CINCH NucWik

Tor Bjørnstad
Section of Radiochemistry
Institute of Chemistry
Faculty of Mathematics and Natural sciences
University of Oslo

1. Understand mother-daughter relations and radioactive equilibrium
2. Understand how a radio-nuclide generator works and how it is used
3. Understand how radioactivity is "growing in"
4. Training in handling radioactive material and safety procedures

The task in this Laboratory Exercise is to record a disintegration curve of ^234mPa and from this curve determine the half-life of the nuclide.
The ^234mPa radionuclide is obtained from a generator system consisting of an ion exchanger column with fixed ²³⁴Th where the daughter is milked by a liquid elution process.
The α particles from the produced ^234mPa-source is recorded by a GM-detector.

The principle behind Mother-Daughter Relationship is illustrated below.

Basic Theory

A radionuclide generator, also popularly called a “cow”, is composed of a mother-daughter radionuclide relationship where the mother has a longer half-life than the daughter. The daughter is continuously produced by decay of the mother in the generator system, and the daughter can be separated (“milked”) from the generator by chemical or physical methods. In this Exercise we are going to use one such system defined in more detail below. From basic lectures on decay we have the following relation between a radioactive nuclide and its radioactive daughter:

where D₂ is the amount of the daughter species, λ₂ is the decay constant of the daughter, λ₁ is the decay constant of the mother, t is the time. If λ₁ « λ₂, i.e. the half-life of the daughter is much shorter than the half-life of the mother, we have:

If the growing-in time t on the generator in (2) is much longer than the half-life of the daughter (T½,2), the exponent will go towards the limit of 0.
This again results in the fact that the disintegration rate of the daughter equals the disintegration rate of the mother on the generator, i.e. the maximum activity that can be produced of the daughter on the generator equals the activity of the mother.
Expressed in mathematical terms for (2):

At this situation we say that we have obtained radioactive equilibrium in the generator system. A practical equilibrium is defined to be reached when t ≤ T½ where D₂ ≤ 0.999 • D₁.

Practical Approach

In general, it is not practical to wait until radioactive equilibrium has been reached before utilizing the generated daughter activity in laboratory experiments.

By using that λ₂ = ln2 / T½,2 and setting t= T½,2 into (2),
we obtain:

i.e. we have obtained 50% of the maximum obtainable activity already after a growing-in time of one daughter half-life.

The Fig. below illustrates how the activity of the daughter increases as a function of the growing-in time in units of T½,2. In the lab exercise where we made a calibration source from uranium, we used the grandaughter of ²³⁸U (as U₃O₈) to get a high-energy beta emitter.
The first part of the ²³⁸U natural radioactive series may be written as:

We observe that this part of the series gives possibility for two generator systems, i.e. ²³⁸U ⇒ ²³⁴Th and ²³⁴Th ⇒ ^234mPa. The first is not practical in short laboratory exercises because of the relatively long half-life of the daughter (24 d), but the second system is suitable.

1. Make a 0.1 M solution of uranyl nitrate or acetate.
2. Use 0.5 mL of the uranyl solution per cartridge. Use a syringe to push the solution through the cartridge.
3. Wash the cartridge using 1.0 M HCl. After 2 mL check with NaAc+ K₄(Fe(CN)₆) if there is any precipitate uranium precipitate.
4. Wash the chloride away with 0.5 M citric acid. After 2 mL, check with silver nitrate if there is any chloride precipitation.
5. Wait X min for the ingrowth. How many minutes are needed?
6. Push 2 mL of citric acid through the cartridge, insert the aluminum counting-vessel into the GM counter and measure the decay of the Pa.
7. After this push 2 mL of citric acid through the cartridge, insert the cartridge into the GM counter measure the ingrowth of Pa.

For this part of the exercise, you will use a GM-probe connected to a simple counter to determine the disintegration rate of ^234mPa. Before you get your sample, make sure you know exactly what to do.
Test the counting procedure without a sample to ensure that this is the case.

1. Make a good background measurement, i.e. use a long counting time (at least 30 min). It would be smart to start the background measurement before you prepare the radionuclide generator, as this will take at least one hour. Then you can start directly with the ^234mPa measurements once the generator is ready.
   
2. Select a preset counting time of 60 s. Make a table in which you can write down your results.
3. Get a stopwatch and learn how to use it.
4. You will count your sample repeatedly in 60 s intervals in order to get the disintegration curve for ^234mPa. Between each interval a break of 30 s is recommended for writing down the result, clearing the spectrum/counter and prepare for the next measurement. Make sure you write down the exact time you start each counting - do not cheat to fit your planned schedule, write down the actual time!
5. Write down the total number of counts in the spectrum for each measurement.
6. Repeat the 60 s counting until there is no more ^234mPa left, then do a 600 s background measurement (remember to change the preset counting time).
7. Repeat the measurement so you get two complete disintegration curves for ^234mPa.
   

Introduction

For this part of the exercise, you will use a NaI detector connected to a Multi-Channel Analyzer (MCA) to determine the disintegration rate of ^234mPa. An alternative and more direct, but "old-fashion" method, is to use a GM-tube connected directly to a simple counter. If you look at the radiation from ^234mPa (look it up in your nuclear chart!) you will notice that ^234mPa only emits very weak gamma-rays. However, due to the high-energy beta-particle we can still measure ^234mPa since this high-energy particle will be able to penetrate through the protective shield around the NaI and interact with the NaI crystal. Alternately, we could mount e.g. a plastic detector (NE 102A or similar) on a PM-tube and use this instead.
The results will largely be the same (but the NaI is more sensitive to gamma-background, which adds uncertainty to the background subtraction).

Principle

This description assumes you have the Maestro MCA software from ORTEC. If you are using an alternative system, you will have to consult the manual to figure out how to use it. The procedure should not be very different, though.
We want to make successive 60 s measurements to determine the half-life curve of ^234mPa.
This can be done manually by successive starting-waiting-stopping-saving-clearing operations.
However, with a modern system this tiresome procedure can be automated.
In Maestro jargon you do this by preparing a job-description file (it would be called a script file or batch file in most other software): this file contains all the instructions you would have to execute, but can be simplified by using the built-in loop structure. Furthermore, once running, it will execute the correct commands at exactly the right time.
Since the commands execute very rapidly, you will also be able to spend practically all the time during the ^234mPa decay actually counting, something which is not possible if you are doing everything manually.

Job-description file:

set_preset_real 60
loop 15
clear
start
wait
save m:\spectra\KJM5911_D130_A???.chn end_loop
set_preset_real 300
clear
start
wait
save
m:\spectra\KJM5911_D130_Background.chn

Notice that we have added a 5-min measurement to check for residual activity after the ^234mPa has decayed.
Any residual activity would be from break-through of ²³⁴Th from the column.

Procedure

Contrary to a simple counting system, the MCA will save spectra containing counts vs. energy. Since we are measuring beta particles, the spectra do not contain specially interesting information and we will simply sum up all the counts in the spectrum and use this number for the decay curve.

The procedure for measuring the ^234mPa decay is as follows:

1. Measure a background spectrum for as long as possible (e.g. during preparation of the radionuclide generator). Remember to save the spectrum and the file name!
2. "Milk" 20 drops into a sample cup from the generator as quickly as possible. Use a stopwatch and start it at the 10 drop.
3. Put the sample cup on the detector (you should protect the detector surface with a thin plastic sheet to avoid contamination etc.).
4. Start the job-file and note down the time difference between milking and starting. Now, sit back and relax! Alternatively (better), if the job-file is saving spectra to a network disk, you can analyze the spectra as they are produced (using another pc which can read the same disk).
5. When the job-file finishes, repeat the measurement. (Remember to rename or move your spectra, otherwise they will be deleted or the job-file stops.)
   

From the spectra, you should get the following data (by opening each spectrum in Maestro): the measurement start time and the gross count (total number of counts in the spectrum).
Use the "sum" command to get the total number of counts (the spectrum must contain no region-of-interest markings).

Use a high-quality data plotting and fitting program (e.g. Origin) to analyse the data. The fitting must take the uncertainty into account (do not use Excel), otherwise you will get the wrong result. Notice that you always shall use the 1/3 of the time into each measurement as the "middle time point". This is due to decay - after 1/3 of the time you will have equally many counts before and after the 1/3 point (i.e. it is the "middle point".

1. For each datapoint calculate the net count (gross count - background count), the uncertainity of the net count (based on uncertainity of both the gross count and the background count). You might want to use e.g. MS Excel or similar for doing this.
2. Enter your data in a table ("worksheet" in Origin jargong): Include measurment time (relative to start of sampling) as x-value, the net count as y-value, and the uncertainity as y-error.
3. Plot the data. Does it look ok?
4. Use the Origin data-fitting functionality to determine the measured half-life and associated uncertainity.

Alternative/Extra: Plot the gross counts instead of the net counts and ask Origin to fit both the background and the decay.

• Chemical safety - nothing particularly dangerous, 1 M HCl and 0.1 M AgNO₃ should of course be handled according to normal safety precautions. DOWEX residues and waste should be collected and handled according to normal procedures.
• Radiation safety - very small amounts of uranyl nitrate is used, so radiation safety is mostly about regulations and not a real health hazard. Remember to collect the Dowex from the ion-exchange columns in separate containers as it is contaminated with 24-day ²³⁴Th (will be inactive after one year).

The equipment needed should be ready. The solutions needed should also be prepared. It is usually a good idea to not use to large columns as the time needed for the solution to pass through the Dowex will increase quite a lot with increased volume.

• ^234mPa nuclide generator
• HCl (MSDS) on 100 mL flasks, one for each student.
• Dowex 50x4 (MSDS) (50-100 mesh).
• Uranyl Nitrate (MSDS) - UO₂(NO₃)₂.
• NaAc (MSDS) + K₄[Fe(CN)₆]] (MSDS) solution (on 100 mL flasks, one for each student), prepared by mixing 8 g of NaC₂H₃O₂ and 40 g of K₄[Fe(CN)₆] in 1 L water.
• 10% citric acid (MSDS) (on 100 mL flasks, one for each student).
• 0.1 M AgNO₃ (MSDS) (on 50 mL flasks).
• Suitable columns which can be fitted with a stopper connected to a rubber ball so it can be pressurized (to quickly elute drops with short lived ²³⁴Pa from the column).
• Stop watches (one for each student).
• Sample holders to catch eluted drops from the column and which can be mounted conveniently in the detector chamber.
• Detectors - GM counters works well, but we have also used plastic scintillators mounted on PMTs and NaI-detectors. High efficiency is necessary to get good counting statistics even after the first 5-6 minutes.