Radiochemistry: Decay of Protactinium-234m

Computer-Interfaced Experiments - Count rate Measurement

Radiochemistry
Decay of Protactinium-234m

Objectives: Determination of the Half-Life, Background Radiation

Peter Keusch

Datalogging using the Program POISSON and the Analog-Digital-Converter
CASSY-E - LEYBOLD DIDACTIC

German version

Apparatus:
Geiger-Mueller counter tube
isotope generator U-238 / Pa-234m (Producer: Müller & Sorensen, Danmark)
stop watch

Safety precautions: To avoid contamination if the isotope generator U-238 / Pa-234m should leak, this must be kept in a tray. Suitable gloves, a lab coat and safety glasses must be worn.

Theoretical background (Download PDF file)

Operation mode of the isotope generator U-238 / Pa-234m:

Fig. 1: Isotope generator
U-238 / Pa-234m The isotope generator consists of a small plastic bottle hermetically sealed by a thin-walled plastic cap (Fig. 1). Inside the container is an acidic, aqueous solution of uranyl nitrate and a ketone. In the aqueous layer a radioactive equilibrium between uranium-238 and its decay products is maintained (Fig. 2). This means that all rates of decay of the different nuclides within the sample are equal when radioactive equilibrium is achieved.
The gamma radiation is not intense. The alpha radiation is completely absorbed inside the generator - also the beta radiation is absorbed to a large extent. Therefore the counter tube aimed towards the surface of the plastic bottle measures only small pulse rates.

Fig. 2: Section of the uranium-238 decay chain

In the upper part of the plastic bottle (cap) is an organic layer (iso-butyl methyl ketone). The generator is activated by vigorously shaking. Shaking mixes the two immiscible liquids and allows the protactinium generated in the uranium layer to go into the organic phase. Due to the better solubility of the short-lived protactinium in organic solvents, the isotope is enriched in the ketone phase and rises to the top as the layers re-establish. The fade away of the nuclide can be followed using a Geiger-Mueller counter tube (Fig. 2). Only the high-energy beta particles from the decay of protactinium-234m are detected by the counter tube.

Experimental procedure:

Fig. 3: Schematic diagram of experimental apparatus

Determination of the background radiation

The Geiger tube is connected to the GM-Box plugged into the available input slots of CASSY INTERFACE.

Matching of the program 'Poisson':
- The menu item <F3>'Select gate time' permits the input of a recording time of 10 s.
- After switching to <F4>'Select max. n and x ® Select upper limit for n' the number of the measurements (n) e.g. 180 can be entered.

Measurement: The Geiger tube is placed in such a manner that the mica window is facing towards the wall of the inactivated generator. By pressing the function key <F1> the sensing software is started.

After data logging is completed, the mean value of the pulse rate (caused by the weak radiation of the isotope generator and by the zero effect) can be determined by means of
<F5 >'Output measured values ® Characteristic statistical data’.

By switching to <F6> 'Evaluate in graph' the poisson distribution is presented as a bar graph (Fig. 4).

Fig. 4: Poisson distribution determination of the background radiation

Data logging - Decay of Pa-234m

Matching of the program 'poisson':
- Under the menu item <F3 >'Select gate time' one enters a recording time of 10 s.
- After switching to <F4> 'Select max. n and x ® Select upper limit for n' the number of measurements (n) is fixed with 1.

Measurement: The generator is activated. When the layers re-establish the Geiger tube is adjusted such that the mica window is facing to the upper layer (organic phase) in the plastic cap (Fig. 3). The stop watch is started and after 30 seconds (this delay will allow time for the phases to seperate fully) the sensing software is started by pressing the function key <F1>. The data are logged at 20 s intervals with running stop watch. After a measured value is noted, a time of 10 s is reserved to switch into the main menu (by pressing the Escape button) and to note the measured number of the pulses. The start time of the measurement and the corresponding count rate are entered into a table. Afterwards one returns to the measuring menu. The measurements are continued until the count rate achieves a constant value.

Data analysis using Microsoft Excel

The data analysis is based on 8 measurement series. A mean value is calculated from the measured count rates. The average background radiation is substracted from the mean value of the experimental readings. The decrease of the measured variable is presented in a graph. Excel is used to draw a "best-fit" smooth exponential curve through the data points. The exponential trendline fits data to the expression y = A e ^{- kx} where k is the decay constant. The exponential equation can be displayed on the chart (Fig. 5).

Fig. 5: Decay curve plot of the corrected count rate against time - determination of half-life

Fig. 5 demonstrates a small deviation of the data points up to 200 s after the measurement was .

The value for the decay constant l (coefficient in front of x in the equation of the potential function) is 0.0097 s^-1. The half-life of Pa-234m can be calculated according to the following equation:
t_½ = ln2 / l = 71.5 s
The half-life can be also determined graphically as shown in Fig. 5.

Also a plot of lnN against time t permits the determination of the decay constant l (Fig. 6 ).

Zerfallskonstante

Fig 6: Determination of the decay constant

Datalogging using a contamination monitor:

In order to estimate the quality of the above measurement result, the determination of the radioactive half-life of Pa-234m was carried out using a lead container and a contamination monitor. Immediately after the generator had been placed in front of the Geiger tube, the sensing software was started. The measurements extended over a period of 5 minutes. The measuring interval was 5 seconds. Also this experiment was based on 8 measurement series, which were analysed using Microsoft Excel. The average background rate measured using the contamination monitor was substracted from the mean value of the count rate.

Fig. 7: Decay curve determination of half-life

Zerfallskonstante

Fig. 8: Plot of lnN against t

Fig. 7 and Fig. 8 show a atypical plateau caused by the incomplete separation of the two phases in the cap of the isotope generator within the first 50 seconds after the beginning of the measurement. From the equation of the exponential function y = 137.71e^-0.0097x or from the equation of the straight line y = -0.0097x + 4.9252 the half-life of 70.5 s can be determined. In the literature a half-life of 70.2 s is indicated.

Note:
· Both Pa-234m and Pa-234 are present in the organic phase. Up to a gate time of 200 seconds the pulses caused by the decay of Pa-234m are dominating. Afterwards the measured values deviate more strongly, because the decay of Pa-234 (t_1/2 = 6,7 h) emitting gamma and beta radiation affects more strongly.
· Moreover, measuring low count rates, statistical variation of the background radiation has a great influence.

References:
Half-life
Measuring the half-life of protactinium

Index of CASSY Experiments