Half life and radioactive equilibrium
TEP
Related topics
Parent substance, daughter substance, rate of decay, disintegration or decay constant, counting rate,
half life, disintegration product.
Principle
The half-life of a Ba-137 m daughter substance eluted (washed) out of a Cs-137 isotope generator is
measured directly and is also determined from the increase in activity after elution.
Equipment
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1
1
1
1
1
1
(1)
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1
Geiger-Müller counter
Unit-construction plate for radioactivity
Counter tube holder, magnet hold
Plate holder, magnet hold
Source holder, magnet hold
Counter tube, type A
Screened cable, BNC, l = 75 cm
Test tube, d = 12 mm, l = 100 mm
Rubber stopper, 14.4/20 without hole
Isotope generator Cs-137/Ba, 400 kBq
13606-99
09200-00
09201-00
09203-00
09202-00
09025-11
07542-11
36307-10
39253-00
09047-60
Fig. 1: Experimental set-up for measuring the decay of the daughter substance.
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Half life and radioactive equilibrium
Tasks
1. Measure the activity of the isotope generator as a function of time immediately after elution.
2. Measure the activity of a freshly eluted solution of Ba-137 m as a function of time.
Set-up
Set up the experiment as shown in Fig. 1.
Procedure
Activate the ”Radioactivity” program module, and start the measurement stand-by phase (cf. Fig. 2).
Measure the background radiation without the radiation source.
To do this, it is advisable to use a gate time of more than 500 s.
The measured background rate remains in the Cobra3’s
memory until it is overwritten by a new background measurement.
Diagram settings for recording the decay curve.
y axis: 0 to 100
x axis: 0 to 700 s
Perform elution of the generator in accordance with its operating
instructions. The eluted liquid in the test tube (sealed with stopper!) is supported by the source holder clamp and positioned directly in front of the counting tube window (Fig. 1).
Set the measuring parameters according to Fig. 3 and then activate the measurement phase by clicking on <Continue>.
After the measurement series has been completed, the display
is automatically scaled; in Fig. 4 the individual data points and Fig. 2: Parameter settings for measuring the
the calculated half-life have also been entered.
background radiation.
Calculation of the half-life: The diagram with the original measured data must be active. Now, click on the <Analysis> and <Half-value time / -layer thickness> buttons. Naturally, the half-life can also be manually determined by
initially calculating the natural logarithm of the measured values
with <Channel modification> and by subsequently fitting a
straight line through the thus-manipulated measured values.
Figure 5 shows the semilogarithmic plot with its calculated regression line. From the regression line’s slope m, the halflife of
the eluted source is determined to be  = 153.69 s.
Measurement of the formation of daughter substance subsequent to disturbance of the equilibrium by elution.
Diagram settings for recording the formation of ”daughter substance”.
y axis: 400 to 600
x axis: 0 to 700 s
Perform elution of the generator in accordance with its operating instructions. The eluted liquid in the test tube (sealed with
Fig. 3: Parameter settings for measuring the
stopper!) is set aside and poured down the drain after it has
decaying Ba-137m.
stood for half an hour. The cylindrical generator sample is fixed
in the source holder and moved to a position directly in front of
the counting tube with its plane side facing the counter (Fig. 6).
Set the measuring parameters according to Fig. 3 and then activate the measurement phase by
clicking on <Continue>.
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Half life and radioactive equilibrium
TEP
Results:
The isotope generator contains 400 kBq of Cs-137, which serves as the parent substance; its half-life is
30.25 years. Cs-137 decays into the barium isotope Ba-137 with the emission of -radiation. This transition occurs, in part, directly (approximately 5%) to the stable ground state of Ba-137 and, in part (approximately 95%) via the meta stable state of Ba-137m. Ba-137m decays with a half-life of only 2.6 min under emission of -radiation (E = 662 keV) in the stable ground state of Ba-137. In the elution process,
the Ba-137m is washed out of the isotope generator. Figure 4 shows the counting rate as a function of
time. A counting rate that decreases exponentially over time results. The logarithmic counting rate is
plotted as a function of time, the straight line given in Fig. 5 is obtained.
Fig. 4:Calculation of the half-life of Ba-137m’s decay, counting rate as a function of time.
Fig. 5: Logarithmic plot of the counting rate of Ba-137m’s decay; counting rate as a function of time, with the regression line.
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Half life and radioactive equilibrium
In this case, the counting rate decreases to half of its original value after a time period  =153.69 s. Thus,
it follows that:
Thus,
By taking the logarithm of
The following is obtained
Comparing the coefficients with the regression line
shows that the slope of the regression line m corresponds to the negative decay constant.
The decay constant  is characteristic for the gradual decline in radioactivity: It is thus linked to the specific time period in which the substance quantity decays to half of its initial radioactivity (half-life ).
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Half life and radioactive equilibrium
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Fig. 6: Experimental setup for measuring the formation of the daughter substance..
Formation of daughter substance subsequent to disturbance of the equilibrium by elution
Calculation of the half-life. At time t an activity is measured that can be calculated according to the following formula:
By subtracting the equilibrium activity after approximately 650 s, which is comprised of
and
,
from the respective actual counting rate, in this case 504.28 (cf. Fig. 7) and calculating the natural logarithm of this variable’s value, the diagram in Figure 8 is obtained. The half-life for this measurement,
 =142.33 s, follows from the slope of the drawn regression line.
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Half life and radioactive equilibrium
Fig 7: Plot of the counting rate of the Ba-137m being formed as a function of time.
Fig 8: Logarithmic counting rateof the Ba-137m being formed as a function of time, with
the regression line.
Remarks
The calculation shown above can be performed using the <Analysis> and <Channel modification> functions using the formula ln(abs(x-504.28)). When using radioactive substances, conform absolutely to the
stipulations of the respective applicable radiation protection regulations. Radioactive substances can be
hazardous to your health! Always reduce the time spent handling radioactive substances to a minimum.
Do not eat or drink anything in the presence of radioactive substances and always wash your hands after
contact with them!
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