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Quiz 1

Quiz 1. (5 Points) Provide a route for the production of 238 Pu? 5 point bonus: What is the use of this isotope? Give an example of where it has been used .

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Quiz 1

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  1. Quiz 1 • (5 Points) Provide a route for the production of 238Pu? 5 point bonus: What is the use of this isotope? Give an example of where it has been used. • (5 Points) Below is a mass parabola from the table of the isotopes for A=40. Use this figure to show which isotopes of A=40 are stable?

  2. Quiz 1 • (15 Points) Identify the daughter and the decay mode for the following isotopes

  3. Quiz 1 • (5 Points) Provide the number of naturally occurring isotopes for the elements below. This includes long lived radioactive isotopes

  4. Quiz 1 • (5 Points) Provide the spin and parity of the following isotopes

  5. Quiz 1 • (10 Points) Provide the cumulative fission yields for the A isobars from 233U, 235U, and 239Pu.

  6. Quiz 1 • (10 Points) Provide the decay constants (in s-1) for the following isotopes • (5 Points) List the 4 stable odd-odd isotopes

  7. Quiz 1 • (15 Points) Determine the Q value for the following reactions • (10 Points) Calculate the mass of 1 mL of nuclear matter. Base the calculation on an 56Fe nucleus, with ro = 1.3 fm to determine the radius of 56Fe.

  8. Quiz 1 • (5 Points) Please provide the gamma decay intensities for the data below • (10 Points) What is nuclear skin thickness? How can one measure nuclear radii?

  9. CHEM 312: Lecture 3Radioactive Decay Kinetics Outline • Readings: Modern Nuclear Chemistry Chapter 3; Nuclear and Radiochemistry Chapters 4 and 5 • Radioactive decay kinetics • Basic decay equations • Utilization of equations • Mixtures • Equilibrium • Branching • Cross section • Natural radiation • Dating

  10. Expected Standard Deviation • Solve with: • Apply to radioactive decay • M is the number of atoms decaying • Number of counts for a detector • Relative error = s-1 • What is a reasonable number of counts • More counts, lower error

  11. Important Equations! • Nt=Noe-lt • N=number of nuclei, l= decay constant, t=time • Also works for A (activity) or C (counts) • At=Aoe-lt, Ct=Coe-lt • A= lN • 1/l=1/(ln2/t1/2)=1.443t1/2=t • Error • M is number of counts

  12. Half-life calculation Using Nt=Noe-lt • For an isotope the initial count rate was 890 Bq. After 180 minutes the count rate was found to be 750 Bq • What is the half-life of the isotope • 750=890exp(-l*180 min) • 750/890=exp(-l*180 min) • ln(750/890)= -l*180 min • -0.171/180 min= -l • 9.5E-4 min-1=l=ln2/t1/2 • t1/2=ln2/9.5E-4=729.6 min

  13. Half-life calculation A=lN • A 0.150 g sample of 248Cm has a alpha activity of 0.636 mCi. • What is the half-life of 248Cm? • Find A • 0.636 E-3 Ci (3.7E10 Bq/Ci)=2.35E7 Bq • Find N • 0.150 g x 1 mole/248 g x 6.02E23/mole= 3.64E20 atoms • l=A/N= 2.35E7 Bq/3.64E20 atoms=6.46E-14 s-1 • t1/2=ln2/l=0.693/6.46E-14 s-1=1.07E13 s • 1.07E13 s=1.79E11 min=2.99E9 h=1.24E8 d =3.4E5 a

  14. Counting A=lN • Your gamma detector efficiency at 59 keV is 15.5 %. What is the expected gamma counts from 75 micromole of 241Am? • Gamma branch is 35.9 % for 241Am • C=(0.155)(0.359)lN • t1/2=432.7 a* (3.16E7 s/a)=1.37E10 s • l=ln2/1.37E10 s=5.08E-11 s-1 • N=75E-6 moles *6.02E23/mole=4.52E19 atoms • C=(0.155)(0.359)5.08E-11 s-1*4.52E19 =1.28E8 counts/second

  15. Mixtures of radionuclides • Composite decay • Sum of all decay particles • Not distinguished by energy • Mixtures of Independently Decaying Activities • if two radioactive species mixed together, observed total activity is sum of two separate activities: At=A1+A2=1N1+2N2 • any complex decay curve may be analyzed into its components • Graphic analysis of data is possible l=0.554 hr-1 t1/2=1.25 hr l=0.067 hr-1 t1/2=10.4 hr

  16. Parent – daughter decay • Isotope can decay into radioactive isotope • Uranium and thorium decay series • Alpha and beta • A change from alpha decay • Different designation • 4n (232Th) • 4n+2 (238U) • 4n+3 (235U) • For a decay parent -> daughter • Rate of daughter formation dependent upon parent decay rate- daughter decay rate

  17. Parent-daughter • Integrate over t • Multiply by e-l2tand solve for N2 Initial daughter Growth of daughter from parent

  18. Parent daughter relationship • Find N, can solve equation for activity from A=lN • Find maximum daughter activity based on dN/dt=0 • Solve for t • For 99mTc (t1/2=6.01 h) from 99Mo (2.75 d), find time for maximum daughter activity • lTc=2.8 d-1, lMo=0.25 d-1

  19. Many Decays • Can use the Bateman solution to calculate entire chain • Bateman assumes only parent present at time 0 Program for Bateman http://www.ergoffice.com/downloads.aspx

  20. Branching decay • Branching Decay • partial decay constants must be considered • Isotope has only one half life • if decay chain branches and two branches are later rejoined, branches are treated as separate chains • production of common member beyond branch point is sum of numbers of atoms formed by the two paths • Branching ratio is based on relative constants • li/lt is the % of the decay branch

  21. Branching Decay • For a branching decay of alpha and beta • lt=la+lb • Branching ratio = li/lt • 1=la /lt+lb /lt • Consider 212Bi, what is the half life for each decay mode? • Alpha branch 36 %, beta branch 64 % • t1/2=60.55 min • lt=0.0114 min-1; 0.36=la /lt; 0.36=la /0.0114 min-1la=0.0041 min-1 • t1/2alpha = 169 min • lt=la+lb; 0.0114 min-1 =0.0041 min-1 +lb; 0.0073 min-1 =lb • t1/2beta = 95.0 min

  22. Cross sections • Accelerator: beam of particles striking a thin target with minimum beam attenuation • When a sample is embedded in a uniform flux of particles incident on it from all direction, such as in a nuclear reactor, the cross section is defined: • Ri= # of processes of type under consideration occurring in the target per unit time • I= # of incident particles per unit time • n= # of nuclei/cm3 • x=target thickness (cm) • =flux of particles/cm2/sec • N=number of nuclei contained in sample 10-24 cm2=1 barn

  23. Production of radionuclides • s=cross section • f=neutron flux • t=time of irradiation • (1-e-(lt)) • maximum level (saturation factor) • Activity of radioactive product at end bombardment is divided by saturation factor, formation rate is obtained • R=A/(1-e-(lt))

  24. Nuclei production: Short irradiation compared to half-life • Find amount of 59Fe (t1/2=44.5 d, l = 1.803E-7 s-1) from irradiation of 1 g of Fe in a neutron flux of 1E13 n/cm2/s for 1 hour • 58Fe(n,g)59Fe: 58Fe+ n g + 59Fe s=1.3E-24 cm2 • No= 1g/55.845 g/mol *6.02E23 atom/mol*0.00282 • No=3.04E19 atom • R= 1E13 n/cm2/s *1.3E-24 cm2 * 3.04E21 atom • R=3.952E8 atoms/sec • 1.423E12 atoms 59Fe in 1 hour

  25. Nuclei production: Long irradiation compared to half-life • Find amount of 56Mn (t1/2=2.578 hr, l = 7.469E-5 s-1) from irradiation of 1 g of Mn in a neutron flux of 1E13 n/cm2/s for 1 hour • 55Mn(n,g)56Mn: 55Mn+ n g + 56Mn s=13.3E-24 cm2 • No= 1g/54.93804 g/mol *6.02E23 atom/mol • No=1.096E22 atom • R= 1E13 n/cm2/s *13.3E-24 cm2 * 1.096E22 atom • R=1.457E12 atoms/sec • 5.247E15 atoms 56Mn in 1 hour (does not account for decay)

  26. Formation rate from activity • R=A/(1-e-(lt)) • 4.603E15 atoms 56Mn (t1/2=2.578 hr, l = 7.469E-5 s-1) from 1 hour irradiation • A=lN= 4.603E15* 7.469E-5 =3.436E11 Bq • R=A/(1-e-(lt)) • R= 3.436E11/(1-exp(- 7.469E-5 *3600)) • R=1.457E12 atom/sec

  27. Dating • Radioactive decay as clock • Based on Nt=Noe-lt • Solve for t • N0 and Nt are the number of radionuclides present at times t=0 and t=t • Nt from A = λN • t the age of the object • Need to determine No • For decay of parent P to daughter D total number of nuclei is constant

  28. Dating • Pt=Poe-lt • Measuring ratio of daughter to parent atoms • No daughter atoms present at t=0 • All daughter due to parent decay • No daughter lost during time t • A mineral has a 206Pb/238U =0.4. What is the age of the mineral? • 2.2E9 years

  29. Dating • 14C dating • Based on constant formation of 14C • No longer uptakes C upon organism death • 227 Bq 14C/kgC at equilibrium • What is the age of a wooden sample with 0.15 Bq/g C?

  30. Dating • Determine when Oklo reactor operated • Today 0.7 % 235U • Reactor 3.5 % 235U • Compare 235U/238U (Ur) ratios and use Nt=Noe-lt

  31. Topic review • Utilize and understand the basic decay equations • Relate half life to lifetime • Understand relationship between count time and error • Utilization of equations for mixtures, equilibrium and branching • Use cross sections for calculation nuclear reactions and isotope production • Utilize the dating equation for isotope pair

  32. Study Questions • Compare and contrast nuclear decay kinetics and chemical kinetics. • If M is the total number of counts, what is the standard deviation and relative error from the counts? • Define Curie and Becquerel • How can half-life be evaluated? • What is the relationship between the decay constant, the half-life, and the average lifetime? • For an isotope the initial count rate was 890 Bq. After 180 minutes the count rate was found to be 750 Bq. What is the half-life of the isotope? • A 0.150 g sample of 248Cm has a alpha activity of 0.636 mCi. What is the half-life of 248Cm?  • What is the half life for each decay mode for the isotope 212Bi? • How are cross sections used to determine isotope production rate? • Determine the amount of 60Co produced from the exposure of 1 g of Co metal to a neutron flux of 1014 n/cm2/sec for 300 seconds. • What are the basic assumptions in using radionuclides for dating?

  33. Pop Quiz • You have a source that is 0.3 Bq and the source is detected with 50 % efficiency. It is counted for 10 minutes. Which total counts shown below are not expected from these conditions? • 95, 81, 73, 104, 90, 97, 87 • Submit by e-mail or bring to class on 24 September • Comment on Blog

  34. Useful projects • Make excel sheets to calculate • Mass or mole to activity • Calculate specific activity • Concentration and volume to activity • Determine activity for counting • Isotope production from irradiation • Parent to progeny • Daughter and granddaughter • i.e., 239U to 239Np to 239Pu

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