Nuclear Course PDF

What%are%the%constituents%of%nucleus? The%atomic nucleus consists%of%nucleons— protons%and%neutrons.% Protons%and%neutrons%are%made%of%quarks% and%held%together%by%the%strong%force% generated%by%gluon%exchange%between% quarks Nucleus(is(positive(charge Nucleus%=%Protons%+%Neutrons The%radius%of%a%nucleus%is%much%smaller% than%that%of%an%atom:10,000%times What%is%the%size%of%the%nucleus? The nucleus is%the%center%of%an%atom.% It%is%made%up%of%nucleons%called%(protons% and%neutrons)%and%is%surrounded%by%the% electron%cloud.% The%size%of%nucleus%is%diameter%of%nucleus. The size (diameter)%of%the nucleus is% between%1.6%fm (10−15 m)%(for%a%proton%in% light%hydrogen)%to%about%15%fm (for%the% heaviest%atoms,%such%as%uranium). What&is&the&function&of&nucleus&in&an&atom? The atomic'nucleus is&a&very&dense&region&in& the&center&of&the atom.& The&nuclear&force&is&a&natural&force&that&holds& protons&and&neutrons&together.& This&force&keeps&the&subatomic&particles&nice& and&tight.& The&nuclear&force&only&works&at&a&close&distance IS$THE$ATOM$FUNDAMENTAL? No Scientists$determine$that$atoms$have$a$tiny$but$dense, Positive$nucleus$and$a$cloud$of$negative$electrons. IS$THE$NUCLEUS$FUNDAMENTAL? NO Nucleus$made$of$positive$charge$protons$and$ Charge$less$neutrons. 11 ARE$PROTONS$AND$NEUTRONS$FUNDAMENTAL? NO Physicists,have,discovered,that,protons,and,neutrons,are, composed,of,even,smaller,particles,called,quarks. Quarks,are,like,points,in,geometry.,They,are,not,made,up of,anything,else. Scientists,suspect,that,quarks,and,the,electron,are, fundamental 12 What$is$proton? The$number$of$protons$in$a$nucleus$is$expressed$ by$the$symbol$Z. Proton&has&the&mass&1837$times$of$an$electron. The$atomic$number$is$the$number$of$protons$in$a$nucleus. Protons have$a$positive$electrical charge of$one$(+1)$and$ a mass of$1$atomic mass unit$(amu),$which$is$ about$1.67×10−27$kilograms What#is#antiproton? An#antiproton#is#an#atomic#particle#that#has#the# mass#of#a#proton#and#the#charge#of#an#electron. What)is)neutron? Neutrons)have)no)charge)/ they)are)electrically)neutral. The)mass)of)a)neutron)is)slightly)greater)than)the)mass of)a)proton,)which)is)1)atomic)mass)unit (amu). (An)atomic)mass)unit)equals)about 1.67×10−27 kilograms.)) A)neutron)also)has)about)the)same)diameter)of)a a)proton,)or 1.7×10−15 meters. The)neutrons)are)in)a)Uranium/235)nucleus)is) 143. Properties)of)Subatomic)Particles Relative0 Mass0 Mass0 Relative0 Particle Symbol Location (amu) (proton0=0 Charge 1) inside)the) proton p+ 1 1 +1 nucleus outside) electron e− 5.45)× 10−4 0.00055 −1 nucleus inside)the) neutron n0 1 1 0 nucleus Summary'of'protons,'electrons'and'neutrons Electrons*are*a*type*of*subatomic*particle*with*a*negative* charge. Protons*are*a*type*of*subatomic*particle*with*a*positive* charge.*Protons*are*bound*together*in*an*atom's*nucleus* as*a*result*of*the*strong*nuclear*force. Neutrons*are*a*type*of*subatomic*particle*with*no*charge* (they're*neutral).*Like*protons,*neutrons*are*bound*into* the*atom's*nucleus*as*a*result*of*the*strong*nuclear*force. Protons'and'neutrons'have'approximately'the' same'mass,'but'they'are'both'much'more' massive'than'electrons'(approximately'2,000' times'as'massive'as'an'electron). The'positive'charge'on'a'proton'is'equal'in' magnitude'to'the'negative'charge'on'an' electron.'As'a'result,'a'neutral'atom'must'have' an'equal'number'of'protons'and'electrons. The'atomic'mass'unit'(amu)'is'a'unit'of'mass' equal'to'oneAtwelfth'the'mass'of'a'carbonA12' atom Mass$number$A Mass$Number$is$defined$as$the$number$of$protons$ plus$the$number$of$neutrons$in$a$nucleus. The$mass$number$(represented$by$the$letter$A)$is defined$as$the$total$number$of$protons$and$neutrons in$an$atom. What$is$atom? The$two$main$parts$of$an$atom$are$orbital$ electron$and$nucleus. As#per#modern#theory,#the#atom#has#a#diameter# of#about#1077mm. In#neutral#atom,#the#electrons#are#bound#to#the# nucleus#by#Electrostatic$force. An$atom$can$be$considered$as$consisting$mostly$ of$empty$space. For$an$atom$to$be$electrically$neutral,$the$ number$of$protons$equals$the$number$of$ electrons. One$atomic$mass$unit$(AMU)$is$equal$to$ 1.66$x$10'24 g Contents Nuclear density Density of atom Atomic model Physical situation, Nomenclature & Equation Some constants Isotopes, Isobar, Isotone Mirror Nuclei Radius of nuclei Stable and unstable nuclei Table of nuclei Magic number Is nuclear density constant? Nuclear density The ratio of mass per unit volume inside the nucleus is called nuclear density. The consequence of this is that the density of nucleus is a constant, independent of mass number for all nuclei. Different nuclei are likes drop of liquid of constant density. Why is the nuclear density almost constant for all nuclei? This means that they are all about the same distance apart and since protons and neutrons have nearly identical mass then there will be the same mass for a given volume regardless of how many nucleons there are, hence the constant density. Why is nuclear density independent of mass number? We use the concept of conservation of energy and distance of closest approach in Rutherford's alpha scattering experiment to find radius of nucleus is proportional to the Mass Number. The consequence of this is that the density of nucleus is a constant, independent of mass number for all nuclei. What is the formula of nuclear density? The usual definition of nuclear density gives for its density: ρnucleus = m / V = 238 x 1.66 x 10-27 / (1.73 x 10-42) = 2.3 x 1017 kg/m3. Thus, the density of nuclear material is more than 2.1014 times greater than that of water. It is an immense density. What is density of an atom? Atomic density means the number of atoms per unit volume. The atomic number of an element represents the number of protons in the nucleus and the number of electrons surrounding it. Atomic models Thomson’s plum puddling model Rutherford’s nuclear model Bohr’s model Summerfield's model Physical situation, Nomenclature & Equation Some constant Electron mass = me = 9.1 x 10-31 kg; mec2 = 0.511 MeV Proton mass = mp = 1.673 x 10-27 kg; mpc2 = 938.3 MeV Neutron mass = mn = 1.675 x 10-27 kg; mnc2 = 939.6 MeV Planck's constant = h = 6.63 x 10-34 Js; hc = 1240 eV nm speed of light c = 3 x 10 8 m/s Properties of Atomic Particles Particle Charge Mass (kg) Mass (u) Mass (MeV/c2) Electron -1.602 x 10-19C 9.109382 x 10-31 5.485 x 10-4 0.510999 Proton 1.602 x 10-19C 1.672622 x 10-27 1.007276 938.27 Neutron 0 1.674927 x 10-27 1.008665 939.57 H-atom 0 1.673534 x 10-27 1.007825 938.783 u 0 1.66053886 x 10-27 1 931.494 Express the atomic mass unit, u in its rest energy equivalent? The nucleus of an atom consists of neutrons and protons, collectively referred to as nucleons. Some Properties of Selected Nuclides Binding Energy Nuclide Z N A Stabilitya Massb (u) Spinc (Me V/nucleon) 1H 1 0 1 99.985% 1.007 825 1/2 — 7Li 3 4 7 92.5% 7.016 004 3/2 5.60 31P 15 16 31 100% 30.973 762 1/2 8.48 84Kr 36 48 84 57.0% 83.911 507 0 8.72 120Sn 50 70 120 32.4% 119.902 197 0 8.51 157Gd 64 93 157 15.7% 156.923 957 3/2 8.21 197Au 79 118 197 100% 196.966 552 3/2 7.91 227Ac 89 138 227 21.8 y 227.027 747 3/2 7.65 239Pu 94 145 239 24 100 y 239.052 157 1/2 7.56 What is Isotope? Isotopes are nuclei with same Z, different A. One of two or more atoms whose nuclei have the same number of protons but different numbers of neutrons. Examples: 15O, 16O,17O The number of known isotopes is roughly 2500. What is isotone? One of two or more atoms whose nuclei have the same number of neutrons but different numbers of protons. Examples: 3H, 4He,5Li What is Isobar? One of two or more atoms whose nuclei have the same number of mass but different numbers of protons and neutrons. Examples: 14C, 14N What is an isomer? The long live excited states of a nucleus is known as isomer. It is a metastable states. Examples: 0.87 micro seconds of pg9/2+ in 79As What is Mirror nuclei? Two nuclei where neutron and proton number exchanged is called mirror nuclei. Examples: 31H2, 32He1 What is radius of a nucleus? R =R0A1/3 R0 =1.2 Fermi meter =1.2 x 10-15 meter * Problem: Determine the radii of 27Al, 64Cu and 235U nuclei? Nuclear Binding Energies The mass M of a nucleus is less than the total mass Σm of its individual protons and neutrons. That means that the mass energy Mc2 of a nucleus is less than the total mass energy Σ(mc2) of its individual protons and neutrons. The difference between these two energies is called the binding energy of the nucleus: Binding energy is not an energy that resides in the nucleus. Rather, it is a difference in mass energy between a nucleus and its individual nucleons: If we were able to separate a nucleus into its nucleons, we would have to transfer a total energy equal to ΔEbe to those particles during the separating process. Although we cannot actually tear apart a nucleus in this way, the nuclear binding energy is still a convenient measure of how well a nucleus is held together, in the sense that it measures how difficult the nucleus would be to take apart. A better measure is the binding energy per nucleon ΔEben, which is the ratio of the binding energy ΔEbe of a nucleus to the number A of nucleons in that nucleus: We can think of the binding energy per nucleon as the average energy needed to separate a nucleus into its individual nucleons. A greater binding energy per nucleon means a more tightly bound nucleus. Plot of the binding energy per nucleon ΔEben versus mass number A The binding energy per nu-cleon for some representative nuclides. The nickel nuclide 62Ni has the highest binding energy per nucleon (about 8.794 60 MeV/nucleon) of any known stable nuclide. Note that the alpha particle (4He) has a higher binding energy per nucleon than its neighbors in the periodic table and thus is also particularly stable. What is the binding energy per nucleon for 120Sn? Problem: Determine the stable nucleus that has a radius 1/3 that of 189Os? Problem: Find the approximate density of a nucleus? R=roA1/3 ro=1.2x10-15 m V=4/3πr3 =4/3πr3A , ρ =M/v 2.3*1017 kg/m3 What is the difference between the binding energies of 3He and 3H? B.E= MC 2 A B.E= (Zmp+Zme+Nmn-M(zX ))*931.5 MeV Mass of 3He is 3.016030 am And 3H is 3.01605 amu What is the binding energy per nucleon for 120Sn? Problem: Determine the binding energy per nucleon of 62Ni. Mass of MH=1.007825 amu Mass of Mn = 1.008665 amu Mass of 62Ni = 61.928346 amu What is stable nuclei? The nuclei do not emit ,  and  are called stable nuclei. Examples: 12C, 81Br What is unstable nuclei? The nuclei emit ,  and  are called unstable nuclei. Examples: 79As, 81As Write down the type of unstable nuclei? There are two types of unstable nuclei: 1) Proton rich nuclei (61As, 63As) 2) Neutron rich nuclei (79As, 81As) What is Proton and neutron rich nuclei? Proton rich nuclei: The nuclei which emit positron or (e+) Neutron rich nuclei: The nuclei which emit beta - or (e-) Table of nuclei A table of nuclides or chart of nuclides is a two-dimensional graph in which one axis represents the number of neutrons and the other represents the number of protons in an atomic nucleus. Stability line The line indicate the difference between neutron rich and proton rich nuclei. What is magic number? Number of protons or neutrons 2, 8, 20, 28, 50, 82, 126 is called magic number. The nucleus consist of those number of protons and neutrons are stable. 2+ states is very high What%is%Nuclear%Physics? Nuclear(Physics(is(defined(as(the(branch(of(physics(deals(with(the( structure(of(the(atomic(nucleus(and(its(interactions. The$fundamentals$of$atomic$nuclei Radius'of'Nucleus ‘R’'represents'the'radius'of'nucleus. R=R0 A1/3 Where, Ro is'the'proportionality'constant'R0'=1.2'Fermi'meter =1.2'x'10C15 meter' A'is'the'mass'number'of'the'element Total'Number'of'Protons'and'Neutrons'in'a'Nucleus The'mass'number'(A),'also'known'as'the'nucleon'number,'is'the'total' number'of'neutrons'N and'protons'in'a'nucleus'Z. A=Z+N Binding&energy&formula and&Mass&Defect Mass&defect&takes&place&when&some&mass&is&lost&during&the&nuclei&generation. The&masses&of&the&Z&electrons&cancel&out&and&the&difference&in&binding&energies&of&the&electrons&in&the&different&atoms&(~eV) is negligible&compared&to& the&nuclear&binding&energy&(~MeV). B.&E.&=&!.m C2 In&terms&of&the&nuclear&masses,&we&write&for&the&binding&energy&B(Z,N)&of&a&nucleus&with&Z&protons&and&N&neutrons B(Z,N)&=&c2(Z*mp +&N*mn J Mnuc(Z,N)). In&terms&of&the&atomic&masses,&we&write B(Z,N)&=&c2(Z*mH +&N*mn J Matom (Z,N)). !.m =&(Z*mp +&N*mn J Mnuc(Z,N))& Where, M'is'the'mass'of'the'nucleus', !.m is'the'difference'between'the'mass'of'the'nucleons'and'mass'of'the'nucleus' !.m is%mass%defect mp is'the'Mass'of'the'Proton mn is' is'the'mass'of'the'Neutron Even%more%on%[eV] So, [eV] IS A UNIT OF ENERGY; It’s not a “type” of energy (such as light, mass, heat, etc). When talking about energies of single photons, or of subatomic particles, we often use this unit of energy, or some variant of it. So, 1 [eV] = 1.6x10-19 [J] (can be used to go back & forth between these two energy units) 1 [keV] = 1000 [eV] = 103 [eV] “k = kilo (103)”” 1 [MeV] = 1,000,000 [eV] = 106 [eV] “M = mega (106)” 1 [GeV] = 1,000,000,000 [eV] = 109 [eV] “G = giga (109)” 4 Packing(Fraction Packing(fraction(is(defined(as(Mass(defect(per(nucleon. Packing(fraction((f)(=(Mass(defect(per nucleons Packing(fraction((f)= (Z*mp +'(A)Z)*mn ) A)/A Nature'of'Nuclear'Force The$nuclear$force$acts$between$the$charges$and$functions$as$the$ gravitational$force$between$masses.$Nuclear$force$acts$between$the$ protons$and$neutrons$of$atoms. Nuclear$force is$much$stronger$than$the$ Coulomb$force.$The$nuclear$physics$is$based$on$the$forces$known$as$ nuclear$force.$The$nature$of$nuclear$force$is$given$as: Nuclear$forces$are$attractive$in$nature. These$forces$are$independent$of$charges. The$range$of$nuclear$forces$is$short. As$the$distance$between$two$nucleons$reduces,$the$nuclear$force$becomes$ weak$between$them. The$nuclear$force$is$dependent$on$the$spin. What%is%nuclear%force? The%nuclear(force (or%nucleon– nucleon%interaction%or%residual% strong%force)%is%the%force%between% two%or%more%nucleons. Strong%force,%Weak%force What%are%Four%fundamental%forces? 1)%Gravitational%force 2)%Electromagnetic%force 3)%Strong%nuclear%force 4)%Weak%nuclear%force Gravitational*force Gravity Gravity,)the)weakest)of)the)four)forces,)is) about)10636 times)the)strength)of)the)strong) force. Electromagnetic-force Electromagnetism The$electromagnetic$force$is$actually$ second$in$effective$strength$only$to$the$ strong$force,$but$it$is$listed$out$of$order$ here$because$it,$like$gravity,$is$more$ familiar$to$most$people.$Its$strength$is$less$ than$1%$of$that$of$the$strong$force,$but$it,$ like$gravity,$has$infinite$range. Weak%nuclear%force The$weak$nuclear$force$is$one$of$the$less$familiar$ fundamental$forces.$ It$operates$only$on$the$extremely$short$distance$ scales$found$in$an$atomic$nucleus.$ The$weak$force$is$responsible$for$radioactive$ decay.$ In$actuality,$it$is$stronger$than$electromagnetism,$ but$its$messenger$particles$(W$and$Z$bosons)$are$ so$massive$and$sluggish$that$they$do$not$ faithfully$transmit$its$intrinsic$strength. Strong'Nuclear'Force The$strong$nuclear$force$is$the$other$unfamiliar$ fundamental$force.$ Like$the$weak$force,$its$range$is$limited$to$ subatomic$distances.$ Its$"duties"$are$keeping$quarks$together$inside$ protons$and$neutrons,$and$keeping$protons$and$ neutrons$inside$atomic$nuclei.$ Its$messenger$particle$is$the$massless$gluon,$so$ named$because$it$"glues"$elementary$particles$ together.$ What%is%Radioactivity? Radioactivity%is%the%phenomenon%exhibited%by%an%atom’s%nuclei%due%to%nuclear%instability.%In%1896,%Henry%Becquerel%discovered this% phenomenon.%Radioactivity%is%a%process%by%which%the%nucleus%of%an%unstable%atom%loses%energy%by%emitting%radiation.%A%small%amount%of% Uranium%compound%was%wrapped%in%black%paper%and%put%in%a%drawer%containing%photographic%plates.%These%plates%were%later%examined,%and% the%results%revealed%that%there%had%been%an%exposure.%Radioactive%Decay%is%the%term%introduced%for%this%phenomenon.%The%elements or% isotopes%that%emit%radiation%and%go%through%radioactivity%are%known%as%radioactive%elements% Units&of&Radioactivity There&are&two&units&of&radioactivity&and&they&are: Curie&(Ci): If&the&radioactive&substance&decay&at&the&rate&of&3.7×1010 decays&per&second,&then&the&unit&used&is&Curie. Rutherford&(rd): If&the&radioactive&substance&decay&at&the&rate&of&106 decays&per&second,&then&the&unit&is&Rutherford. Radioactivity Radioactivity is a process by which alpha, beta and gamma emit from a nucleus. Radioactivity,is,the,process,of,an,unstable,nucleus,becoming,stable. There are two types of radioactivity 1) Natural radioactivity 2) Artificial radioactivity Three types of radiation were emit from a nucleus: 1) Alpha particles (!) 2) Beta particles (") 3) Gamma-rays (# ) 14 Uranium(series 15 Where do these ‘particles’ come from ? !These particles generally come from the nuclei of atomic isotopes which are not stable. ! The decay chain of Uranium produces all three of these forms of radiation. ! Let’s look at them in more detail… 16 Note: This is the atomic weight, which is the number of Alpha&Particles&(!) protons plus neutrons Radium Radon + n p p n R226 Rn222 ! (4He) 88 protons 86 protons 2 protons 138 neutrons 136 neutrons 2 neutrons The alpha-particle (!) is a Helium nucleus (charge = +2) It’s the same as the element Helium, but without the electrons ! 17 Alpha&decay&(! decay) Alpha&decay&is&a&consequence&of&repulsion&between&protons heavy&nuclei&(A&>&209)&disintegrate&with&α&decay "#$ "#( !"U → !'Th +, ! particle&is&4He&nucleus Ra226 226 88.1(.X - → 01"Y + ("He 222 86 222 Rn 4 2 He4 energies&of&! particles&are&several&MeV 18 Beta%Particles%(!) Carbon Nitrogen + + C14 e- " N14 6 protons 7 protons electron 8 neutrons 7 neutrons (beta-particle) More on this n ! p + e- + " bugger later… The electron emerges with relatively high energy in this “disintegration” (decay) process. We see that one of the neutrons from the C14 nucleus “converted” into a proton, and an electron was ejected. The remaining nucleus contains 7p and 7n, which is a nitrogen nucleus. In symbolic notation, the following process occurred: 19 Beta%decay%(! decay) 20 beta%decay%is%a%consequence%of%ratio&between&the&number&of&protons&and&neutrons outside%the%stability%range subtypes%of%! decay:%!6,%!+,%and%electron%capture%(ε) nuclei%with%surplus%of%neutrons%disintegrate%with%!6 decay nuclei%with%surplus%of%protons%disintegrate%with%!+ decay%or%ε !6 particle%is%electron,%!+ particle%is%positron beta%decay%produces%also%neutrino%ν which%carries%some%energy neutrino%has%practically%no%influence%on%matter%or%the%environment !! decay 21 " !H → "%He + ( ) + *X → + *-!Y + () during'!( decay,'the'following'transition'occurs'inside'the'nucleus: n'→'p'+'e( 137 137 Cs 55 5 137 Ba 137 56 5 !' p e' n energies'of'! particles:'~100'keV ( MeV !+ decay 22 #$ #$ !"P → !'Si + +,. -X →. -0!Y + +, during'β+ decay,'the'following'transition'occurs'inside' the'nucleus: p'→'n'+'β+ when'positron'encounters'a'regular'electron,' annihilation occurs e9 and'e+ disappear,'2'photons'with'E'='511'keV are'created 22 11 Na 22 10 Ne e+ n positron e+ p Gamma$particles$(!) In much the same way that electrons in atoms can be in an excited state, so can a nucleus. Neon Neon Ne20 Ne20 + 10 protons 10 protons gamma 10 neutrons 10 neutrons (in excited state) (lowest energy state) A gamma is a high energy light particle (short for gamma ray). It is NOT visible to your naked eye because it is not in the visible part of the EM spectrum. 23 ! decay 24 nucleons(in(nucleus(can(occupy(only(specific(energy(levels ! decay(is(a(transition(from(excited(state(of(nucleus(to(ground(state ! decay&usually&follows&" or&# decays 60 27 Co&(5.27&years) ! Q! =&318.2&keV 2505.8&keV " 1332.5&keV " 0 60 Ni&&(stable) energies(of(! rays:(~100(keV – MeV( 28 Gamma$Rays Neon Ne20 Neon Ne20 + The gamma from nuclear decay is in the Gamma ray part of the EM spectrum (very energetic!) 25 Nuclear(changes 26 In#α#and#β#decays,#the#structure#of#nuclei#changes radioactive#decay#is#a#spontaneous change#of#nuclei In#any#change#of#structure#of#nuclei,#the#following#is# conserved: number#of#nucleons electric#charge "&( " !X → %&'Y + ('He Examples: " " %X → %-.Y + &./e α#decay: " ∗ %X → "%X + //γ β#decay: γ decay: Explain(properties(of(Alpha,(beta(and(gamma? ! particle:* They*are*positive*charge*particles*and*their*charge*is*twice*that*of*an*electron Their*mass*is*equal*to*helium*nucleus They*are*deflected*from*their*paths*be*electric*and*magnetic*fields ß:particle: These*particles*posses*negative*charge Their*mass*equal*to*that*of*an*electron.* They*are*deflected*by*the*application*of*electrostatic*and*magnetic*fields " ray These*are*electromagnetic*waves*of*very*small*wave*length*(wave*length*less*than*X:rays) They*move*with*the*velocity*of*light*and*having*low*ionizing*power They*are*not*affected*by*electric*and*magnetic*fields. They*have*very*high*penetrating*power. How$do$these$particles$differ$? Particle Mass Charge Gamma (!) 0 0 Electron mass is Beta (") ~1/2000th of -1 (Electron) a proton’s mass ~4 times a proton’s mp = proton mass mn = neutron mass Alpha (#) mass (since mp$ mn). +2 Back to “Structure of Matter” 28 Decay&constany (λ) What%is%decay%constant%(λ)%? The%inverse%of%average%life%period%of%a%radioactive%atoms%are%called%decay Constant. ! λ =% "# The%unit%of%decay%constant%=%1/second Half%life:) Half%life(t1/2 is(the(time(in(which(the(number(of(radioactive(nuclei(decreases( by(half The(number(of(radioactive(nuclei(is(further(halved(with(each(passing(of(half% life: t =(0: n0 nuclei t =(t1/2: ½((n0)(=(n0/2(nuclei t =(2(t1/2: ½((n0/2)(=(n0/4(nuclei t =(3(t1/2: ½((n0/4)(=(n0/8(nuclei … t =(m ! t1/2: n0/2m nuclei The(number(of(radioactive(nuclei(decreases(exponentially with(time. Find%the%relationship%between%the% Decay%Constant%and%the%Half%Life. Average'or'mean'life:' Average'life'period:'Average'Life'/'Mean'Life'of'a' radioactive'substance'is'defined'as'the'ratio'of'total'life' time'of'all'the'radioactive'atoms'to'the'total'number'of' atoms'in'it.'''''''''''''''''''' # !" ='λ Decay&Scheme The$decay$scheme$of$a$radioactive$substance$is$a$graphical$ presentation$of$all$the$transitions$occurring$in$a$decay,$and$of their$relationships. 34 The$exponential$law$of$radioactive$decay n0 n(t ) = n0 2!t / t1 / 2 n0 2 n(t)... number of nuclei that have not decayed after time t n0... number of radioactive nuclei at time t = 0 n0 t1/2... half-life 4 n0 8 t1/2 2$t1/2 3$t1/2 Mean%lifetime%τ is%the%average%time%from%formation% of%radioactive%nucleus%to%its%decay Relation%to%half6life: τ =%1.44%t1/2 Production*of*radioactive*materials Two$types Naturally$occurring$radioactive$materials Man$made$radioactive$materials Example(1 A Cobalt-60 nucleus is unstable, and undergoes a decay where a 1173 [keV] photon is emitted. From what region of the electromagnetic spectrum does this come? The energy is 1173 [keV], which is 1173 [keV] = 1173x103 [eV] = 1.173x106 [eV]. * First convert this energy to [J], E = 1.173x106 [eV] * (1.6x10-19 [J] / 1 [eV]) = 1.88x10-13 [J] * Now, to get the wavelength, we use: E = hc/!, that is ! = hc/E. So, ! = 6.63x10-34[J s]*3x108[m/s]/1.88x10-13 [J] = 1.1 x 10-12 [m] * Now, convert [m] to [nm], 1.1 x 10-12 [m] * (109 [nm] / 1 [m]) = 1.1x10-3 [nm] ! It’s a GAMMA Ray 36 Example(2 An electron has a mass of 9.1x10-31 [kg]. What is it’s rest mass energy in [J] and in [eV]. E = mc2 = 9.1x10-31*(3x108)2 = 8.2x10-14 [J] Now convert to [eV] ! 1&[eV] " 8.2x10!14 [J] # $ = 5.1x10 &[eV]=0.51&[MeV] 5 !19 % 1.6x10 [J] & What is an electron’s rest mass? According to Einstein, m = E/c2, that is: [mass] = [Energy] / c2 m = E / c2 = 0.51 [MeV/c2] 37 Example(3 A proton has a mass of 1.67x10-27 [kg]. What is it’s rest mass energy in [J] and in [eV]. E = mc2 = 1.67x10-27 *(3x108)2 = 1.5x10-10 [J] Now convert to [eV] ! 1&[eV] " 1.5x10!10 [J] # $ = 9.4x10 &[eV]=940&[MeV] 8 !19 % 1.6x10 [J] & What is a proton’s rest mass? According to Einstein, m = E/c2, that is: [mass] = [Energy] / c2 m = E / c2 = 940 [MeV/c2] 38 Proton&vs&Electron&Mass How much more massive is a proton than an electron ? Ratio = proton mass / electron mass = 940 (MeV/c2) / 0.51 (MeV/c2) = 1843 times more massive You’d get exactly the same answer if you used: electron mass = 9.1x10-31 [kg] Proton mass = 1.67x10-27 [kg] Using [MeV/c2] as units of energy is easier… 39 Atomic'Radiation It is now “known” that when an electron is in an “excited state”, it spontaneously decays to a lower-energy stable state. E5 > E4 > E3 > E2 > E1 The difference in energy, !E, is given by: !E = E5 – E1 = h" = #photon One example could be: h = Planck’s constant = 6.6x10-34 [J s] Energy Electron Energy Electron " = frequency of light [hz] in excited in lowest state state (higher PE) (lower PE) The energy of the light is DIRECTLY PROPORTIONAL to the frequency, ". E5 n=5 E5 n=5 Recall that the frequency, ", is related to E4 n=4 E4 n=4 the wavelength by: c = "$ (" = c / $) E3 n=3 E3 n=3 So, higher frequency ! higher energy E2 E2 ! lower wavelength n=2 n=2 E1 n=1 E1 n=1 Before After 40 The Law of Radioactivity A B The number of disintegration per second Activity A 7 A = Ao e - lt 10 Calculate the activity of: i- One gram of Radium 226Ra, whose half life is 1622 years. Ii- 3×10-9 Kg of active gold 200Au, Whose half life time is 48 mins. 226 gm ﬁ 6.03 ¥ 1023 1 gm ﬁ N 1 gm ¥ 6.03 ¥ 1023 N= 226 = 2.66 ¥ 1021 atoms 10 ln 2 A = lN = t1 / 2 0. 693 = Ci ¥ 2. 66 ¥ 10 21 1622 ¥ 365 ¥ 24 ¥ 60 ¥ 60 = 3. 604 ¥ 10 10 di sin tegration / sec 3. 604 ¥ 10 10 di sin tegration / sec = 3. 7 ¥ 10 10 di sin tegration / sec = 0. 974 Ci 11 In archaeological expedition, charcoal from an ancient fire-pit was excavated. This sample showed a 14C activity of 11.3 counts/gm/min. The absolute activity of 14C in a living tree is independent of species and it is nearly 15.3 counts/gm/min. Estimate the age of the charcoal sample? A = Ao e - lt 0.693 0.693 l= = T 5730 = 0.000121 11.3 0.000121 t =e 15.3 t = age of charcoal sample t = 2504. 65 Years 12 Sixty hours after a sample of beta emitter 24Na has been prepared, only 6.25% of it remains un decayed. What is the half life of this isotope? N = N o e - lt N = e - lt No 0. 0625 = e - l (16 hr ) ln (0. 0625 ) = -l 16 16 T = = 5. 77 hrs ln (0. 0625 ) lA lB A B C Stable No Is the initial number of nuclei in the parent A 8 NB = N ol A lB - lA ( e-l t - e-l A B t ) 13 Show that if there is initially N0 radioactive nuclei of the parent present, the time at which the number of radioactive daughter nuclei is maximum is given as: Êl ˆ logÁÁ B ˜˜ tmax = Ë lA ¯ lB - l A Solution 8 NB = N ol A lB - lA ( e-l t - e-l A B t ) For NB to be maximum, dN B dt =0= N ol A lB - l A - l Ae - l ( t A max - ( -1)l B e - l t B max ) Definition of tmax It is the time at which the activity of the daughter nuclei reaches a maximum value equal to the activity of the parent nuclei. dNB \ at =0 dt t = tmax Activity of parent = Activity of daughter l AN A = l B NB Ideal l A N B (t1 / 2 )A TA Equilibrium = = = l B N A (t1 / 2 )B TB For a daughter shorter-lived transient than the parent Equilibrium TA > TB lB NB TA = l A N A T A - TB For a daughter much Secular shorter-lived than the Equilibrium parent TA >> TB l B TA = l A TB The 4 Natural Decay Series A=4n A=4n+1 A=4n+2 A=4n+3 Types of Decay 232Th 232Th Series Decay α 228Ra A=4n β- 228Th ! 224Ra ! 220Rn ! 216Po ! 212Pb 212Bi β- 212Po 208Tl β- ! 208Pb 238U 238U Series Decay α 234Th A=4n+2 β- 234U ! ! Th 230 226Ra ! 222Rn ! 218Po ! 214Pb 214Bi β- 214Po 210Tl ! 210Pbβ- 210Po ! 208Pb Interactions of Gamma rays with Matter The Main 4 interactions are depending on the incident energy: Photoelectric Compton absorption Scattering 0.1 MeV < E < 0.5 MeV 0.5 MeV < E < 3.5 MeV Rayleigh Pair Production E E > 0.1 0.5< E 230, and it is a slow reaction. Induced Fission Reaction By irradiating samples of heavy nuclides with slow-moving thermal neutrons, it is possible to induce fission reactions. When 235U absorbs a thermal neutron, for example, it splits into two particles of uneven mass and releases an average of 2.5 neutrons, as shown in the figure below. Natural 235U of 0.72% abundanc e Fission Material Fissionable Fertile Nuclei which can only absorb n Nuclei which can undergoes fission To convert to another nuclei to some fission fragments And then by fission to fission fragments such as 235U, 239Pu, and 233U Such as 238U which converts to 239Pu LDM- Fission Equilibrium ³Saddle´ Shapes A heavy nucleus can fission if the activation energy exceeded Fusion Reaction The graph of binding energy per nucleon suggests another way of obtaining useful energy from nuclear reactions. Fusing two light nuclei can liberate as much energy as the fission of 235U or 239Pu. 2 1 H +13H ﬁ 24He + 01n + 24.7 MeV The Fusion Reaction in Stars (Stellar Reactions) Conditions for Fusion Reaction to occur -A thermal energy is needed to overcome the attractive nuclear force between the light nuclei (Coulomb barrier) to fuse them. Temperature T>108 -The product of ion density n and the confinement time t has to exceed a minimum value for the fusion reaction to continue This is known as Lawson Criterion: 12 kT nt > < sv > Q Where Q is the released energy per reaction, is the average product of cross section and particle velocity. Solar Fusion Reaction The basic reaction in the stars is the Hydrogen to Helium reaction releasing energy of 26.7 MeV. 411Hﬁ24He+ e+ + n + 26.7 MeV Novae are frequently (perhaps always) members of binary systems where the more massive star evolves more quickly and becomes a white dwarf. The less massive star loses some of its hydrogen-rich outer atmosphere to the white dwarf where it collects. The high gravity and intense heat of the white dwarf make conditions suitable for hydrogen fusion into helium. When enough hydrogen collects, it explodes in a fusion reaction, causing a nova. The gas ejected in the explosion is moving outwards at 1000-2000 kms/sec. The Fusion Reaction in Stars (CNO) cycle Core collapse: During the first 0.4 sec of the core collapse, many neutrinos are formed leading to a burst of neutrino emission. Gravitational waves are also likely to be emitted from the rapidly collapsing core but have never been observed. Eventually the surrounding material becomes so hot it begins to boil and starts the explosive outwards shock that ignites the hydrogen in the outer layers, causing the huge energy release in the supernova. At the end the star turns to be a black hole. The Fusion Reaction in Stars (CNO) cycle p+12Cﬁ13N+g Q=1.94MeV Nﬁ13C+e+ +n 13 Q=1.2MeV p+13Cﬁ14N+g Q=7.55MeV p+14Nﬁ15O+g Q=7.29MeV Oﬁ15N+e+ +n 15 Q=1.37MeV p+15Nﬁ12C+24He Q=4.96MeV The proton-proton cycle (P-P) p + p ﬁd + e+ + n Q = 0.42MeV p + dﬁ23He+ gM Q = 5.49 MeV 3 3 4 2 He+2 Heﬁ p + p+2He Q = 12.86MeV The Hydrogen Nuclear Reaction Deuterium cycle (d-d) d + d ﬁ 23He + n Q = 3.3 MeV d + d ﬁ 13H ( = t ) + p Q = 4 MeV d + t ﬁ 24He + n Q = 17.6 MeV d + 23He ﬁ 24He + p Q = 18.3 MeV The Liquid Drop Model of a Nucleus Weizsäcker in 1935 recognized the experimental evidence which suggested that in some way, a nucleus resembles a drop of a liquid. This model is to describe the behavior of the binding energy per nucleon of a nucleus. In 1939, Bohr and Wheeler employed a liquid drop model of the nucleus in their theory of nuclear fission. Analogy between the nucleus and the liquid drop Nucleons in the interior is surrounded by full complement of neighbours and hence is more strongly bound than a nucleon on the surface which has fewer neighbours. B/A Binding Energy nearly does not depend on the size of nucleus A=30 1- B/A/ falls off at small values of A. This is because very light nuclei have a larger fraction of their nucleons residing on the surface rather than inside. This reduces the B/A/ value as a surface nucleon is surrounded by fewer nucleons compared to the nucleon residing in the interior and is not so strongly bound. This is similar to the case of a liquid drop. Where, surface molecules are less bound compared to the interior molecules in the drop. 4 Volume term Surface term Coulomb Asymmetry {Binding of {Binding Energy of Energy term Energy term particles in particles near the surface} {Electrical {Binding Energy interior} repulsion of Depends on Excess Protons} of Neutron (N-Z)} Mass Parabolas: Prediction of Stability Against ‫ﺲ‬- Decay For Members of An Isobaric Family 5 Isobar Family A=91 Odd Value 91Kr M(A, Z) β- 91Rb β- 91Sr 91Mo β- β+ 91Y β-β+ 91Nb 91Zr Z 36 37 38 39 40 41 42 Isobar Family A=104 Even Value 104Mo β- Even-Even Curve M(A, Z) Odd-Odd Curve 104Tc 104Cd 104Ag EC b β- 104Rh Zo = - β+ 2C EC β- 104Ru 104Pd Z 42 43 44 45 46 47 48 The Shell Model of a Nucleus Experimental Evidence That Leads to The Shell Model Analogy The nuclear shell model is a model of the atomic nucleus which uses the Pauli principle to describe the structure of the nucleus in terms of energy levels is analogous to the atomic shell model for the electrons arrangement inside the atom. Assumption The shell model of the nucleus presumes that a given nucleon moves in an effective attractive potential formed by all the other nucleons. If that is true, then the potential is probably roughly proportional to the nuclear density and therefore could be expressed in the form: All shell are full We include a spin-orbit interaction (L.S) Coupling. First we have to describe the system (Nucleus) by the quantum numbers n, j ,mj and parity instead of l ,ml and ms, as in the Hydrogen-like atom. 6 _ All Nucleons have + ve Parity by (Convention) Pauli`s Exclusion principle stated that no tow nucleon can occupy the same quantum state. All nucleons are occupying states denoted by symbols s, p, d, f, g, h, …… Each state is denoted by a quantum number n=1, 2, 3, 4, 5, …. s state is filled with 2 nucleons, p state is filled totally with 6 nucleons, d state is filled totally with 10 nucleons, f is filled totally with 14 and g is filled totally with 18 nucleons. Each sub-state has a subscript referred to the orbital quantum number j, so it is pj, dj, fj, gj, ….. l = 0, 1, 2, 3, 4, 5, 6,…. Corresponding to the states s, p, d, f, g, h, …….. Do not forget that j = l ± s, so j= l ± 1/2 The degeneracy of each level is 2j+1. Note that 1,2,3,4 Sj pj dj fj gj hj 5,6,. l 0 1 2 3 4 5 s ½ 1/2 1/2 1/2 1/2 1/2 J = l± s ½ 1/2, 3/2, 5/2, 7/2, 9/2, 3/2 5/2 7/2 9/2 11/2 S1/2 P1/2 d3/2 f5/2 g7/2 h9/2 P3/2 d5/2 f7/2 g9/2 h11/2 8 17 40 43 Using the shell model, build the nucleus for 9 F8 , 20Ca20 , 21Se22 And then determine the spin and parity of their ground states: l =2, j = 5/2, +ve parity l =2, j = 5/2, +ve parity 9 40 20 Ca20 1d3/2 2S1/2 l =2, j = 3/2, +ve parity Ionizing Radiation Safety Ionizing'Radiation:"Radiation"that"have"enough"energy" to"cause"ionization"to"detach"electrons"from"atoms"or" molecule. Non-ionizing'Radiation:"Radiation"have"energy"enough" to"vibrate"the"atom"around"or"make"vibration"but"not"to" remove"or"detach"electrons" For'example: microwave,"visible"light,"IR(inferred" radiation"),"sound"wave(radio"wave) Occurrence'of'ionization'by'radiation'depends'on'the' energy'not'on'the'number'of'particles'or'photons Generally'particles'or'photons'with'energies'above'a'few' electron'volts'(eV)'are'ionizing. Non'ionizing'generally'! harmless'whenever'below'the' level'of'heating' Types&of&ionizing&Radiation&(wave&or& particle&) 19 Electromagnetic&wave 29 Subatomic&particles&(&electron,&proton&or&atoms) 39 Particles Electromagnetic-wave 19 uv (ultraviolet) 29 x_ray 39 γ_ray short9wavelength&! high&frequency&! high&energy&! ionizing 2" Subatomic*particles β_particles (e" ,0000e+000)0 (electron0mission0,0positron0emission) (β" ,000β+00) high0energy00high0speed0electrons0emitted0by0radioactive0 atomic0nuclei0(potassium040) Free0neutrons (n’s) Zero0electric0charge0they0can’t0ionize0direct0only0by0fast0 neutrons0interact0with0proton0in0Hydrogen0to0produce0fast0 proton0with0ionize0because0it0is0charged.0 3"# Particles Charged"or"neutrons"atoms"("in"particle"accelerator") α#particles"(He"+2)≅"He#nucleus Cosmic"ray"from"sun"and"other"in"space. α#particles"and"Cosmic"ray"are"high"energy. Ionizing'radiation'produced'by' Or Source'of'ionic' radiation: 1" radioactive,,materials,[cobalt"60,,Radium"226,,cesium"137,,, Potassium"40]. 2" X"ray,tubes 3" particle,accelerators. 4" nuclear,,reactors,,nuclear,fission,and,nuclear,fusion 5" In,environment,{e.g.,radioactive,iodine},its,accumulation, causes,thyroid,cancer. Ionic&radiation&are&invisible,&but&can&be&detected&by& special&detectors&{e.g.&Geiger&counter} Usage&of&Ionic&Radiation Medicine&(radiotherapy) Industry, Research,&and& Construction Health'hazard'of'ionic'radiation 1]#at#low#doses: (low#doses#=#long#term#problem) causes#{cancer,#tumors,#genetic#damage} 2]#at#high#doses: causes#{tissue#damage,#skin#burns,# radioactive#sickness#and#poisoning#death} 1]#Direct#ionization By#charged#particles#interact#electromagnetically#with# atom#(e.g.#α,#β) High;energy#beta#particles#β#may#produce 1)#Bremsstrahlung#rad#(X;ray)# 2)#Secondary#electrons#(δ;electrons) 2]#Indirect#ionization 2.1)%γ'ray:%do%not%ionize%in%their%path,%but%interact%with%matter% in%one%of%3%ways:% 1' photoelectric%effect%% 2' Compton%effect% 3' pair%production {lead%to%ionizing%radiation} 2.2)$by$neutrons (n’s) n’s:$zero$charge$(neutral)$interactless n’s$don’t$interact$with$electrons’$only$with$protons fast$n’s$! collision$with$protons$(p’s) ! fast$p$"! ionization$(as$it$is$charged) and$can$interact$with$electrons. n< interact$with$nuclei$of$Hydrogen ! radioactive$nuclei$! radioactive$decay$!chain reaction Radioactivity: Spontaneous*emission*of*radiation*from*an*unstable*atomic* nuclei. Radioactivity=*decay/*sec. =*disintegration/sec. Becquaral: The*SI=unit*of*radioactivity Curie (Ci)%unit%of%radioactivity Dose: amount'of'radiation. Absorbed*dose: The'amount'of'radiation'absorbed'by'matter. Absorbed'dose! J/Kg'='Gray'(Gy)'in'SI Equivalent*Dose*=*Dose*equivalent The'amount'of'dose'absorbed'by'biological'tissue. Dose'equivalent! J/Kg='Sievert'(SV)'in'SI Gray (GY):'SI'unit'of'absorbed'dose' Gray:&absorption*of*1J*of*ionizing*radiation*by*1*Kg*of* matter. 1*Gy =*100*Rad* Rad: old*unit*of*radiation*absorbed*dose. Sievert (Sv)%SI%unit%of%dose%equivalent. Sievert:%is%defined%as%absorption%of%1%J%of%ion%by%1%Kg%of% biological%tissue. REM (Röntgen equivalent.man.or.mamals) old.unit.of.dose.equivalent 1.rem.= 10.m.Sv =.0.01.Sv is.used.to.measure.dose.in.diagnostic.medical. 1.Sv =.100.rem Radiation(poisoning If#Dose##6#Sv ! Survival#is#unlikely. If#Dose#effect##>#10#Sv (>1000#rem)#! almost#fatal To#gauge#biological#effect Absorbed(dose(=(Equivalent(dose(× Radiation(weighting(factor(WR where:(WR=Q×N Q: quality(factor(depend(on(type(of(radiation((dimensionless) N: depend(on(factors(as:(time,(volume,(body(irradiated Q:(RBE((Relative(Biological(Effectiveness) RBE: health(physics(concepts(that(different(type(of(radiation(will(affect( living(tissue((or(organisms)(differently( A(higher(RBE(equates(with(greater(biological(damage(for(equivalent radiation(exposure‭.‬

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