TECHNOLOGY, ENERGY, AND RISK
TECHNOLOGY, ENERGY, AND RISK CH 374
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This 46 page Class Notes was uploaded by Dariana Wolff on Monday October 19, 2015. The Class Notes belongs to CH 374 at Oregon State University taught by Staff in Fall. Since its upload, it has received 18 views. For similar materials see /class/224554/ch-374-oregon-state-university in Chemistry at Oregon State University.
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Date Created: 10/19/15
Nuclear Masses and Binding Energy Lesson 3 Nuclear Masses 0 Nuclear masses and atomic masses 2 2 atomicc zmelectronc Belectron Belectron 1573Z736V 2 mmlc M Because B situations Zis so small it is neglected in most electron Mass Changes in Beta Decay 3 decay 14CemN H v Energy 6meleclron m14N 6meleclron nI c2 Energy M14 C M14Nc2 3 decay 64Cue64Ni39 3 ve Energy 29melectran 28melectran melectran m362 Energy M64Cu M64Ni 2m c2 electron Mass Changes in Beta Decay 0 EC decay 2078f equot eme v6 Energy m207Bi 83melemn m207Pb 82melemn c2 Energy M 2078i M 207Pbc2 Conclusion All calculations can be done with atomic masses Nomenclature 0 Sign convention 2 Qm as S es reactantsm as S es products c Q has the opposite Sign as AH Q exothermic Q endothermic Nomenclature 0 Total binding energy Bt0tAZ Bra12 ZM1HAZMnMAZ1c2 0 Binding energy per nucleon BaveAz MaoA 0 Mass excess A MAZ A See appendix of book for mass tables Nomenclature 0 Packing fraction MAA 0 Separation energy S SnMA1ZMnMAZcz SPIMA1Z1M1IDMAZCZ Binding energy per nucleon Separation energy systematics I I I I I 10 282 5 2quot m gt DO 5 I O 2 E 5 G On a Atomic number Z 20 40 60 80 20 40 60 80 Neutron number N 120 40 ON 00 O O I l 100 Abundances Semiempirical mass equation 2 2 Bt0tAZ aVA azSAZ3 ac Z18 aa M i 6 A A Terms Volume aVA Surface asA23 Coulomb aCZZIA13 3 Zze2 ECoulomb g R R 12A 3 2 ECoulomb Z 13 A Asymmetry term a A ZZ a N Z2 a Neutron states A Proton states Lg KW Egg 339 a A To make AZ from Z NA2 need to move q protons qA in energy thus the work involved is q2ANZ2A4 If we add that AIA we are done Pairing term stable 201 69 61 Doom 4 oommN omomz 611A3912ee 600660 6 11A391200 Relative importance of terms 16 8 Volume energy 2 14 g Surface energy E 12 Q 10 Coulomb energy on gt a a 5 2 g r r on Net binding g 0 6 energy Asymmetry 3 energy amp 4 E a 0quot Mn lt 833 Cues I127 Pt195 Bk245 0 I II I I I l I I I l I l l 0 30 60 90 120 150 180 210 240 270 Mass number A Values of coej cients av 1556MeV as 1723MeV ac 07MeV ad 23 285MeV Modern version ofsemi empirical mass equation Myers and S wiatecki N Z 2 N Z 2 22 22 Bl0lAZC1A1 kT C2A231 kT C3FC4j6 C1 15677MeV 62 1856MeV C3 0717MeV c4 1211MeV k 179 5 11A3912 Mass parabolas and Valley of beta stability MZ A z M1H A Z Mn BWZA 22 A 2Z2 BtotZ AaVAasA23 ac A13 all A 2 2 2 2 aaA 22 aaA 4AZ4Z 61 A4Z4z A A A 4 M A Mn av aa ZM1HMn 4Zaa 22333 This is the equation of a parabola abZcZ2 A111 M A MEV 40 80 A112 sa oddaodd eveneven 1 in 56 x x x x x x x x x x a 2 i E 7 3 2 E 7 E 2 2 lt lt i 7 NbMolTillem lEl w w M w w w 52 53 54 55T55 57 58 41 42 43 44T45 45 47 4s 2 24 2A 57 ZA447 Where is the minimum of the parabolas 0b2cZA 52 A b M1H Mn 4a 26 ac 4a 2A13 A ZA 1 81 A N 2 80 06A2 3 ZA Valley of Beta Stabili I kquot I J 7 T h n 739 wvwi 0 r a inquot 39vwviwvvvii 39i Mo o if q o o 39t39 x nu 9 o r J quotnonMM a nu u a on M c9 a v A I 7 cf 0 I 0139 93 x t ii0 a quotiiil Q 4 G 1 Man EEDJKH new Lecture 2 Radioactive Decay Kinetics Basic Decay Equations Radioactive decay is a rst order process ie the number of decayss OC the number of nuclei present In eqn form dNdt W where the constant 7 is the decay constant A 7 N Rearranging m dt d N At N N Noe M where N0 is the number of nuclei present at t0 If we remember the basic equation relating activity to number of nuclei in a sample AMV then we can write A AOe39M T has we have two equations that look the same but have very di erent meanings N A AoeW Graphically lOO 100 01 O I 80 J O I 60 6 I 40 U1 I Observed acTiviTy linear scale Observed ac rivi ry log scale 20 N I l L l O N J 4 Decay constants t1 2 100 Radioactivity 51l3 o 1536 078 I l 39 I l I o 1 2 3 4 5 6 7 A 1 Lt12 6 A0 2 t 1n2 0693 12 A A Note that if t1 2 has units of time 7 has units of time391 7 is probability per unit time of getting a decay Use of basic decay equation ALN A A mass radionuclide 023 AtWt What do these equations really mean An easy decay rate to measure is 10 dpm of a nuclide with a t1 2 0f 20 min Then N A 20 288 A ln2 Mass LBALWL 5x10 20 g 602x10 Mean Life 1 T L 114431 12 N0 Et 1 1 11 fth ftAthAfte No N0t0 N0 0 0 Signi cance of mean life AE om 2 h TE At h 0658x10 15ev g W r Units 1 Bq1 Becquera1 ds 1Curie1Ci37x1O10 Bq Mixture 0f independently decaying activities AW A1 A2 Aloe A Age M y log ed ocTiviT Observ Radioactive Decay E quilibria Consider 192939 rate of change 0f2rate of production of 2 by decay of rate of decay of 2 dN dt2 HNl AQNz sz AQNZdt AlNldt N1 N106 sz det ANfe A dt ek39sz AzNzeMdt LleeA2 A dt dN2e 239 AlNloeMZ A dt 0 Aral Nze gtl HNle 0 A2 A1 0 Nze gt N HN106A27A1I 1 A2 A1 0 N2t am 3239 Nge k39 2 0 A2t e 3239 Age k39 2 O N2t A1N1 64 64 N364 A2 A1 0 A2t aw e M Age M A2 A1 Special Cases N0 equilibrium pradact is stable 0x20 sz N dt A1 sz AINldt Ame Wt t 0 N2 L39N1 e xlt N101 e4 LI 0 aat vity m mmnrlmrh mw units 39Tii afr 5x 339 Special Cases 0 Transient Equilibrium k2 10x k1 ARA e M ltlt e M Nze w a 0 0 N2t L1Nl 1e t e4 Ngewt 2 0 N20 AINI 6 th A2 1 N1 Moe M i A2 1 N2 A v4 u CI an Inpurll a n 125 IE 275 PM Timefd Special Cases Secular Equilibrium 0x2 gtgt M i2 2 1 Activity 0 C mim 1 Importance of Secular Equilibrium Naturally occurring decay series EH its 19 7 rm 139 EPE JI jg39lif Iv I H as 39 ram h 1 i E fif xllmg n ii39m quotquot 39 v 74 39 39h L a I WHEI E39F Twill 713quot 3 w A me 7 M 131 If a uni if Ll FIFlt 39 W i Hg is as 7 7 El 7 39quot E 1 I H an Pm 5 Hf BETH wuz39 i MW F1 Elli l lar l 7 i j a I 7 7 Fl Pig gig quotMn 7 J Ta Eli ii iii a i E d V VI E2 L i l 39 aw n Fa FIL I q r H 3 as lm quotquot i K m quot t 7 7 J i J mm h w pa up r all H f I I a 41 39 391 IF quot5 quot 5 RE FEE Pym 3 m 1 m Hung a by I iir m ma fag rig m nag E W 39 Importance of Secular Equilibrium 0 Production of radionuclides in a nuclear reaction 0 Nuclear reaction a 2 a N3 0 Rate R ANI N20 6quot1 equot2 Llltlt2 N2t Alia e42 2 A20 AZNZ R1 e39M Arctiuily mormn izcdl 113 gt f f 1214391 If f Jr J gt 7 Jrquot 2 3 an E u39n 7 41 Jun 1 rm H equot39m fin is l 9 A 5 3T 11 5391 Accu luhtiun Lirrm l his Bateman equations Consider the general case 1 2 a 3 a 4n Assume NE N fo N 0 N Cle39Al Cze39AQ Cge39A Cue M C1 AWAZ Ln 1 N10 A2 MW MIA A C2 AWAZ Ln 1 N10 1 A2 39n 2 2 C AA2An 1 N10 A A005 Anvn1 A Branching Decay Suppose a nucleus decays by several different modes such as ocdecay SFdecay and EC decay Then the total decay probability km is the sum of the probabilities of decaying by each mode ie Not A06quotVSIquot39VEC Foe each mode of decay there is an associated partial halflife ie t12or ln 2 ma Naturally occurring radion aclides Primordial Cosmogenic Anthropogenic Environmentally interesting radian uclides 222R 40K 0 3H I4 cosmic ray OH willedUh products rhermq neutron MN nucleus 6 m cC o axidafion pro on quot39032 39CN 2139 40 U phoiaaynih 5I5 I 1 dissolved C02 3 Carbonares Radionuclide dating At AOe A t lnA0A lnN0 N A A Tricks oAMS Variati0ns in A 0 0r N0
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