Ge/Ch 127  Nuclear Chemistry                 Winter Term 2003

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Finding people:                                                                                               Updated: 2/24/03

 

Professor: Don Burnett

Office: 101 North Mudd (room to the left)

Phone: x6117

E-mail: burnett@gps.caltech.edu

Available: open office hours

 

 

TA: Sarah Miller

Office: 060 Arms

Phone: x3452

E-mail: smiller@gps.caltech.edu

Available:  Official office hours are 1-2 pm Monday, Wednesday, and Friday.  We can also arrange a mutually convenient time to meet if those don’t work for you.

 

Text: (Optional) Nuclear and Radiochemistry. Friedlander, Kennedy, Macias, Miller, 3rd ed., 1981.

            Since this is just a suggested reference text, the 2nd edition (1964) is also a good option and can be ordered

            from any number of on-line sellers for $5-10 if you feel so inclined.  Amazon’s $105.00 for the 3rd edition probably

            isn’t worth it.  The book is also available on reserve for this course in the Geology Library (2nd floor of North Mudd).

            If you want to have access to this library past 5:00 pm weekdays and on weekends, see me and we’ll get you

            special card access so you can enter North Mudd after-hours.

 

 

Homework:

5th assignment was handed out Thursday, February 20th.

DUE: Thursday, February 27th.

 

 

Hints: Problem Set 7

 

1.         a)         Cancel terms in M(Z,A) and M(Z/2,A/2) from the general expression Q = M(Z,A) – 2*M(Z/2,A/2) to show surface energy and Coulomb energy dependence.

b)                  Just use Z and A for 236U* in the equation above for the Q of symmetrical fission.

c)                  Consider plotting Z vs. A and N vs. A for fission fragments for which N/Z is conserved and for values of beta stability (i.e., equation for minimum of stable beta parabola with A ranging from 75 to 150).

d)                  The natural abundances of these Xe isotopes are also a good clue.

 

2.                  b)  How can we tell from the nuclide chart that 248Cm is on the line of b stability?

c)      If you’re having trouble envisioning how isotope dilution can be used to measure specific activity, check out p. 432 of Friedlander, Kennedy, Macias, and Miller [3rd ed.].

3.         a)  Don’t forget to use the Enge energy level diagram found on page 21 of the 2/18/03 notes (for class consistency).  Further discussion of the Shell Model may be found starting p. 379 of the Friedlander et al. [3rd ed] text.

 

4.                  a)  Just follow the principal (top entry) decay modes starting at the blank box that would be 241U (assume a beta decay to 241Np and you’re off!).

b)            Now work backwards for each of the isotopes through the (top entry) alpha and beta decays that produce them…and their parents…and their parents….  This is mostly just bookkeeping.  If you can find a complete Chart of the Nuclides that hasn’t been segmented into a book, this exercise becomes much quicker.  I think Don has one, and there’s a complete chart posted to a bulletin board in the Arms 251 classroom.  You can get there by turning right out of our North Mudd 212 classroom, going across the outdoor walkway, and 251 is the first door on your left.  How many values of A are contributing to 235U, 238U, and 232Th in your decay chains?

 

5.         Note that we are given initial ratio proportions of the ratios of interest.  Calculate how those ratios will change over the time interval between the formation of the galaxy and the formation of the solar system.  Remember back to our work with radioactive decay in Problem Set 1.

 

 

 Problem Set 6

 

1.                  a)  Ion beam energy is equal to the charge difference of the ions before and after the electron stripping  encounter with the N2 gas multiplied by the accelerating potential.

b)      If there are 106 10Be atoms in the sample and we’ve also separated out 1 mg of pure 9Be, what is 10Be/9Be?

c)      One hour of analysis produces a useful yield of 1/104 (number detected/number in sample).  Solve for time from the decay of 106 radioactive 10Be atoms to a number of decays equal to the useful yield number for the hour-long analysis. 

d)      Remember range ratio equation: R ratio = (m1/z12)*(z22/m2).

e)      Again, more range scaling.

 

2.   a)  Build the 4He nucleus and solve for Q:   2 p  +  2 n à 4He + Q

b)      Set Qa equal to BE(A) – BE(A-4) and solve for A.

 

3.   More binding energy calculations. 

 

4.  The 12th page of the 2/13/03 class notes discuss the isobaric form of the liquid drop equation.  Constants may be found on the back of the 8th page.  Not so hard, but lots of little calculations.

     

           

 

Problem Set 5

 

  1. a) Refer to the 2/6/03 notes on the electron capture Q-M relation

b) Same concept.  Remember reaction notation-ex., 56Fe(a,g) is 56Fe + a à 60Ni + g

  1. Use the Hf isotope that would be most difficult to resolve as HfO2+ from 206Pb.  Don’t forget to convert

from MeV to amu.  You can also do this calculation using just the masses and not the mass defects; the difference

between the two methods is only 1.2*10-6.

  1. a. Q2b= ?  Since E = mc2, what is m here?

     “Justify” = just calculate the energy and note that the sign is positive (energy released)

      b. Given: there are 104 atoms of 130Xe.  How many atoms of 130Te in 1 kg of Te?  Consider the number of

      130Te atoms to have remained constant (more or less) over the time period of interest.  

  1. Assume natural isotope abundances of K as listed in Chart of the Nuclides.  If you feel you’d like more information

on isotope dilution, check out p. 28-31 of Dickin (1995, Radiogenic Isotope Geology).

5.  What are the possible mass (isotopic) configurations of Br2+ ions and what are the relative amounts of each      configuration?

 

 

Problem Set 4

 

1.      a) Solve for the desired energy of the x-ray, which would be the sum of which energies?

c) Start with the Al K x-ray energy and determine the range of detectable L-shell binding energies.

2.      Remember to alter the mass used in the ‘H-like atom’ equations to fit the particle relevant to the subproblem.

3.      a) Another instance of collimated beam attenuation.

 

Problem Set 2

 

  1.  How precise do we need the background measurement to be?
  2. Remember, we only care about the “to 210Bi ground state” cross-section.
  3. A.      What are the proportions of 235U and 238U in U ore?

B.     a.  What is the density of the Pb target?

b.      “Show”  = “Derive” here.

4.  Consider in terms of a collimated beam and exponential adsorption.

5.  You can compare your results to those of the article “Krypton and xenon in some lunar samples and the age of the North Ray Crater” K. Marti, B. D. Lightner, and T. W. Osborn. Proceedings of the Fourth Lunar and Planetary Science Conference (March 1973), v. 2, p. 2037-2048.

 

 

Problem Set 1

 

Your lifetime for  #1 should be on the order of nanoseconds.

If you’d like to read some additional context for problems 2 and 3 (especially), check out this reference:

Radiogenic Isotope Geology. Alan P. Dickin. 1995.   Don suggests linearizing part b of #3, so the ratio of the Th-230 and U-238 activities is = time/t230, instead of = 1-exp(-l230*time).