Quiz (15 Points) Identify the daughter and the decay mode for the following isotopes 3-2. Parent isotope Decay mode Daughter Isotope.

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1 Quiz. (5 Poins) Provide a roue for he producion of 38 Pu? 5 poin bonus: Wha is he use of his isoope? Give an example of where i has been used.. (5 Poins) Below is a mass parabola from he able of he isoopes for A40. Use his figure o show which isoopes of A40 are sable? 3-

2 Quiz 3. (5 Poins) Idenify he daugher and he decay mode for he following isoopes Paren isoope Decay mode Daugher Isoope 0 Po 96 Pb 04 Bi A 99m Tc 99 Tc 4 C 39 Pu 6 Rf 3-

3 Quiz 4. (5 Poins) Provide he number of naurally occurring isoopes for he elemens below. This includes long lived radioacive isoopes Elemen Re V K La Sn Sb In H Pm umber of Sable Isoopes Lr 3-3

4 Quiz 5. (5 Poins) Provide he spin and pariy of he following isoopes Isoope Spin Pariy 4m Am 39 Pu 40 Pu 9m Sn 65 i 99 Tc 4 Am 79m Hf 3-4

5 Quiz 6. (0 Poins) Provide he cumulaive fission yields for he A isobars from 33 U, 35 U, and 39 Pu. A 33 U 35 U 39 Pu

6 Quiz 7. (0 Poins) Provide he decay consans (in s - ) for he following isoopes Isoope (s - ) 50 Ca 8 Zn 95 Zr 37 Cs 5 Sm 4 Am 4 Pu 8. (5 Poins) Lis he 4 sable odd-odd isoopes 3-6

7 Quiz 9. (5 Poins) Deermine he Q value for he following reacions Reacion or decay Alpha decay of 39 Pu 45 Sc + 4 He 5 H+ 44 Ti Q value (MeV) b - decay of 37 Cs n+ 35 U 3 Th+α n+ 35 U 36 U EC of 9 Hg Formaion of sable Au from bombarding 08 Pb wih a proon 0. (0 Poins) Calculae he mass of ml of nuclear maer. Base he calculaion on an 56 Fe nucleus, wih r o.3 fm o deermine he 3-7 radius of 56 Fe.

8 Quiz. (5 Poins) Please provide he gamma decay inensiies for he daa below Isoope 46 Sc 0.5 Gamma Energy (kev) %γ 03 Ru Au Am Eu.8 5 Eu Eu (0 Poins) Wha is nuclear skin hickness? How can one measure nuclear radii? 3-8

9 CHEM 3: Lecure 3 Radioacive Decay Kineics Ouline Readings: Modern uclear Chemisry Chaper 3; uclear and Radiochemisry Chapers 4 and 5 Radioacive decay kineics Basic decay equaions Uilizaion of equaions Mixures Equilibrium Branching Cross secion aural radiaion Daing 3-9

10 Solve wih: σ σ r r n p Expeced Sandard Deviaion np np( p) r np + np n p p) Apply o radioacive decay M is he number of aoms decaying umber of couns for a deecor σ Since in couning Relaive error σ - Wha is a reasonable number of couns More couns, lower error o np( ( e pracice is small, e σ M ) e Me Couns error % error

11 o e - Imporan Equaions! number of nuclei, decay consan, ime A Also works for A (aciviy) or C (couns) * A A o e -, C C o e - //(ln/ / ).443 / τ Error M is number of couns σ M 3-

12 Half-life calculaion Using o e - For an isoope he iniial coun rae was 890 Bq. Afer 80 minues he coun rae was found o be 750 Bq Wha is he half-life of he isoope exp(-*80 min) 750/890exp(-*80 min) ln(750/890) -*80 min -0.7/80 min - 9.5Ε 4 min - ln/ / / ln/9.5e min 3-

13 A Half-life calculaion A 0.50 g sample of 48 Cm has a alpha aciviy of mci. Wha is he half-life of 48 Cm? Find A * E-3 Ci (3.7E0 Bq/Ci).35E7 Bq Find * 0.50 g x mole/48 g x 6.0E3/mole 3.64E0 aoms A/.35E7 Bq/3.64E0 aoms6.46e-4 s - * / ln/0.693/6.46e-4 s -.07E3 s *.07E3 s.79e min.99e9 h.4e8 d 3.4E5 a 3-3

14 Couning A Your gamma deecor efficiency a 59 kev is 5.5 %. Wha is he expeced gamma couns from 75 micromole of 4 Am? Gamma branch is 35.9 % for 4 Am C(0.55)(0.359) / 43.7 a* (3.6E7 s/a).37e0 s ln/.37e0 s5.08e- s - 75E-6 moles *6.0E3/mole4.5E9 aoms C(0.55)(0.359)5.08E- s - *4.5E9.8E8 couns/second 3-4

15 Mixures of radionuclides Composie decay Sum of all decay paricles o disinguished by energy Mixures of Independenly Decaying Aciviies if wo radioacive species mixed ogeher, observed oal aciviy is sum of wo separae aciviies: A A +A + any complex decay curve may be analyzed ino is componens Graphic analysis of daa is possible oal Bq hr - /.5 hr hr - / 0.4 hr T (hr) y m*exp(-m*x)+m3*exp(-m4... m m m3 m4 Chisq R Value e Error e e-8 A A

16 Paren daugher decay Isoope can decay ino radioacive isoope Uranium and horium decay series Alpha and bea * A change from alpha decay Differen designaion 4n ( 3 Th) 4n+ ( 38 U) 4n+3 ( 35 U) For a decay paren -> daugher Rae of daugher formaion dependen upon paren decay raedaugher decay rae 3-6

17 3-7 Paren-daugher Inegrae over Muliply by e - and solve for ) ( ) ( 0 ) ( 0 o o o e e e e o o e e e ) ( ) ( + Growh of daugher from paren Iniial daugher

18 Paren daugher relaionship Find, can solve equaion for aciviy from AΝ A o( e e ) + A oe Find maximum daugher aciviy based on d/d0 Solve for ln( ) e e ( ) For 99m Tc ( / 6.0 h) from 99 Mo (.75 d), find ime for maximum daugher aciviy Tc.8 d -, Mo 0.5 d -.8 ln( ) ln(.) days 3-8 (.8 0.5).55

19 Many Decays d 3 d 3 3 Can use he Baeman soluion o calculae enire chain Baeman assumes only paren presen a ime 0 n C e + C e + C n e n C... (n ) ( )( 3 )...( n ) o C... (n ) ( )( 3 )...( n ) o Program for Baeman hp:// 3-9

20 Branching Decay Branching decay parial decay consans mus be considered Isoope has only one half life if decay chain branches and wo branches are laer rejoined, branches are reaed as separae chains producion of common member beyond branch poin is sum of numbers of aoms formed by he wo pahs Branching raio is based on relaive consans i/ is he % of he decay branch i ; i 3-0 i / i /

21 Branching Decay For a branching decay of alpha and bea α + β i Branching raio i/ i α / + β / Consider Bi, wha is he half life for each decay mode? Alpha branch 36 %, bea branch 64 % / min 0.04 min - ; 0.36 α / ; 0.36 α /0.04 min - α min - / alpha 69 min α + β ; 0.04 min min - + β ; min - β / bea 95.0 min 3-

22 Cross secions Acceleraor: beam of paricles sriking a hin arge wih minimum beam aenuaion When a sample is embedded in a uniform flux of paricles inciden on i from all direcion, such as in a nuclear reacor, he cross secion is defined: R i # of processes of ype under consideraion occurring in he arge per uni ime I # of inciden paricles per uni ime n # of nuclei/cm 3 R xarge hickness (cm) φflux of paricles/cm /sec number of nuclei conained in sample i R i φ σ i Inx σ i 0-4 cm barn 3-

23 Producion of radionuclides 0σφ σcross secion ( e ) φneuron flux ime of irradiaion A 0σφ( e ) (-e -() ) * maximum level (sauraion facor) Aciviy of radioacive produc a end bombardmen is divided by sauraion facor, formaion rae is obained RA/(-e -() ) half life %

24 uclei producion: Shor irradiaion compared o half-life Find amoun of 59 Fe ( / 44.5 d,.803e-7 s - ) from irradiaion of g of Fe in a neuron flux of E3 n/cm /s for hour 58 Fe(n,γ) 59 Fe: 58 Fe+ n γ + 59 Fe σ.3e-4 cm o g/ g/mol *6.0E3 aom/mol*0.008 o 3.04E9 aom R E3 n/cm /s *.3E-4 cm * 3.04E aom R φ R3.95E8 aoms/sec.43e aoms 59 Fe in hour i σ i 3.04E9(.3E - 4)(E3).803E-7*3600 ( e ).803E E8 ( 9.994E ).803E - 7.9E5(6.489E 4).4E aoms 0σφ ( e 3-4 )

25 uclei producion: Long irradiaion compared o half-life Find amoun of 56 Mn ( /.578 hr, 7.469E-5 s - ) from irradiaion of g of Mn in a neuron flux of E3 n/cm /s for hour 55 Mn(n,γ) 56 Mn: 55 Mn+ n γ + 56 Mn σ3.3e-4 cm o g/ g/mol *6.0E3 aom/mol o.096e aom R E3 n/cm /s *3.3E-4 cm *.096E aom Ri φ R.457E aoms/sec 5.47E5 aoms 56 Mn in hour (does no accoun for decay) σ i.096e(3.3e - 4)(E3) ( e 7.469E E ( 7.64E ) 7.469E -5.95E6(.358E ) 4.603E5aoms 7.469E-5*3600 ) 0σφ ( e 3-5 )

26 Formaion rae from aciviy RA/(-e -() ) 4.603E5 aoms 56 Mn ( /.578 hr, 7.469E- 5 s - ) from hour irradiaion A 4.603E5* 7.469E E Bq RA/(-e -() ) R 3.436E/(-exp( E-5 *3600)) R.457E aom/sec 3-6

27 Daing Radioacive decay as clock Based on o e - o ln ln Solve for o 0 and are he number of radionuclides presen a imes 0 and from A he age of he objec eed o deermine o For decay of paren P o daugher D oal number of nuclei is consan D ( ) + P( ) P o 3-7

28 P P o e - Daing Measuring raio of daugher o paren aoms o daugher aoms presen a 0 All daugher due o paren decay o daugher los during ime A mineral has a 06 Pb/ 38 U 0.4. Wha is he age of he mineral?.e9 years ln( + D P ln 4.5E9a ) ln( + 0.4) 3-8

29 4 C daing Daing Based on consan formaion of 4 C o longer upakes C upon organism deah 7 Bq 4 C /kgc a equilibrium ln( Wha is he age of a wooden sample wih 0.5 Bq/g C? 4 4 C C eq sample 0.7 ln( ) 340years ln ( ) years ) 3-9

30 Daing Deermine when Oklo reacor operaed U ln r Today 0.7 % 35 U Reacor 3.5 % 35 U Compare 35 U/ 38 U (U r ) raios and use o e - () U U r r () (o) ln (- U 35 r e (o) e (- Ur () Ur (o) ) U 38 r ) (o)e ( ) 7.05E - 3 ln 3.63E -.97E years (-9.85E E 0)

31 Topic review Uilize and undersand he basic decay equaions Relae half life o lifeime Undersand relaionship beween coun ime and error Uilizaion of equaions for mixures, equilibrium and branching Use cross secions for calculaion nuclear reacions and isoope producion Uilize he daing equaion for isoope pair 3-3

32 Sudy Quesions Compare and conras nuclear decay kineics and chemical kineics. If M is he oal number of couns, wha is he sandard deviaion and relaive error from he couns? Define Curie and Becquerel How can half-life be evaluaed? Wha is he relaionship beween he decay consan, he half-life, and he average lifeime? For an isoope he iniial coun rae was 890 Bq. Afer 80 minues he coun rae was found o be 750 Bq. Wha is he half-life of he isoope? A 0.50 g sample of 48 Cm has a alpha aciviy of mci. Wha is he half-life of 48 Cm? Wha is he half life for each decay mode for he isoope Bi? How are cross secions used o deermine isoope producion rae? Deermine he amoun of 60 Co produced from he exposure of g of Co meal o a neuron flux of 0 4 n/cm /sec for 300 seconds. Wha are he basic assumpions in using radionuclides for daing? 3-3

33 Pop Quiz You have a source ha is 0.3 Bq and he source is deeced wih 50 % efficiency. I is couned for 0 minues. Which oal couns shown below are no expeced from hese condiions? 95, 8, 73, 04, 90, 97, 87 Submi by or bring o class on 4 Sepember Commen on Blog 3-33

34 Useful projecs Make excel shees o calculae Mass or mole o aciviy Calculae specific aciviy Concenraion and volume o aciviy Deermine aciviy for couning Isoope producion from irradiaion Paren o progeny Daugher and granddaugher * i.e., 39 U o 39 p o 39 Pu 3-34