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
Parent isotope
Decay mode
Daughter Isotope
210Po
196Pb
204Bi
222At
99mTc
99Tc
14C
239Pu
261Rf

3. Quiz 1
(5 Points) Provide the number of naturally occurring isotopes for the elements below. This includes long lived radioactive isotopes
Element
Number of Stable Isotopes Re V K La Sn Sb In H Pm Lr

4. Quiz 1
(5 Points) Provide the spin and parity of the following isotopes
Isotope
Spin
Parity
242mAm
239Pu
240Pu
119mSn
65Ni
99Tc
242Am
179mHf

5. Quiz 1
(10 Points) Provide the cumulative fission yields for the A isobars from 233U, 235U, and 239Pu. A
233U
235U
239Pu
116 95 72
160 99

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
Isotope
l (s-1)
50Ca
81Zn
95Zr
137Cs
151Sm
241Am
242Pu

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.
Reaction or decay
Q value (MeV)
Alpha decay of 239Pu
45Sc + 4He5H+44Ti
b- decay of 137Cs
n+ 235U232Th+α
n+ 235U236U
EC of 192Hg
Formation of stable Au from bombarding 208Pb with a proton

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?
Isotope
Gamma Energy (keV) %g
46Sc
1120.5
103Ru
497.1
198Au
411.8
241Am
59.1
152Eu
121.8
1408.0
344.3

9. CHEM 312: Lecture 3 Radioactive 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
Counts
error
% error 10
3.16
31.62
100
10.00
1000
10000
100.00
1.00

11. Important Equations! 1/l=1/(ln2/t1/2)=1.443t1/2=t Error
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 g sample of 248Cm has a alpha activity of 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-l2t and 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

20. Branching decay li/lt is the % of the decay branch
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= min-1; 0.36=la /lt; 0.36=la / min-1 la= min-1
t1/2 alpha = 169 min
lt=la+lb; min-1 = min-1 +lb; min-1 =lb
t1/2 beta = 95.0 min

22. Cross sections 10-24 cm2=1 barn
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))
half life % 1 50 2 75 3
87.5 4
93.75 5
96.875

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/ g/mol *6.02E23 atom/mol*
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/ 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= 3.436E11/(1-exp( E-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 g sample of 248Cm has a alpha activity of 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 or bring to class on 24 September
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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