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Abstract
In the experiment, G.M. Counter voltage characteristics were studied to find the appropriate operating voltage and half life of a short lived radioisotope was determined. An unsuccessful try for determining the half lives of two mixed isotopes was also made using the same setup. At the end dead time of the used G.M. tube was determined by two source method assuming that our system followed the nonparalysable model.
Introduction
Geiger-Muller (GM) Counter:
A typical G.M. Counter consists of a GM tube having a thin, mica end-window, a high voltage supply for
the tube, a counter to record the number of particles detected by the tube, and a timer which will stop
the action of the counter at the end of a preset interval.
The sensitivity of the GM tube is such that any particle capable of ionizing a single atom of the filling gas
of the tube will initiate an avalanche of ionization in the tube. The collection of the ionization thus
produced results in the formation of a pulse of voltage at the output of the tube. The amplitude of this
pulse, on the order of a volt or so, is sufficient to operate the counter circuit with little further
amplification.
Some of the advantages of using a Geiger Counter are:
They are relatively inexpensive They are durable and easily portable They can detect all type of radiation
Some of the disadvantages of using Geiger Counter are:
They can not differentiate which type of radiation is being detected They can not be used to determine the exact energy of the detected radiation They have a very low efficiency
Characteristics Curve of GM Counter:
Every GM tube has a characteristic response of counting rate versus voltage applied to the tube. A
curve representing the variation of counting rate with voltage is called a characteristic curve because of
its appearance. The characteristic curve of every tube that is to be used for the first time should be
drawn in order to determine the optimum operating voltage. A typical GM Counter Characteristic Curve
is shown below;
FIGURE 1. TYPICAL GM COUNTER CHARACTERISTIC CURVE
The optimum operating voltage will be about the middle of the plateau, usually some 150 to 200 volts
above the knee of the curve.
Half-Life Determination of an Unknown Radioisotope:
The activity (number of disintegrations per second) of a radioisotope is expressed as
A(t) = Ao e-λt
where
A(t) = Activity at the end of an interval t Ao = Activity at the beginning of the interval t = Decay constant, characteristic of the radioisotope
Now, the counting rate of a sample of a radioisotope may be considered to be directly proportional to
the activity at the moment of measurement provided that the counting interval is short compared to the
half-life. Reasonably short half-lives can be determined by measuring counts at regular intervals.
C(t) α A(t)
So
C(t) = C 0 e-λt Ln(C) = Ln(C 0 )-λt
This is a straight line with negative slope = -λ.
The half-life, T½ of a radioisotope is defined to be that interval during which the activity (counts)
decreases to one-half its value at the beginning of the internal. We know that
T½ = ln2/λ
FIGURE 3.ILLUSTRATION OF TWO ASSUMED MODEL OF DEAD TIME BEHAVIOR
If
n = True interaction rate m = Measured count rate
= Detector dead time
Then according to Non Paralysable Model
m
n=
1-m
And according to Paralysable Model
n = me n^
Methods for Dead Time Measurement:
1)Decaying Source Method
For short lived radioisotopes source decaying source method is also available. In this case departure of
observed counting rate from known exponential decay of source can be used to calculate the dead time.
This technique is based on known behavior of the true rate n:
0
t
n n e nb
^
Where n 0 is true rate at the beginning of measurement and λ is the decay constant of the particular
isotopes used for the measurement
0
n n e ^ ^ t
For Non Paralysable Model
0 0
me ^ ^^ t^ n m n
For Paralysable Model
In the limit of negligible background, a simple graphical procedure can be applied to analyzing the
resulting data.
The decaying source method has the advantages of not only being able to measure the value of dead
time but also being able to test the validity of the assumed method.
ln( ) 0 ln 0
t m n e ^ t n
FIGURE 4. GRAPHICAL ILLUSTRATION OF TWO ASSUMED MODEL OF DEAD TIME BEHAVIOR
Table 1. GM TUBE CHARACTERISTICS
VOLTAGE(VOLTS) COUNTS (Cpm)
AVG
COUNTS Error
AVG. COUNT -
ERROR
AVG.
COUNTS+ERROR
Count rate vs. voltage plot was drawn in order to estimate the operating voltage for the GM counter as described in the introduction. The operating voltage was found to be about 850 volts. Plot is shown below.
0
100
200
300
400
500
600
700
800
900
1000
1100
500 600 700 800 900 1000
Cpm
V (Volts)
FIGURE 6. GM COUNTER CHARACTERISTICS
After applying 850 volts to GM tube an unknown short lived source was placed under the tube and
counts/min were recorded for a time interval of 75 minutes (i.e. 75 readings continuously ) and natural logarithm of count rate vs. time plot was drawn which is a straight line as shown below in figure 7.
TABLE 2. HAIF LIFE MEASUREMENT
Which was found to be 54.5 min. From literature it was confirmed that a radioisotope having half life
Same procedure was then adopted for determining the half lives of two mixed isotopes of same element. The observations and calculations are shown below. TABLE 3. MIXED ISOTOPE COUNTS DATA
- 1 1000 6. Time (min) Cpm (C) LN(C)
- 2 1019 6.
- 3 1042 6.
- 4 934 6.
- 5 985 6.
- 6 956 6.
- 7 993 6.
- 8 926 6.
- 9 919 6.
- 10 964 6.
- 11 872 6.
- 12 927 6.
- 13 888 6.
- 14 880 6.
- 15 839 6.
- 16 864 6.
- 17 864 6.
- 18 816 6.
- 19 807 6.
- 20 834 6.
- 21 808 6.
- 22 773 6.
- 23 811 6.
- 24 726 6.
- 25 780 6. - 26 731 6. - 27 720 6. - 28 684 6. - 29 752 6. - 30 743 6. - 31 724 6. - 32 721 6. - 33 673 6. - 34 643 6. - 35 725 6. - 36 673 6. - 37 651 6. - 38 638 6. - 39 686 6. - 40 599 6. - 41 633 6. - 42 664 6. - 43 601 6. - 44 605 6. - 45 579 6. - 46 544 6. - 47 543 6. - 48 588 6. - 49 551 6. - 50 559 6. - 51 557 6. - 52 527 6. - 53 509 6. - 54 558 6. - 55 516 6. - 56 531 6. - 57 514 6. - 58 511 6. - 59 456 6. - 60 472 6. - 61 476 6. - 62 474 6. - 63 476 6. - 64 420 6. - 65 438 6. - 66 479 6. - 67 446 6. - 68 414 6. - 69 489 6. - 70 426 6. - 71 422 6. - 72 441 6. - 73 400 5. - 74 401 5. - 75 412 6.
- equal to 54.1 minutes is In - 5 81 4. time (sec) Counts C ln C - 10 49 3. - 15 48 3. - 20 48 3. - 25 30 3. - 30 43 3. - 35 33 3. - 40 34 3. - 45 33 3. - 50 27 3. - 55 27 3. - 60 19 2. - 65 17 2. - 70 21 3. - 75 29 3. - 80 20 2. - 85 13 2. - 90 16 2. - 95 13 2.
- 100 13 2.
- 105 11 2.
- 110 19 2.
- 115 14 2.
- 120 7 1.
- 125 12 2.
- 130 13 2. - 135 9 2. - 140 6 1. - 145 10 2. - 150 4 1. - 155 9 2. - 160 11 2. - 165 14 2. - 170 10 2. - 175 8 2. - 180 10 2. - 185 3 1. - 190 9 2. - 195 8 2. - 200 7 1. - 205 10 2. - 210 4 1. - 215 8 2. - 220 4 1. - 225 11 2. - 230 6 1. - 240 1 0. 235 0 undefined - 245 4 1. - 250 6 1.
This data was unable to differentiate between short lived and comparatively long lived isotope of the two mixed isotopes. Thus their half lives could not be determined.
Next, the dead time of the detector was determined using the two source method as described in the introduction. For this purpose two semicircular disk sources were used. First a single source designated as source 1 was placed under the tube window and three readings of count rate were taken and their mean was calculated said as M1. Then source 2 was also placed under the detector without disturbing the position of source 1 and M12 was determined similarly. Then source 1 was removed without disturbing source 2 and M2 was determined. The observations, calculations and results are shown below. Note that for all cases count rate unit is counts /min.
TABLE 4. DEAD TIME MEASUREMENT DATA
BACKGROUND
COUNTS SOURCE 1 SOURCE 1+2 SOURCE 2
18 17553 26430 16792
16 17326 26847 16637
17 17607 26544 16637
0 20 40 60 80 100 120 140 160 180 200 220 240 260
ln C
time (seconds)
FIGURE 8. FOR MIXED ISOTOPES
seven or eight half lives might be possible to had passed away before staring to collect counts. This all is indicated by the fact that the plot in figure 8 has only one straight line trend but it would have an elbowed line trend, the portion of which with lesser slope would be the decay constant of long lived isotope and might be subtracted from the slope of comparatively larger slope portion of the line in order to give the decay constant of short lived isotope. These decay constants then might be used to calculate the respective half lives of the isotopes.
The dead time determination was done using two source method assuming that the experimental setup followed nonparalysable model. The dead time approximated for low count rate was also calculated from the same counts data. It was found that the difference between the two dead time values was much large. So the count rate was high and not low.
Conclusion
The operating voltage of the GM counter was found to be 850 volts and it was done by plotting GM tube characteristics curve. The half life of an unknown radioisotope was determined to identify that isotope and it was found that the radioisotope was In^116. It was also extracted from very much less difference in actual and calculated values of half life that our experimental setup was enough efficient. The dead time of the GM detector was determined by two source method and it was found to be nearly 1msec. It was also found that count rate was high for the sources used dead time measurement.
References
- Knoll, G.F. ; Radiation Detection and Measurement, John Wiley & Sons (1999)
- Nasir Ahmad ; Experimental Radiation Detection, CNS-20, (1987)
