1 / 34

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 .

viveka
Download Presentation

Quiz 1

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related