Exp1 Gamma Decay Stats

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Nuclear & Particle physics Lab IV

Counting statistics of ray source Experiment # 1

Name: Prateek Verma

Roll no. : 09MS061

Date: 9 & 10 Jan 2012

Partners name: Suman Basak (09MS094)

Avinash Kumar Gupta (09MS083)


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Date: 9 & 10 Feb 2012 Experiment #: 1

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Aim:

Study of Geiger-Muller Counter and counting statistics by -ray source.

Keywords:

GM counter, attenuation, operating voltage, avalanche, Quenching, Gaussian

distribution, Poisson distribution.

Apparatus:

Set-up for PNC-1G (Para Nuclear Counter) GM Tube and stand Shelf stand, serial cable, and a source holder Radioactive Source (Ba-133)

Purpose:

To study the characteristic of GM counter and hence measure optimal

operating voltage of the counter.

To study the distribution curve of the counts from radioactive decay and

determine mean value and standard deviation

Theory:

Geiger-Mller Counter

Geiger-Mller (GM) counter was invented by H. Geiger and E.W. Mller in

1928, and is used to detect radioactive particles. Geiger-Muller counter,

commonly known as GM counter is one of the oldest and widely used radiation

detectors.

Principle: All nuclear radiations, whether they are charged particles or gamma

rays, it will ionize atoms/molecules while passing through a gaseous medium.

This ionizing property of a nuclear radiation is utilized for its detection.


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Set Up: A typical GM Counter consists consist of a metallic tube with a thin

wire mounted along its axis. In this tube the anode is tungsten wire and

cathode is in the form of graphite coating inside the glass envelope or may

simply be a copper cylinder. The wire is insulated from the tube using a non-

conducting ceramic feed through. The central wire (anode) is kept at a positive

potential of a few hundreds of volt or more with respect to the cathode, which

is grounded. The tube is filled with argon gas mixed with 5-10% of ethyl alcohol

or halogens (chlorine or bromine).

Working: When an ionizing radiation enters the Geiger tube some of the energy

of the radiation may get transferred to a gas molecule within the tube. This

absorption of energy results in ionization, producing positive ions and

electrons. In

presence of high

voltage between

cathode and anode,

electrons move

(accelerate) towardsanode and positive

ions towards

cathode. In process

electrons collides

with other Argon gas

molecules producing

Figure 1: Schematic of GM counter

positive ions and electrons. Hence an avalanche of ions and electrons are

created. The arrival of these avalanches at the anode causes a drop in the

potential between the central wire and the cylinder. This process gives rise to a

very large pulse with amplitude independent of the type and energy of the


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incident radiation. The pulse is communicated to Pulse Processing Circuit,

Microcontroller and finally in the form of number of counts to the LCD display.

Suitable arrangements are made to measure the counts for a preset time

interval.

Statistical Nature of Radioactive Decay

The phenomenon of radioactivity is statistical in nature. One cannot say which

radioactive nucleus in the sample will decay at a given instant of time, though

one can predict what portion of the given sample will decay in an interval of

time, provided the sample contains large number of nuclei. Hence thadisintegration law:

N = N 0

is valid when N (number of radioactive material at a given instant of time t) is

very large compared to dN (number of nuclei decaying between times t and

t+dt ) which is usually the case. Truly speaking N varies discontinuously and

the smallest value of dN is one, corresponding to the decay of a single nucleus.

Statistical Errors of Nuclear Physics

In this experiment we have used Geiger-Mller (GM) counter for counting the

radioactive particles. The time t necessary for the observation of any finite

number of counts N is subject to statistical fluctuations. This causes an error

in the observed counting rate, n = . It worth noting that this is not the

property of the instrument and this is fundamental to the phenomenon of

radioactivity.


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Let us consider that the probability that N particles are observed in the time t

be P N and the time interval t is divided into n equal intervals so small that the

probability of emission of two particle within an interval is negligible. Therefore

the probability of the emission of one particle in a given interval is /n. where = average number.

Hence the probability P N is given by:

PN = ( )

This is known as binomial distribution and when n

PN =

is known as Poisson distribution. If N becomes large, which is usually the case

we deal with the Poisson distribution curve of P N versus N becomes

symmetrical about the maximum and approaches a Gauss error curve. Then

PN = exp


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Figure 2: Poisson distribution approaching Gaussian function with increasing N

Procedure:

Counting time was set to 30 sec. Number of runs was set to 1 run only. source was place in slotnumber 4.

HV was set to its minimum value (it came out to be 6 V) by turning the HV.

Number of counts was recorded for the preset time and noted.HV was increased your in a step of 50 and counts number was noted down up to HV = 250 volts.Then the step gap was reduced to ~10 volts and recording was taken for HV = 270,288, 300, 310,320, 330, 420, 430, 450 volts (see observation table1)

After HV = 450 volt recording steps (+50 volts) was increased again till HV = 950V and thenreduced to 20 volts steps up to HV= 1050 volts (see observation table1)

GM counter was determined by taking the middle value of the plateau region.


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Data

Table1: The characteristics curve of the GM-counter and the operating voltage.

No. of counts(in 30 sec)

Averagefrequency(per sec)

No. of counts(in 30 secs)

Averagefrequency(per sec)Run 1 Run 2 Run 1 Run 2

0 0 0.00 240 250 8.170 0 0.00 248 256 8.400 0 0.00 256 243 8.320 0 0.00 236 264 8.330 0 0.00 233 261 8.230 0 0.00 246 259 8.420 0 0.00 238 262 8.330 0 0.00 247 260 8.450 0 0.00 257 252 8.48

75 61 2.27 268 302 9.50198 183 6.35 322 288 10.17230 231 7.68 339 330 11.15206 225 7.18 386 378 12.73211 242 7.55 311 353 11.07

234 223 7.62 409 410 13.65275 244 8.65 395 447 14.03226 252 7.97 418 467 14.75256 240 8.27 524 504 17.13245 269 8.57 681 634 21.92249 228 7.95 1233 21593 380.43265 199 7.73

Table2: Number of counts per 30 sec by Gamma ray source.


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S.no. Number of counts

(per 30 secs)

Counts(per sec)


(per 30 secs)

Counts (persec)

1 243 8.10 108 256 8.53

2 261 8.70 109 245 8.173 245 8.17 110 236 7.87

4 221 7.37 111 247 8.23

5 277 9.23 112 261 8.70

6 245 8.17 113 251 8.37

7 254 8.47 114 253 8.43

8 260 8.67 115 263 8.77

9 222 7.40 116 241 8.03

10 251 8.37 117 235 7.83

11 256 8.53 118 238 7.93

12 268 8.93 119 258 8.60

13 262 8.73 120 244 8.13

14 252 8.40 121 250 8.33

15 262 8.73 122 260 8.67

16 243 8.10 123 251 8.37

17 253 8.43 124 230 7.67

18 252 8.40 125 234 7.80

19 237 7.90 126 227 7.57

20 240 8.00 127 242 8.07

21 255 8.50 128 256 8.5322 270 9.00 129 234 7.80

23 223 7.43 130 242 8.07

24 247 8.23 131 260 8.67

25 250 8.33 132 249 8.30

26 272 9.07 133 247 8.23

27 230 7.67 134 252 8.40

28 247 8.23 135 234 7.80

29 244 8.13 136 245 8.17

30 219 7.30 137 240 8.00

31 251 8.37 138 224 7.47

32 230 7.67 139 247 8.23

33 219 7.30 140 235 7.83

34 249 8.30 141 236 7.87

35 241 8.03 142 211 7.03

36 246 8.20 143 224 7.47


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S.no. Number of

counts(per 30 secs)

Counts(per sec)


(per 30 secs)

Counts(per sec)

37 238 7.93 144 245 8.17

38 258 8.60 145 231 7.7039 250 8.33 146 220 7.33

40 274 9.13 147 225 7.50

41 258 8.60 148 268 8.93

42 258 8.60 149 234 7.80

43 257 8.57 150 270 9.00

44 266 8.87 151 256 8.53

45 248 8.27 152 240 8.00

46 237 7.90 153 243 8.10

47 234 7.80 154 259 8.63

48 265 8.83 155 229 7.63

49 242 8.07 156 261 8.70

50 278 9.27 157 273 9.10

51 221 7.37 158 250 8.33

52 242 8.07 159 233 7.77

53 255 8.50 160 247 8.23

54 232 7.73 161 236 7.87

55 253 8.43 162 231 7.70

56 281 9.37 163 238 7.93

57 239 7.97 164 243 8.1058 250 8.33 165 245 8.17

59 242 8.07 166 252 8.40

60 247 8.23 167 249 8.30

61 225 7.50 168 237 7.90

62 232 7.73 169 267 8.90

63 226 7.53 170 222 7.40

64 233 7.77 171 261 8.70

65 223 7.43 172 241 8.03

66 253 8.43 173 239 7.97

67 234 7.80 174 227 7.57

68 236 7.87 175 247 8.23

69 247 8.23 176 253 8.43

70 240 8.00 177 249 8.30

71 236 7.87 178 237 7.90

72 257 8.57 179 240 8.00

73 242 8.07 180 230 7.67


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(per 30 secs)

Counts(per sec)


(per 30 secs)

Counts(per sec)

74 225 7.50 181 262 8.7375 245 8.17 182 235 7.8376 265 8.83 183 257 8.5777 258 8.60 184 245 8.1778 238 7.93 185 239 7.9779 247 8.23 186 255 8.5080 247 8.23 187 248 8.2781 259 8.63 188 269 8.9782 238 7.93 189 255 8.5083 209 6.97 190 239 7.97

84 227 7.57 191 242 8.0785 253 8.43 192 255 8.5086 263 8.77 193 268 8.9387 244 8.13 194 254 8.4788 251 8.37 195 259 8.6389 242 8.07 196 262 8.7390 232 7.73 197 238 7.9391 272 9.07 198 221 7.3792 264 8.80 199 259 8.6393 242 8.07 200 241 8.0394 242 8.07 201 247 8.2395 249 8.30 202 253 8.4396 216 7.20 203 255 8.5097 271 9.03 204 220 7.3398 273 9.10 205 250 8.3399 222 7.40 206 255 8.50

100 252 8.40 207 223 7.43101 272 9.07 208 239 7.97102 238 7.93 209 262 8.73

103 271 9.03 210 248 8.27104 223 7.43 211 265 8.83105 257 8.57 212 268 8.93106 234 7.80 213 239 7.97107 227 7.57


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Table3: Frequency table

S. no. Lower limit Upper limit Class marks Frequency1 200 205 202.5 02 205 210 207.5 13 210 215 212.5 14 215 220 217.5 55 220 225 222.5 176 225 230 227.5 137 230 235 232.5 218 235 240 237.5 309 240 245 242.5 34

10 245 250 247.5 3511 250 255 252.5 3212 255 260 257.5 2713 260 265 262.5 1814 265 270 267.5 1215 270 275 272.5 1016 275 280 277.5 217 280 285 282.5 1

Matlab program to find out the frequency of counts in the given two limits:

load( 'data1.txt' )X = data1(:,1);xl = [200,205,210,215,220,225,230,235,240,245,250,255,260,265,270,275,280];xu = [205,210,215,220,225,230,235,240,245,250,255,260,265,270,275,280,285];l = ( xu + xl )/2;f = zeros(1,length(xl));for j=1:length(xl)

for i = 1:length(X)if X(i) >= xl(j) && X(i)


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Graphs 1: Plot of number of counts versus applied voltage, to find out the

operational voltage of GM counter.


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Graph2: Histogram showing of Gamma-radiation counts.

200 210 220 230 240 250 260 270 2800

5

10

15

20

25

30

35

F r e q u e n c y o

f c o u n

t s

Number of Counts (per 30 sec)

Frequency of countsGauss of Frequency of counts


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Error Sources:

Fluctuation in the background radiation causes error in the count each

time we take the reading.

Voltage fluctuation also causes random errors in the radiation count.

The GM counter that we were using has a finite resolving time. In this

time interval alone it can differentiate between two different radiation

particles. So if the duration between the entries of two gamma rays is

within the dead time the GM counter would be unable to detect them and

hence our measured count would be less than the actual count.

Result & Conclusion:

The operating voltage for GM counter was determined experimentally to

be 685 volts from the characteristics of GM counter by taking the middle

value of the plateau region.

The distribution curve of the counts from radioactive decay of Ba-133 is

Gaussian curve as seen from the graph 2. This observation is inaccordance to the expected behaviour.

Mean value of the fitted Gaussian curve is 246 and standard deviation is

15.54.


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