KJM5900 - Autumn 2004

KJM 5900 Exercise 10: Neutron Activation Analysis.

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Introduction

In this exercise you will calculate yields for neutron activation analysis (NAA) of different samples. Each student will get her or his individual sample to perform calculations on. The individual sample descriptions will include what kind of sample (e.g. a piece of iron) and which elements you are looking for in your particular sample. Your task is to choose the best possible isotopes of each element which are to be determined and optimise irradiation time, "cooling-off" time and measurement time in order to determine the amount each of the given elements. You will need to consider a range of parameters, among them are half-life, cross-section, isotopic abundance, gamma-ray intensity, detector efficiency, etc. You also need to consider how the other elements present in the sample might affect your measurement: I.e. if your chosen irradiation time, etc. produce 10.000 times more activity from the sample material than from the element you are trying to determine it will not be possible to measure it!


Learning Goals:

  1. To understand how NAA is performed.
  2. Understand how irradiation time, cooling-off time and measurement time affect your ability to produce and measure radioactivity.
  3. Understand how gamma-intensity affect your ability to measure radioactivity.
  4. Training in organising complex set of calculations.
The theory behind this exercise you should know by now, but you might want to freshen your memory by reading e.g. chapter 8.5 in Lieser.


"Mappe" Exercise

This exercise is the third "Mappe" exercise. I.e. it will be graded and counts 10% on the determination of your final grade. Be aware that you must be prepared to explain your choices and calculations made in this exercise during the final, oral examination.

You are free to use any help you find useful in performing the exercise. This includes discussions with fellow students - something we highly recommend! But do make sure you thorougly understand how you obtain your answers! The criteria which will be used to grade this exercise is explained at the end of this document, in appendix A.

Your sample description will be e-mailed to you on Wednesday morning around 8 o'clock. The deadline is Friday at 4 PM sharp (the dates for Wednesday and Friday are given on the main exercise web-page). Submitting your answer after 4:00 PM imply that you fail on this part. (But you are still required to submit an answer to the exercise, as this is a requirement to qualify for presenting yourself for the final oral examination.)

Aids needed

                            efficiency = 10-2*log (Energy) + 2

          or read the numbers of the equivalent graph linked here.
          For gamma-energies below 100 keV the formula do not work and you must use the plot.


Exercise tasks

Please be certain to observe the following assumptions and restrictions:
  1. Irradiation time must be longer than one (-1-) minute.
  2. Cooling-off time can be 0 (i.e. we can use an automated and rapid sample transport between irradiation position and measurement position). The cooling off time must be shorter than one month. ["cooling off" time means the time you store your sample between end of irradiation and start of measurement]
  3. Measurement time must be longer than one (-1-) minute, and less than one day.
  4. Assume you plan to use a NaI gamma-detector for your measurements. Thus the number of counts of a gamma-line you want to measure must either be: a) More intense than any other peak in the spectrum with a factor of 10 or b) Not weaker than one-fifth of any other gamma-peak in the spectrum and separated from it by at least 200 keV.
  5. We only consider gamma rays listed in the nuclear chart. If it is listed within parenthesises it means it's very week and you can ignore it.
  6. To calculate the number of counts during a measurement one integrates the decay curve for the duration of the measurement. As this takes some time and mathematic skills, we make the following simplification: The number of counts measured is assumed to be equal to the count rate 1/3 into the measurement period multiplied with the duration of the measurement period. E.g. if you have calculated (with the ordinary disintegration formula) that 100 seconds into a 300 seconds measurment the activity is 25 cps, the number of counts measured is 300 seconds times 25 cps = 750 counts. [This simplification results in that a measurement period significantly longer than the half-life will give you zero counts (make sure you figure out why!). In reality you would have got a number of counts during the first part of your measurement, but then as the activity died and you continue to measure the background (and any longer lived activity which might have been produced), these counts will "drown".]
  7. We only consider nuclei with half-lives longer than one (-1-) minute.
  8. Assume that each of the elements to be determined in your sample are present in the amount of 10 micro-grams (10-6 g).

Task 10A: Calculation of Amount of Activity after a Specific n-irradiation

Calculate the amount of activity of nuclide A you would get if you irradiate your sample with 1013 thermalised neutrons per cm2 per second for 30 minutes, with a cooling-off time of 10 minutes.


Task 10B: Calculation of Count Rate for the Activity Produced in Task 10A

Calculate how many counts you would get when measuring the activity produced in task 10A  for a reasonable counting time (explain your choice of counting time). Use the efficiency calibration values  from the plot or formula given in the "Aids" section.


Task 10C: Which Elements can be Determined?

Which of the elements indicated to be present in your sample (in 10 micro-gram amounts) can be determined with a neutron source yielding 109 n/cm2s thermalised neutrons? And if you use a source yielding 1013 n/cm2s thermalised neutrons?


Task 10D: Optimise Irradiation Time, Cooling-off Time and Measurement Time

Suggest irradiation, cooling-off and counting times you could use to measure the elements present in your sample if you have a 1013 n/cm2s thermalised-neutron source. You are allowed to irradiate and/or measure the sample several times, if you want to.


Hints and Guidance

You can perform the necessary calculations using an ordinary calculator, but this is tedious and error prone. You would probably be much better of if you use a spread sheet (like Excel) or write a small program or calculation script (e.g. in C or in the script/programming languages of the more advanced calculators).

When you write your answers, you must make certain that you document how each calculation was performed. However, you are not required to write the intermediate results for each calculation when they are of the same type. In fact, this will probably result in that you loose points with respect to how "good and clear" your presentaion is (see Appendix A).  Good use of tables is probably the best way to organise your answers.

You are allowed, but not requieded, to perform several irradiations, with different irradiation, cooling-off and measurement times. The choice is yours and you should clearly state why you made the different choices.

You are not required to write a complete report for this exercise. Answer the questions as you would have this been questions in a written exam.


Appendix A: Criteria for grading

Each task (10A to 10D, four in all) will earn you up to 5 points - 5 points imply you have made the calculation correctly, used the correct assumptions and made the right choices. The points for each task is awarded according to the following rules: Correct answer - 1 point; Correct formula - 1 point; Correct selection of parameter values - 1 point; Correct argument for selection of parameter values - 1 point; Good and clear presentation of how you solved the task (i.e. sensible tabulation of numbers, well laid out logic, etc.)  - 1 point.

Finaly the overall impression of your answers seen as a whole will be judged on a scale of 0 to 5: 5 being awarded for a concise, clearcut and well laid out answer. 0 will be given to - well, you can figure that one out yourself.... The number of overall points will not be higher than the lowest score on any individual task. Thus, if you have scored 5, 4, 4, and 3 on the individual tasks, the overall score will be 3 and you end up with 19 out of a possible of 25. If you had scored 4 on all four individual tasks, the overall score would be 4 and you would have got 20 out of a possible 25.

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Last updated 16. November 2004 by Jon Petter Omtvedt