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1、第三章 放射性核素的衰变规律,Radioactive decay,目的,熟悉各种衰变的特点掌握衰变规律与活度计算了解放射性平衡及放射系,内容,衰变衰变衰变衰变规律放射性平衡放射系,引言,放射性的发现：贝可勒尔与居里夫妇放射线的分类及本质放射性与放射性核素的概念自发的含义核衰变的概念与分类各种放射性核素通过衰变趋向稳定线对各类衰变，要求熟悉其含义、方程、对象、能量和纲图,Henri Becquerel,18521908,FranceFrench physicist who discovered radioactivity through his investigations of uranium
2、 and other substances.In 1903 he shared the Nobel Prize for Physics with Pierre and Marie Curie,Marie Curie,born Nov.7,1867,Warsaw,Poland,Russian Empiredied July 4,1934,near Sallanches,FrancePolish-born French physicist famous for her work on radioactivity and twice a winner of the Nobel Prize.With
3、Henri Becquerel and her husband,Pierre Curie,she was awarded the 1903 Nobel Prize for Physics.She was then sole winner of the 1911 Nobel Prize for Chemistry.She was the first woman to win a Nobel Prize,Pierre Curie,born May 15,1859,Paris,Francedied April 19,1906,ParisFrench physical chemist and cowi
4、nner of the Nobel Prize for Physics in 1903.He and his wife,Marie Curie,discovered radium and polonium in their investigation of radioactivity.,放射线的分类及本质,放射性(radioactivity),原子核自发放出、等粒子的性质the spontaneous disintegration of atomic nuclei,with the emission of usu.penetrating radiation or particles(Oxfor
5、d)property exhibited by certain types of matter of emitting energy and subatomic particles spontaneously.It is,in essence,an attribute of individual atomic nuclei.(EB)Note:a major source of heat in the interior of both the Earth and the Moon is provided by radioactive decay.(EB),放射性核素(radionuclide),
6、具有放射性的核素a radioactive nuclide(Oxford)a radioactive nuclide(Merriam-Webster)radioactive isotope(radioisotope):any of several species of the same chemical element with different masses whose nuclei are unstable and dissipate excess energy by spontaneously emitting radiation in the form of alpha,beta,a
7、nd gamma rays(EB),（核，放射性）衰变(decay,disintegration),原子核自发放出、等粒子的过程(of a substance etc.)undergo change by radioactivity(Oxford)any process in which a nucleus emits a particle or particles or divides into smaller nuclei(Oxford)原子核自发的结构或能量转变过程,衰变,Alpha decay,衰变的定义,放射性原子核自发放出粒子而变为另一种原子核的过程type of radioact
8、ive disintegration in which some unstable atomic nuclei dissipate excess energy by spontaneously ejecting an alpha particle 粒子的实质：高速运动的氦原子核,衰变的方程,或：例：注：衰变过程满足质量数守恒、电荷守恒、能量守恒以及动量守恒,衰变的衰变能和衰变条件,衰变能：衰变条件：即：只有比较重(A140)的原子核才可能发生衰变,衰变的对象,丰质子的核素,衰变的动能分配,粒子的动能远大于子核的反冲动能 或：衰变能绝大部分被粒子带走原子核的基态与激发态粒子的能谱是分立的线状谱短
9、射程粒子与长射程粒子,讨论和提问,（13分钟）,衰变的纲图(decay scheme),一个问题,从Ra-226的衰变纲图看，只有和粒子的发射，为何在发自镭源的射线（图3-1）中显示有粒子的发射？,衰变,beta decay,衰变的定义,-衰变、+衰变和电子俘获(EC)的统称同量异位跃迁(isobaric transition)any of three processes of radioactive disintegration by which some unstable atomic nuclei spontaneously dissipate excess energy and und
10、ergo a change of one unit of positive charge without any change in mass number.The three processes are electron emission,positron(positive electron)emission,and electron capture.,-衰变(negative beta decay),放射性原子核自发放出-粒子，变为原子序数加1而质量数相同的核素的过程-粒子的实质：高速运动的电子,-粒子能谱之谜,-粒子能谱之谜,-粒子能谱是连续谱泡利中微子假说费米弱相互作用理论,-衰变的方
11、程,例：实质：,-衰变的衰变能和衰变条件,衰变能：衰变条件：即：当母核的原子质量大于子核的原子质量时才能发生-衰变,-衰变的对象,丰中子的核素:3H,14C,-衰变能的分配,绝大部分衰变能被-粒子和反中微子带走，子核带走的反冲动能微不足道-粒子的最大能量(Em)等于衰变能-粒子的平均能量约为衰变能的1/3，而反中微子的平均能量约为衰变能的2/3,-衰变的纲图,讨论和提问,（13分钟）,+衰变,放射性原子核自发放出+粒子，变为原子序数减1而质量数相同的核素的过程+粒子的实质：高速运动的正电子发生+衰变的核素基本是人工放射性核素,+衰变的方程,例：实质：,+衰变的衰变能和衰变条件,衰变能：衰变条件
12、：即：只有母核与子核的原子质量之差大于两个电子的静止质量才可能发生+衰变,+衰变的对象,丰质子的核素:11C,15O,+衰变的能量,+粒子的能谱与-粒子的能谱相似,+衰变的纲图,+粒子的命运,正电子湮没(annihilation)当+粒子的能量耗尽时，旋即与物质中的电子结合而转化为电磁辐射的过程湮没辐射(annihilation radiation)正电子湮没时产生的电磁辐射：能量均为0.511MeV，反向发射的两个光子,讨论和提问,（13分钟）,电子俘获,原子核俘获轨道电子的衰变过程K俘获 原子核俘获K层电子的衰变过程注：俘获K层电子比俘获其他壳层电子的概率都大,电子俘获的方程,例：实质：,
13、电子俘获的条件,即：只有母核与子核的原子质量之差大于壳层电子的结合能（相应的质量）才能发生电子俘获从能量条件看，能发生+衰变的，也能发生电子俘获，反之则不尽然,电子俘获的对象,丰质子的核素,电子俘获的能量,子核与中微子的能量都是单一的（杨福家引述王淦昌探测中微子的思想）7Li的反冲能为56eV（7Be的衰变能等于0.86MeV）,电子俘获的继发过程,子核的原子伴随特征X射线或俄歇电子的发射特征X射线或俄歇电子的能量都是单一的间接证实电子俘获存在的方法或途径：观察原子特征X射线或俄歇电子的发射,电子俘获的衰变纲图,衰变小结,衰变都是同量异位素之间的跃迁衰变包括-衰变、+衰变和电子俘获(EC)发生
14、-衰变的是丰中子的核素，而发生+衰变和电子俘获(EC)的是丰质子的核素有些放射性核素能同时发生三种衰变,能同时发生三种衰变的放射性核素,讨论和提问,（13分钟）,衰变,Gamma decay,Gamma decay,type of radioactivity in which some unstable atomic nuclei dissipate excess energy by a spontaneous electromagnetic process In the most common form of gamma decay,known as gamma emission,gamma
15、 rays(photons,or packets of electromagnetic energy,of extremely short wavelength)are radiatedGamma decay also includes two other electromagnetic processes,internal conversion and internal pair production,发射(gamma emission),放射性原子核自发放出粒子的过程粒子的本质：光子，电磁波或电磁辐射,发射的方程,例：,内转换(internal conversion,IC),激发态原子核将
16、多余的能量直接传给核外电子，使其脱离核的束缚而成为自由电子的过程被发射的核外电子称为内转换电子Note:No neutrinos are involved in internal conversion(Nuclear Radiation Physics),内转换电子的能量,内转换电子的能量是单一的，分立的，不连续的内转换电子的能谱是线状谱,内转换能谱,内转换的继发过程,与电子俘获(EC)一样，内转换(IC)也会继发特征X射线或俄歇电子,内转换系数,发生衰变时，发射内转换电子与光子的概率之比（内转换电子数与光子数之比）一般说来，重核低激发态的跃迁，发生内转换的概率较大,电子对内转换(intern
17、al pair production),激发态原子核直接发射一对正、负电子而回到基态的过程正、负电子的动能之和条件：激发能大于1.02MeV,其他放射性,自发裂变(spontaneous fission,SF)重原子核自发分裂成两个较轻的核，并同时释放2到3个中子的过程Most of the heavy atoms having an uneven number of neutrons are fissionable and are also radioactive(Radiation and Health),讨论和提问,（13分钟）,衰变规律,Decay law,放射性核素的衰变规律,单一核
18、素的衰变规律递次衰变规律,单一核素的衰变规律,指数衰减规律衰变常量半衰期平均寿命放射性活度多分支衰变情形生物半排期和有效半衰期比活度与放射性浓度,单一核素的衰变规律,指数衰减规律,实验表明，任何放射性物质在单独存在时都服从这样的规律式中的是一个常量，称为衰变常量,衰变常量(decay constant),物理意义：单位时间内每个原子核的衰变概率,半衰期(half-life),放射性原子核的数目衰减至原来一半所需的时间,平均寿命(mean lifetime),放射性原子核的平均生存时间,放射性核素的特征量,衰变常量、半衰期T1/2和平均寿命，都可以作为放射性核素的特征量大量实验表明，衰变常量几乎
19、与外界条件（温度、压力、磁场等）没有任何关系,放射性活度(activity),放射源在单位时间内发生衰变的原子核数，或放射性核素的衰变率,放射性活度的单位,国际制单位：贝可(Bq)1 Bq=1 s-1 表示每秒钟有一次核衰变惯用单位：居里(Ci)1 Ci=3.71010 Bq常用单位：kBq,MBq,GBq;mCi,Ci,放射性活度的计算（1）,1g Ra-226(1602a)的活度（以Bq为单位）1Bq C-14(5730y)的原子数和质量,讨论和提问,（13分钟）,Exercise:Carbon-14 dating,Some archeologists found a piece of w
20、ood which they assumed could be from a Viking ship.In order to find out more about this hypothesis they decided to determine the age of the piece of wood by C-14 analysis.All living organic materials contain C-14 at a concentration of 15.4 dpm per gram of pure carbon.The piece found by the archeolog
21、ists weighed 2 gram.The activity was 11.8 dpm.The carbon content of the wood was 44%.How old was the piece of wood?,Exercise:Cesium from Chernobyl,The most important isotope released in the Chernobyl accident was Cs-137,with a half-life of 30 years.The amount released in the accident was given as 85
22、,000 TBq.What is the weight of the Cs-137 released in the accident?,Exercise:A scenario with pollution by isotopes,In a research laboratory,work is going on with the radioactive isotope Na-24.One day an accident occurred resulting in contamination of the laboratory.The radiation authorities found th
23、at the activity was 100 times that acceptable.They decided to close the laboratory until the activity reached an acceptable level.Na-24 has a half-life of 15 hours.For how long a time must the laboratory be closed?,多分支衰变情形,总衰变常量部分放射性活度 注意：部分放射性活度随时间按 而非 衰减总放射性活度,生物半排期和有效半衰期,生物半排期(biological half lif
24、e,Tb)生物体内的放射性核素经各种代谢途径从体内排出一半所需的时间有效半衰期(effective half life,Te)生物体内的放射性核素经物理衰变和生物代谢二者共同作用，使体内放射性减少一半所需的时间,生物半排期和有效半衰期,Exercise:Biological half-life for K-40 in humans,The largest natural contribution to internal radiation dose is due to K-40.The level of K-40 is rather constant even though it varies
25、 with age and sex.In this exercise,we assume that the total body contains a constant level of 5000 Bq(about 70 Bq/kg).Furthermore,we assume that the daily consumption of potassium is approximately 2.5 gram.Since 0.0118%of the potassium consists of the radioactive isotope K-40,you can calculate that
26、each day you eat about 76 Bq of K-40.1.Carry out this calculation.2.Calculate the biological half-life for K-40 if you eat 76 Bq per day and the level in your body is constant at 5,000 Bq.Physical half-life for K-40 is 1.27 billion years.,比活度与放射性浓度,比活度(specific activity)单位质量放射源的放射性活度 注：本征比活度放射性浓度 单位
27、体积放射源的放射性活度放射性活度与放射性强度,讨论和提问,（13分钟）,递次衰变规律,递次衰变母核的衰变规律第一代子核的衰变规律贝特曼公式,递次衰变(serial decay),一代接一代的连续衰变过程，即例如：,母核的衰变规律,母核的数目随时间的变化规律有：母核的活度：,第一代子核的衰变规律,第一代子核的数目随时间的变化规律有：第一代子核的活度：,贝特曼公式,第n代子核的数目随时间的变化规律有：式中：,放射性平衡,Radioactive equilibrium,放射性平衡,研究对象：（第一代）子核与母核的数目及活度关系长期平衡暂时平衡不成平衡,长期平衡(secular equilibrium
28、),条件：结果：例如：68Ge(280d)68Ga(68m)对递次衰变系列(T1Ti,i=2,3,)，有：,长期平衡,讨论和提问,（13分钟）,暂时平衡(transient equilibrium),条件：结果：例如：99Mo(66.0h)99mTc(6.0h),暂时平衡,子体的极值问题,子体的活度达到最大值的时间,不成平衡,条件：结果：例如：“冷却”反应堆裂变产物,不成平衡,子体的极值问题,子体的活度达到最大值的时间,放射平衡小结,三种平衡的共同点在于：达到平衡后，衰变规律随半衰期较长的核素长期平衡与暂时平衡：平衡后，子核按母核的半衰期（较长）衰变不成平衡：平衡后，母核消失，子核按自身的半衰
29、期（较长）衰变,放射系,Radioactive series,放射系,递次衰变系列的统称三个天然放射系：铀系，钍系和锕系一个人工放射系：镎系,铀系(uranium series),钍系(thorium series),锕系(actinium series),镎系(neptunium series),The neptunium series,(4n+1),The(4n+1)series is unique in that it contains no gaseous member.Both astatine(85)and francium(87),long missing from the pe
30、riodic table,are members of this series.Again,branching occurs at a bismuth isotope,in this case 213Bi.The series terminates with an isotope of bismuth instead of at lead,as is the case for the other three series.It should be noted that the termination of the neptunium series is at 209Bi,which has a
31、 magic neutron number 126.,放射系小结,讨论和提问,（13分钟）,小结,核辐射的来源：放射性衰变 衰变能来自原子核的质量亏损，体现了能量最低原理 衰变类型：，放射性衰变的规律：指数衰减 放射源的活度与原子核数成正比，与半衰期成反比 放射源的活度随时间按指数规律衰减,思考题,课后习题：4，9，10，11，12，16(U-234)三种常见放射性衰变的含义、方程（举例）、对象、粒子能谱和衰变纲图（会看）单一放射性核素的衰变规律及相关概念放射性活度的单位和计算各种放射性平衡的条件和举例放射系释放的气体核素,Evaluation of Avogadros number,By c
32、ounting the flashes of light produced by alpha particles when they strike a screen coated with zinc sulfide,Sir William Ramsay and Professor Frederick Soddy found that 1 g of radium gives off 13.81010 alpha particles(nuclei of helium atoms)per second.They also measured the amount of helium gas produ
33、ced in this way,finding 0.158cm3(at 0oC and 1 atm)per year per gram of radium.At this temperature and pressure 1 l of helium weighs 0.179g.Avogadros number of helium atoms weighs 4.003 g(the atomic mass of helium is 4.003).From these data calculate an approximate value of Avogadros number.(Chemistry by L.Pauling&P.Pauling,p.106),参考文献,卢希庭 主编，原子核物理杨福家 主编，原子核物理Lapp and Andrews,Nuclear Radiation PhysicsEB(Encyclopedia Britannica)Saha,Physics and Radiobiology of Nuclear Medicine,THANK YOU!,谢谢大家！,感谢您的观看！,
