Determination of the Dead Time and Randomness of Nuclear Disintegration for a Geiger-Muller Tube Using two Radioactive Source Co 60 and Sr 90

Abstract

This study utilized standard two-source Co60 and Sr90 to determine the dead time and randomness of
nuclear disintegration of a Geiger Muller (GM) tube. The experimental result obtained from this research
was�22�ms�dead�time�of�a�
M�counter�(τ).�In�order�to�understand�random�nuclear�disintegration,�the�value�
of�the�standard�deviation�residual�(σresidual),�which�represents�the�experimental�mean�square�deviation,�was�
determined� for� the� radiation� activity� of� the� "o60 source� to� be� 15,�which� was� then� compared�with�the�
theoretically�expected�standard�deviation�(σexpected)�of�15.71.�These�values�indicate�a�correlation�between�
the� two� values� with� a� relative� standard� deviation� (RS*)� error� of� 5%.� The� value� of� the� standard� error�
residual� (δresidual)�was� also� estimated�to� be�3.35,� and� compared�with�the� expected� standard�error� value�
(δexpected)�of�3.51.�The�values�were�consistent�with�a�relative�standard�deviation�error�of�5%,�and�the�errors�
can be attributed to the random nature of nuclear decay.

Full text

NeuroQuantology | February 2020 | Volume 18 | Issue 2 | Page 101-105 | doi: 10.14704/nq.2020.18.2.NQ20133
Abbas Abdulhussein Mohammed, Determination of the Dead Time and Randomness of Nuclear Disintegration for a Geiger-Muller Tube Using two
Radioactive Source Co60 and Sr90
101
Determination of the Dead Time and Randomness
of Nuclear Disintegration for a Geiger-Muller Tube
Using two Radioactive Source Co60 and Sr90
Abbas Abdulhussein Mohammed1*, Zaid Saud Razzaq2, Hayder Salah Naeem3
Abstract
This study utilized standard two-source Co
60
and Sr
90
to determine the dead time and randomness of
nuclear disintegration of a Geiger Muller (GM) tube. The experimental result obtained from this research


residual


60


expected



residual


expected

can be attributed to the random nature of nuclear decay
.
Key Words:

DOI Number: 10.14704/nq.2020.18.2.NQ20133 NeuroQuantology 2020; 18(2):101-105
Introductions
The Geiger Muller (GM) counter is commonly used
       
reliability and cost-  
experiments can be set up using a GM counter
determination of a GM's plateau
      
-
classified as a filled gas detector [6].

produces an ion pair consisting of a po
and an electron [7]. The electrons are attracted to


ions. This also increases the radius of the anode
     rts the
       


of the potential will be dictated by the applied

Corresponding author: Abbas Abdulhussein Mohammed
Address: 1*-; 2
-Muthann3
-
1*-
2-
3-
Relevant conflicts of interest/financial disclosures: The authors declare that the research was conducted in the absence of
any commercial or financial relationships that could be construed as a potential conflict of interest.
Received: 11 January 2020 Accepted: 
eISSN 1303-5150 www.neuroquantology.com

NeuroQuantology | February 2020 | Volume 18 | Issue 2 | Page 101-105 | doi: 10.14704/nq.2020.18.2.NQ20133
Abbas Abdulhussein Mohammed, Determination of the Dead Time and Randomness of Nuclear Disintegration for a Geiger-Muller Tube Using two
Radioactive Source Co60 and Sr90
102


 
means that the loss of count depends on the rate of
particle emission from the source and its
      
schematic of the GM tube and its associated
electronics.
Fig. 1. Schematic diagram of the GM tube and the associated
electronics
     
exhibited by Geiger counters; the first is the
        



age reaches the


which the counting system first records pulses is
      
ation increases
and the number of pulses increase rapidly to a flat

which is the Geiger tube region where the count
rate is nearly independent of the potential

     


      
        
recog      
collection as it is closely related to the dead time
phenomenon [11].
Fig. 2. Plateau of Geiger Muller tube
The Dead Time of a GM
Let 
 be the number of particles entering the GM
tube per second and the counter is showing counts
 as
the number of particles entering GM tube per
second counted particles
is
�:

=
(1)
 there are two different sources S1 and S2.
Suppose the sources are placed together in such a
way that total number particles entering the tube
2 and if the time count rate shown
by the 3[1013]:
(
1+
2)
3=
1+
23 (2)
When the source S2  keeping S1 the
 1 and 
1=
1 (3)
2=
2(4)

1 and 
2 s. (3) & (4) and
reflecting the higher order terms:
= 1+23
212
(5)
Where: 1 = Count rate with source S1.
2 = Count rate with source S2 .
3 = Count rate with source S1+S2 .
Randomness of Nuclear Disintegration
To study the random of radio

with any counting system is the 
 actual count rate due
to the random nature of radio
we consider
that the 
remains constant for a considerable amount of time
and if the series of counts N1 2 

will differ from mean count N
calculated
from the absolute result .
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Abbas Abdulhussein Mohammed, Determination of the Dead Time and Randomness of Nuclear Disintegration for a Geiger-Muller Tube Using two
Radioactive Source Co60 and Sr90
103
the randomness of nuclear disintegration:

=

The standard  residual residual is the most
likely an  and is
defined as:
2=(
)2
1

=1 (6)
 expected is defined
as :
 =
 (7)
The standard error is defined as :
 =2

 =

 (9)
Where: 
N
 = mean of count.
Ni 
MATERIALS AND METHODS
An experimental setup was prepared
Scheme 1. The dead time of a GM tube (Model
ST360 Counter) was determined using a double-
source slot plate method and applied 
 s were taken from the
Co60sourceS1(half-life of 
- and energy decay of0.31MeV)at count per 30
secs. After 1were taken
from theSr90 source S2(half-life of 
- and energy decay 0.6MeV)at count per
30 secs    were taken for
the(S1&S2) ) at count per 30 secs.
Scheme 1. 
Results and Calculations
The counting measurements of the Co60 and Sr90
sources were taken for 30 secs after a decay period
using a GM with the 
to 450 Vare
shown in Table 1 as a function of decay times. The
      
detector was ~624 count per 30 secs for both
sources due to the dead time effect.
Table 1. time

Obs. No.
60 count/30 sec
90 count/30 sec
 Co60+Sr90
count/30 sec
1
242
244
572
2
240
256
624
3
221
223
565
4
230
240
594
5

246

6
239
252
595
7
239
232
552

254
264
619
9
249
251
557
10
251
265
605
11
259
253

12
271
265
555
13
237
265
572
14
227
253
597
15
252


16

247
600
17
255
249




590
19
256
245
602
20

265
602
Mean count for Co60


=4937

=4937
20 =246.
Mean count for Sr90


=4971

=4971
20 =.55
Mean count for Co60+Sr90


=11731

=11731
20 = 5.55
eISSN 1303-5150 www.neuroquantology.com

NeuroQuantology | February 2020 | Volume 18 | Issue 2 | Page 101-105 | doi: 10.14704/nq.2020.18.2.NQ20133
Abbas Abdulhussein Mohammed, Determination of the Dead Time and Randomness of Nuclear Disintegration for a Geiger-Muller Tube Using two
Radioactive Source Co60 and Sr90
104
the dead time of the GM 
result from Table(1):
i) 60
1=

30 =246.
30 =.23  

ii) 90
2=

30 =.55
30 =.  

iii) 60 + Sr90
3=

30 =.55
30 =19.55  

 we can determinethe dead time for
GM tube:
=(1+2)3
212
=(.23 +.)19.55
2.23 .
=3.035
136.37 = 0.022  =22
Table 2. 
Obs.
No.
Ni for Co60
count/30sec



(

)2
1
242
-
23.53
2
240
-
46.92
3
221
-


4
230
-


5

-

355.32
6
239
-
61.62
7
239
-
61.62

254
7.15
51.12
9
249
2.15
4.62
10
251
4.15
17.22
11
259
12.15
147.62
12
271
24.15

13
237
-
97.02
14
227
-

394.02
15
252
5.15
26.52
16

1.15
1.32
17
255

66.42


11.15
124.32
19
256
9.15

20

34.15
1166.22
s.6 7 calculate the
the randomness of
   its corresponding
standard error:
2=(
)2
1  

=1
= {(
)2
1

=1
}12
=[4264.51
20 1]12

=15
 =
=246.=15.71
 =2
=15
20 = 3.35
 =

=246.
20 = 3.51
DISCUSSION AND CONCLUSIONS
According to the resultst
decay is random and unpredictable within a

     source is
independent of each other. When taking a large
number of  

       
counting rate N    
measurements by counting the statistics for nuclear
radiation.
Practically tof the count
mean count in the unit of
timecan be predicted usingthe statistical count of
nuclear radiation.
of the practical
  were
N. At
 Nwith
 more
significant .
The measured data were fitted using the mean

 described the dead time of a GM
being studied. The actual dead time of a GM counter
is dependent on the counting rate.
The residual can be calculated by using 6
 sourceCo60 and was
determined to be15
to the theoretically expected calculated using  7
and determined to be 15.71.   
cor  (

    standard error residual
()was calculated using 
eISSN 1303-5150 www.neuroquantology.com

NeuroQuantology | February 2020 | Volume 18 | Issue 2 | Page 101-105 | doi: 10.14704/nq.2020.18.2.NQ20133
Abbas Abdulhussein Mohammed, Determination of the Dead Time and Randomness of Nuclear Disintegration for a Geiger-Muller Tube Using two
Radioactive Source Co60 and Sr90
105
Co60 and was found to be 3.35
compared with the expected standard error
() calculated using 9 and found to
were consistent with a 
 ( 
These errors result from the random nature of the

related to the same source and indeterminate
errors resulting from the effects that occur during
   -absorption and

tables.
Acknowledgments
The authors gratefully acknowledge the
 
Al- .
       

his encouragement.
Authors' Contributions
All authors contributed 
Conflict of Interest
The authors declare no conflict of interest.
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Parameter    
     
Models. ; 72(10): 1133–.
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