadioactiveEquilibriumC.L.Liu*C.L.LiuPracticalApplicationsofS.R.E.C.L.Liu*C.L.LiuPracticalApplicationsofS.R.E. Determinationofthelonghalf-lifeofamothernuclidebymeasuringthemassratioofdaughterandmothernuclide; CalculationofmassratiosofradionuclidesthatareinSRE; Calculationofthemassofamothernuclidefromthemeasuredactivityofadaughternuclide. Theradioactivedaughtersource.C.L.Liu*C.L.LiuTransientEquilibrium Thehalf-lifeoftheparentisapproximately3-10timeslongerthanthatofthedaughter,butisshortenoughsothereisameasurabledecayoftheparentduringtheexperiment. After3-5half-livesofthedaughternuclide,theterme-l2twillbecomeverysmallandcanbeignored.C.L.Liu*C.L.LiuTransientEquilibrium(暂时平衡）C.L.Liu*C.L.LiuC.L.Liu*C.L.LiuHalf-lifeofMotherNuclideshorterthanHalf-lifeofDaughterNuclideC.L.Liu*C.L.Liu218Po218Po()214Pb(-)C.L.Liu*C.L.LiuThechangeoftotalactivitywithdifferent1/2.C.L.Liu*C.L.LiuSimilarHalf-livesC.L.Liu*C.L.LiuParentwithMultipleRadioactivedaughters Therearemanyradionuclidesthatdecaytoproduceasequenceofradioactivedaughters.C.L.Liu*C.L.Liu多子体衰变ParentwithMultipleRadioactivedaughtersWhent=0N1(0)=N1，0N2(0)=N3(0)=N4(0)=0 Batemanequation Twoassumptions: Onlytheparentispresentatt=0; Notwodecayconstantsinthechainareequal.C.L.Liu*C.L.LiuParentwithMultipleRadioactivedaughtersC.L.Liu*C.L.LiuParentwithMultipleRadioactivedaughtersC.L.Liu*C.L.LiuParentwithMultipleRadioactivedaughtersExample:Asampleof222Rnhasanactivityof1.00Ci.Calculatetheactivityofthedaughternuclide214Pbafter1.00h.ThedecayisC.L.Liu*C.L.LiuThenumberofatomsoftheparentnuclide,222Rn,isC.L.Liu*C.L.LiuC.L.Liu*C.L.Liu四个天然衰变系C.L.Liu*C.L.LiuDecaySeries Thoriumdecayseries(thoriumfamily):A=4n; Uranium-radiumseries(uraniumfamily):A=4n+2; Actiniumdecayseries(actiniumfamily):A=4n+3;C.L.Liu*C.L.Liu铀系：4n+2C.L.Liu*C.L.Liu铀系（4n+2) 8次衰变，6次-衰变； 238U与234U达到平衡的时间：7t1/2(234U)1.9106a; 比较重要的子体：226Ra,210Po(用于制备中子源）； 226Ra及其子体的射线用于治疗癌症； 222Rn是唯一的气体。C.L.Liu*C.L.Liu锕系：4n+3C.L.Liu*C.L.Liu锕系：4n+3 8次衰变，4次-衰变； 235U与231Pa达到平衡的时间：7t1/2(231Pa)2.3105a; C.L.Liu*C.L.Liu钍系：4nC.L.Liu*C.L.Liu镎系：4n+1C.L.Liu*C.L.Liu镎系：4n+1 自然界中存在4n、4n+2、4n+3,3个放射系，缺少4n+1放射系。 4n+1放射系是用人工方法得到的； 在该衰变链中，237Np的寿命最长，其他核素都衰变完了，只剩下237Np； 除209Bi外，其他子体在自然界中的存量很小，因此长时间未被发现。C.L.Liu*C.L.LiuBranchingDecay(分支衰变) Theparentnuclide(A)decaysbytwo(orpossiblymore)separateddecaymodes(lB,lC,…). Eachdecaybranchisindependentoftheother,andwillhaveitsowncharacteristichalf-lifeanddecayconstant.Thesearecalledpartialdecayconstant. TotalactivityofAisequaltothesumoftheactivityofeachbranch.Theoveralldecayconstantisthesumoftheindividualdecayconstant.C.L.Liu*C.L.LiuExperimentalMethodsforDeterminationofHalf-Life t1/2,animportantcharacteristicofanuclide; t1/2,averylargerange<10-18sto>1022years; Nosingletechniqueissufficienttomeasureallofthem.Dividedthemintofourgroups: Long(severalyearsandup); Medium(secondstoafewyears); Short(secondstomilliseconds); Veryshort(lessthanmilliseconds).C.L.Liu*C.L.LiuSpecificactivitymethod Itisimpossibletomonitorthechangeofactivityovertime Aquantitythatcanbedirectlydeterminedandrelatedtohalf-lifeisthespecificactivity(As,比活度)ofthesubstance.TheAsistheactivityperunitmass:C.L.Liu*C.L.LiuSpecificactivitymethod Todeterminethehalf-life,weneedonlymeasuretheabsoluteactivity(绝对活度)ofthesampleanditsmass.C.L.Liu*C.L.LiuSpecificactivitymethod 4pcountersC.L.Liu*C.L.LiuMediumHalf-lives Simpledecaycurvemethod TheSimpledecaycurvemethodgivesbestresultsifapureradionuclidesourceisused. Chemicalseparation; Countonlythedesiredactivity; Useabsorbers;C.L.Liu*C.L.Liu Mixtureoftworadionuclides Theactivityofmixturemeasuredandplotted,asdoneinsingleradionuclide; Resolvedintotwocomponents;C.L.Liu*C.L.LiuTheendofChapter4C.L.Liu*C.L.LiuC.L.Liu*C.L.LiuAtomicbombC.L.Liu*C.L.Liu简单推导C.L.Liu