University of Bremen Department of Physics and Electrical Engineering

Natural and Man-Made Radioactivityin Soil

lab report on the advanced experiment

FP 21

author

Alexander Erlich

tutors and supervisors

Daniela Pittauerova

Ahmed Ali Husein Qwasmeh

date of experiment October 15th 2009

Contents

1 Introduction 2

2 Theory 221 Modes of Decay 222 Several Basics of Probability Theory 323 The Poisson Distribution 424 Interaction of radiation with matter 525 Exponential radioactive decay 7

3 Experimental Setup 831 High Purity Germanium detector 832 Evaluation of γ spectra 9

4 Experimental Procedure 1041 Test source with one γ line 1142 Test sources with multiple lines - energy calibration 1143 Eciency calibration 1144 Soil sample spectrum measurement calculating activities 11

5 Analysis 1151 Test source with one gamma line 1152 Test sources with multiple lines - energy calibration 1253 Eciency calibration 1354 Data analysis of soil sample measurement 1455 Calculating activities of three prominent lines 17

6 Conclusion 18

A function peak_counter for calculating activities 20

B Laboratorys eciency calibration curve for point source geometry 21

C Laboratorys eciency calibration curve for Marinelli beaker geometry 21

D Measurement Report 21

cover picture Chernobyl atomic power station by nikel303 on deviantART seehttpnikel303deviantartcomartChernobyl-atomic-power-station-34320902

The artist displayed the Chernobyl sarcophagus (photo taken in June 2006) The unitof the number displayed on the counter is micro roentgen which is a measurement forionizing radiation 1R = 258 middot 10=4Ckg

1

Contents

1 Introduction 2

2 Theory 221 Modes of Decay 222 Several Basics of Probability Theory 323 The Poisson Distribution 424 Interaction of radiation with matter 525 Exponential radioactive decay 7

3 Experimental Setup 831 High Purity Germanium detector 832 Evaluation of γ spectra 9

4 Experimental Procedure 1041 Test source with one γ line 1142 Test sources with multiple lines - energy calibration 1143 Eciency calibration 1144 Soil sample spectrum measurement calculating activities 11

5 Analysis 1151 Test source with one gamma line 1152 Test sources with multiple lines - energy calibration 1253 Eciency calibration 1354 Data analysis of soil sample measurement 1455 Calculating activities of three prominent lines 17

6 Conclusion 18

A function peak_counter for calculating activities 20

B Laboratorys eciency calibration curve for point source geometry 21

C Laboratorys eciency calibration curve for Marinelli beaker geometry 21

D Measurement Report 21

cover picture Chernobyl atomic power station by nikel303 on deviantART seehttpnikel303deviantartcomartChernobyl-atomic-power-station-34320902

The artist displayed the Chernobyl sarcophagus (photo taken in June 2006) The unitof the number displayed on the counter is micro roentgen which is a measurement forionizing radiation 1R = 258 middot 10=4Ckg

1

1 Introduction

Apart from natural radioactivity it is possible to trace articial radioactivity in everydaylife objects Provided that the detector is sensitive enough it is even possible to clearlyidentify individual isotopes like Cs-137 The existence of this isotope in Germany ispartly due to global fallout after atmospheric nuclear bomb tests but partly originates inthe 1986 Chernobyl accident The special aim of the experiment Natural and Man-Made

Radioactivity in Soil is to detect the Cs-137 isotope and to analyze its activity For thispurpose a High Purity Germanium (HPGe) detector will be calibrated and employed toinvestigate a self-fetched soil sample The high resolution of the HPGe detector will allowto clearly identify many radionuclides in the soil sample among them Cs-137

2 Theory

21 Modes of Decay

Nuclides which are unstable are called radioactive Their decay is a transformation todierent less heavy nuclides It is always accompanied by a certain type of radiationwhich may be electromagnetic radiation but also a radiation of particles (like electronsor neutrons) The four principal types of radioactive decay are presented below

α decay

In α decay an α particle (which is a Helium nucleus 42α equals 4

2He) is emitted whilethe mother nucleus loses two protons and two neutrons α decay usually occurs in heavynuclei (roughly Z gt 83) Unlike in case of β decay (see below) α particles have arelatively sharply dened kinetic energies so there is no need to introduce a third particleto understand the energy distribution Here is an example of naturalα decay

232Thrarr228 Ra +4 He

When α decay occurs the daughters themselves can also experience α decay Thus adecay chain can be formed It is interesting to note that α decay has been convincinglyexplained using tunneling George Gamow claimed in 1928 that tunneling is responsiblefor the escape of an α particle from the Coulomb potential wall erected by the nucleusIn classical terms the wall would be insurmountable for the α particle

βminus decay

β decay is usually subdivided into βminus and β+ decay In case of βminus the reason for thedecay is a proton excess in a nucleus In this case a neutron (n) is transformed into aproton (p) an electron and an anitneutrino (νe)

βminus decay nrarr p + βminus + νe

Note that in terms of β decay electrons (eminus) are referred to as βminus particles and positrons(e+) are referred to as β+ particles 1) It is also interesting to note that there is no

1The three kinds of radioactive radiance were called α decay β decay and γ decay before it wasfound that α particles are helium-4 particles β particles are electrons or positrons and γ rays are highlyenergetic photons

2

(apparent) need for the neutrino when it comes to charge and mass conservation Howeverit was found that the βminus particles of a certain radioactive process do not have a constantenergy but an energy distribution It was proposed by Pauli in 1930 to introduce aneutrino which would help to explain energy and momentum conservation Its existencewas proven by an experiment in 1956

β+ decay

Proton excess is the common reason for β+ decay In this case a proton is transformedinto a neutron (which remains part of the nucleus) a positron and a neutrino (νe) Asuch transformation never occurs in free protons but only when a proton is part of anatoms nucleus and thus subject to the atoms Coulomb and binding potential Similarlyto βminus decay the energy is distributed between the β+ particle and the neutrino Here isa typical example of β+ decay

137 Nrarr 13

6 C + βminus + νe

γ decay

Unlike in α or β decay a nucleus which experiences γ decay does not change its numberof protons or neutrons γ occurs when an excited nucleus relaxes and drops into a lowerenergy state This results in the emission of highly energetic gamma rays (the wavelengthdimension are usually about 1 pm)

γ decay is usually preceded by α decay or β decay For example think of a radioac-tive mother nucleus which experiences β decay Its daughter nucleus then drops into itsground state by emitting γ rays

22 Several Basics of Probability Theory

First of all a couple of terms from probability theory shall be introduced They are cru-cial for the theoretical understanding of the experiment

Let the expected or mean value of a random variable X be micro = E(X) Then the varianceVar (X) is given by

Var (X) = E[(X minus micro)2]

The standard deviation (frequently abbreviated as sdev or stdev) is given by

σ =radicE[(X minus micro)2] =

radicVar (X)

The standard deviation can be regarded as a measure of the variability or dispersion ofa random variable X (which might be eg a dataset from a physical experiment) Alow standard deviation indicates that the data points tend to be very close to the meanwhereas high standard deviation indicates that the data are spread out over a large rangeof values

Also the standard deviation has a very important meaning in connection to the Gaussian(normal) distribution In a normal distribution the likelihood that X isin [microminus σ micro+ σ]occurs is 68 [microminus σ micro+ σ] is called a condence interval It is qualied by its condence

3

Figure 1 standard deviation diagram (own design)

condence level interval radius

68 σ90 1 64σ95 1 96σ

Table 1 Several important condence levels and the corresponding interval radii

level (which is 68 in this example) In other words think of a statistical experiment (likeradioactive decay) which is approximated by a Gaussian distribution2 The probabilitythat the experiment yields a result which is within the above condence interval is givenby the condence level 68 The most important condence levels and interval radiiare given in table 1 Two of them the 68 condence interval and the 95 condenceinterval are illustrated in gure 1

23 The Poisson Distribution

The Poisson distribution can be applied to systems with a large number of possible eventseach of which is rare Also for large numbers the Gaussian is a very good approximationfor the Poissonian so variance and condence interval calculus can be applied On topof that the variance of the Poissonian can be calculated very easily (see below) Thatswhy the Poissonian is quite perfect for this experiments purpose of statistically describingradioactive decay The Poisson distribution and its variance are given by

Poisson distribution Pn =NneminusN

nn = 0 1 2 variance σ =

radicN

where n is the occurring event and N the expected or average event (being not exactlybut close to the most probable event) Several plots of Poissonians are given in gure 2In this experiment n will be the corresponding channel number (to which after an energycalibration it will be possible to assign an energy level of the incident photon) Pn will bethe number of impulses counted by the MCA for every channel (or energy level)

2Working with the MCA (see section 31) in this experiment the spectra are discrete whereas aGaussian distribution is continuous But that is not much of a problem here as a discrete Gaussian iscalled a Bernoulli distribution and has very similar properties

4

0 2 4 6 8 10 12 14 16 18 200

005

01

015

02

025

03

035

04

occuring event n

prob

abili

ty P

n

average event N=1

N=4

N=10

Figure 2 Plot of several Poissonians for dierent average values N (own design)

24 Interaction of radiation with matter

Briey the γ detector which is used in this experiment is based on the photoelectriceect Once it has been performed an electron causes multiple ionization (which in turnis dependent upon the photons and thus the electrons kinetic energy) The Comptoneect as well as pair production are not desired in this experiment (ie they add noiseand thereby deteriorate the measurement) Yet all of these eects actually are possiblewithin the energy range of the photons in this experiment (about 40keV to several MeV also see gure 4 for a graphical representation) Therefore all of the eects need to beconsidered

Photoelectric eect3

Let the frequency of a γ particle be ν Then its energy is E = hν (h being Plancksconstant) The most important presumption of the photoelectric eect is that the photonis absorbed entirely by a metal object (this diers from eg the Compton scatteringwhere the energy of the photon is only partly absorbed) The photons energy is thentransferred to a delocalized electron from the surface of the metal A part of the energyis used to make the electron escape the potential barrier of the metal object This part iscalled the work function ϕ = hν0 where ν0 is the threshold frequency which enables theelectron to escape the potential barrier Naturally the kinetic energy of the photon mustbe Ekin ge ϕ for the photoelectric eect to occur The remaining energy transferred tothe electrons kinetic energy E = hν minus ϕ See gure 3 (a) for a graphical representationof the energies

3The photoelectric eect has been correctly interpreted by Einstein in 1905 The Nobel Prize hasbeen awarded to him in 1921 especially for his discovery of the law of the photoelectric eect (not forthe Theory of Relativity which was very disputed even at that time)

5

(a) kinetic energy of the electron in dependenceof incident photons energy

(b) momentum before and after Compton scat-tering

Figure 3 photoelectric eect and Compton eect (own design)

Compton eect (also referred to as Compton scattering)

The Compton eect occurs when only a part of the photons energy is absorbed by anatom In this case the photon performs an inelastic scattering process with one of theatom shells electrons The total (relativistic) energy as well as the momentum areconserved (see gure 3 (b)) Using the equation of momentum conservation pγ = pprimeγ + pe(where pγ is the photons momentum before the scattering process pprimeγ its momentum afterscattering and pe = pprimee the electrons momentum after scattering) combined with energyconservation Eγ = E primeγ + Eekin

(Eγ and E primeγ being the photons energies before and afterscattering and Eekin

being the electrons kinetic energy after scattering) and combiningthese with de Broglies relation the relativistic energy momentum invariance equationand several other relations one obtains the Compton scattering formula4

λprimeγ = λγ +h

mec(1minus cos θ)

λγ and λprimeγ being the photons wavelengths before and after scattering and θ being thescattering angle

Pair production

A photon is transformed into an electron and a positron The positron has the same massas the electron but the inverse (that is positive) charge This process only occurs withphoton energies greater than 102MeV Also for the process to happen the electric eldof a nucleus is required

See gure 4 for a comparison of cross sections at dierent energies It helps to distinguishwhich of the eects (photoelectric eect Compton scattering pair production) is mostprobable at a given energy

4See httpenwikipediaorgwikiCompton_effect for a good derivation of Comptons scatter-ing formula

6

(apparent) need for the neutrino when it comes to charge and mass conservation Howeverit was found that the βminus particles of a certain radioactive process do not have a constantenergy but an energy distribution It was proposed by Pauli in 1930 to introduce aneutrino which would help to explain energy and momentum conservation Its existencewas proven by an experiment in 1956

β+ decay

Proton excess is the common reason for β+ decay In this case a proton is transformedinto a neutron (which remains part of the nucleus) a positron and a neutrino (νe) Asuch transformation never occurs in free protons but only when a proton is part of anatoms nucleus and thus subject to the atoms Coulomb and binding potential Similarlyto βminus decay the energy is distributed between the β+ particle and the neutrino Here isa typical example of β+ decay

137 Nrarr 13

6 C + βminus + νe

γ decay

Unlike in α or β decay a nucleus which experiences γ decay does not change its numberof protons or neutrons γ occurs when an excited nucleus relaxes and drops into a lowerenergy state This results in the emission of highly energetic gamma rays (the wavelengthdimension are usually about 1 pm)

γ decay is usually preceded by α decay or β decay For example think of a radioac-tive mother nucleus which experiences β decay Its daughter nucleus then drops into itsground state by emitting γ rays

22 Several Basics of Probability Theory

First of all a couple of terms from probability theory shall be introduced They are cru-cial for the theoretical understanding of the experiment

Let the expected or mean value of a random variable X be micro = E(X) Then the varianceVar (X) is given by

Var (X) = E[(X minus micro)2]

The standard deviation (frequently abbreviated as sdev or stdev) is given by

σ =radicE[(X minus micro)2] =

radicVar (X)

The standard deviation can be regarded as a measure of the variability or dispersion ofa random variable X (which might be eg a dataset from a physical experiment) Alow standard deviation indicates that the data points tend to be very close to the meanwhereas high standard deviation indicates that the data are spread out over a large rangeof values

Also the standard deviation has a very important meaning in connection to the Gaussian(normal) distribution In a normal distribution the likelihood that X isin [microminus σ micro+ σ]occurs is 68 [microminus σ micro+ σ] is called a condence interval It is qualied by its condence

3

Figure 1 standard deviation diagram (own design)

condence level interval radius

68 σ90 1 64σ95 1 96σ

Table 1 Several important condence levels and the corresponding interval radii

level (which is 68 in this example) In other words think of a statistical experiment (likeradioactive decay) which is approximated by a Gaussian distribution2 The probabilitythat the experiment yields a result which is within the above condence interval is givenby the condence level 68 The most important condence levels and interval radiiare given in table 1 Two of them the 68 condence interval and the 95 condenceinterval are illustrated in gure 1

23 The Poisson Distribution

The Poisson distribution can be applied to systems with a large number of possible eventseach of which is rare Also for large numbers the Gaussian is a very good approximationfor the Poissonian so variance and condence interval calculus can be applied On topof that the variance of the Poissonian can be calculated very easily (see below) Thatswhy the Poissonian is quite perfect for this experiments purpose of statistically describingradioactive decay The Poisson distribution and its variance are given by

Poisson distribution Pn =NneminusN

nn = 0 1 2 variance σ =

radicN

where n is the occurring event and N the expected or average event (being not exactlybut close to the most probable event) Several plots of Poissonians are given in gure 2In this experiment n will be the corresponding channel number (to which after an energycalibration it will be possible to assign an energy level of the incident photon) Pn will bethe number of impulses counted by the MCA for every channel (or energy level)

2Working with the MCA (see section 31) in this experiment the spectra are discrete whereas aGaussian distribution is continuous But that is not much of a problem here as a discrete Gaussian iscalled a Bernoulli distribution and has very similar properties

4

0 2 4 6 8 10 12 14 16 18 200

005

01

015

02

025

03

035

04

occuring event n

prob

abili

ty P

n

average event N=1

N=4

N=10

Figure 2 Plot of several Poissonians for dierent average values N (own design)

24 Interaction of radiation with matter

Briey the γ detector which is used in this experiment is based on the photoelectriceect Once it has been performed an electron causes multiple ionization (which in turnis dependent upon the photons and thus the electrons kinetic energy) The Comptoneect as well as pair production are not desired in this experiment (ie they add noiseand thereby deteriorate the measurement) Yet all of these eects actually are possiblewithin the energy range of the photons in this experiment (about 40keV to several MeV also see gure 4 for a graphical representation) Therefore all of the eects need to beconsidered

Photoelectric eect3

Let the frequency of a γ particle be ν Then its energy is E = hν (h being Plancksconstant) The most important presumption of the photoelectric eect is that the photonis absorbed entirely by a metal object (this diers from eg the Compton scatteringwhere the energy of the photon is only partly absorbed) The photons energy is thentransferred to a delocalized electron from the surface of the metal A part of the energyis used to make the electron escape the potential barrier of the metal object This part iscalled the work function ϕ = hν0 where ν0 is the threshold frequency which enables theelectron to escape the potential barrier Naturally the kinetic energy of the photon mustbe Ekin ge ϕ for the photoelectric eect to occur The remaining energy transferred tothe electrons kinetic energy E = hν minus ϕ See gure 3 (a) for a graphical representationof the energies

3The photoelectric eect has been correctly interpreted by Einstein in 1905 The Nobel Prize hasbeen awarded to him in 1921 especially for his discovery of the law of the photoelectric eect (not forthe Theory of Relativity which was very disputed even at that time)

5

(a) kinetic energy of the electron in dependenceof incident photons energy

(b) momentum before and after Compton scat-tering

Figure 3 photoelectric eect and Compton eect (own design)

Compton eect (also referred to as Compton scattering)

The Compton eect occurs when only a part of the photons energy is absorbed by anatom In this case the photon performs an inelastic scattering process with one of theatom shells electrons The total (relativistic) energy as well as the momentum areconserved (see gure 3 (b)) Using the equation of momentum conservation pγ = pprimeγ + pe(where pγ is the photons momentum before the scattering process pprimeγ its momentum afterscattering and pe = pprimee the electrons momentum after scattering) combined with energyconservation Eγ = E primeγ + Eekin

(Eγ and E primeγ being the photons energies before and afterscattering and Eekin

being the electrons kinetic energy after scattering) and combiningthese with de Broglies relation the relativistic energy momentum invariance equationand several other relations one obtains the Compton scattering formula4

λprimeγ = λγ +h

mec(1minus cos θ)

λγ and λprimeγ being the photons wavelengths before and after scattering and θ being thescattering angle

Pair production

A photon is transformed into an electron and a positron The positron has the same massas the electron but the inverse (that is positive) charge This process only occurs withphoton energies greater than 102MeV Also for the process to happen the electric eldof a nucleus is required

See gure 4 for a comparison of cross sections at dierent energies It helps to distinguishwhich of the eects (photoelectric eect Compton scattering pair production) is mostprobable at a given energy

4See httpenwikipediaorgwikiCompton_effect for a good derivation of Comptons scatter-ing formula

6

Figure 1 standard deviation diagram (own design)

condence level interval radius

68 σ90 1 64σ95 1 96σ

Table 1 Several important condence levels and the corresponding interval radii

level (which is 68 in this example) In other words think of a statistical experiment (likeradioactive decay) which is approximated by a Gaussian distribution2 The probabilitythat the experiment yields a result which is within the above condence interval is givenby the condence level 68 The most important condence levels and interval radiiare given in table 1 Two of them the 68 condence interval and the 95 condenceinterval are illustrated in gure 1

23 The Poisson Distribution

The Poisson distribution can be applied to systems with a large number of possible eventseach of which is rare Also for large numbers the Gaussian is a very good approximationfor the Poissonian so variance and condence interval calculus can be applied On topof that the variance of the Poissonian can be calculated very easily (see below) Thatswhy the Poissonian is quite perfect for this experiments purpose of statistically describingradioactive decay The Poisson distribution and its variance are given by

Poisson distribution Pn =NneminusN

nn = 0 1 2 variance σ =

radicN

where n is the occurring event and N the expected or average event (being not exactlybut close to the most probable event) Several plots of Poissonians are given in gure 2In this experiment n will be the corresponding channel number (to which after an energycalibration it will be possible to assign an energy level of the incident photon) Pn will bethe number of impulses counted by the MCA for every channel (or energy level)

2Working with the MCA (see section 31) in this experiment the spectra are discrete whereas aGaussian distribution is continuous But that is not much of a problem here as a discrete Gaussian iscalled a Bernoulli distribution and has very similar properties

4

0 2 4 6 8 10 12 14 16 18 200

005

01

015

02

025

03

035

04

occuring event n

prob

abili

ty P

n

average event N=1

N=4

N=10

Figure 2 Plot of several Poissonians for dierent average values N (own design)

24 Interaction of radiation with matter

Briey the γ detector which is used in this experiment is based on the photoelectriceect Once it has been performed an electron causes multiple ionization (which in turnis dependent upon the photons and thus the electrons kinetic energy) The Comptoneect as well as pair production are not desired in this experiment (ie they add noiseand thereby deteriorate the measurement) Yet all of these eects actually are possiblewithin the energy range of the photons in this experiment (about 40keV to several MeV also see gure 4 for a graphical representation) Therefore all of the eects need to beconsidered

Photoelectric eect3

Let the frequency of a γ particle be ν Then its energy is E = hν (h being Plancksconstant) The most important presumption of the photoelectric eect is that the photonis absorbed entirely by a metal object (this diers from eg the Compton scatteringwhere the energy of the photon is only partly absorbed) The photons energy is thentransferred to a delocalized electron from the surface of the metal A part of the energyis used to make the electron escape the potential barrier of the metal object This part iscalled the work function ϕ = hν0 where ν0 is the threshold frequency which enables theelectron to escape the potential barrier Naturally the kinetic energy of the photon mustbe Ekin ge ϕ for the photoelectric eect to occur The remaining energy transferred tothe electrons kinetic energy E = hν minus ϕ See gure 3 (a) for a graphical representationof the energies

3The photoelectric eect has been correctly interpreted by Einstein in 1905 The Nobel Prize hasbeen awarded to him in 1921 especially for his discovery of the law of the photoelectric eect (not forthe Theory of Relativity which was very disputed even at that time)

5

(a) kinetic energy of the electron in dependenceof incident photons energy

(b) momentum before and after Compton scat-tering

Figure 3 photoelectric eect and Compton eect (own design)

Compton eect (also referred to as Compton scattering)

The Compton eect occurs when only a part of the photons energy is absorbed by anatom In this case the photon performs an inelastic scattering process with one of theatom shells electrons The total (relativistic) energy as well as the momentum areconserved (see gure 3 (b)) Using the equation of momentum conservation pγ = pprimeγ + pe(where pγ is the photons momentum before the scattering process pprimeγ its momentum afterscattering and pe = pprimee the electrons momentum after scattering) combined with energyconservation Eγ = E primeγ + Eekin

(Eγ and E primeγ being the photons energies before and afterscattering and Eekin

being the electrons kinetic energy after scattering) and combiningthese with de Broglies relation the relativistic energy momentum invariance equationand several other relations one obtains the Compton scattering formula4

λprimeγ = λγ +h

mec(1minus cos θ)

λγ and λprimeγ being the photons wavelengths before and after scattering and θ being thescattering angle

Pair production

A photon is transformed into an electron and a positron The positron has the same massas the electron but the inverse (that is positive) charge This process only occurs withphoton energies greater than 102MeV Also for the process to happen the electric eldof a nucleus is required

See gure 4 for a comparison of cross sections at dierent energies It helps to distinguishwhich of the eects (photoelectric eect Compton scattering pair production) is mostprobable at a given energy

4See httpenwikipediaorgwikiCompton_effect for a good derivation of Comptons scatter-ing formula

6

0 2 4 6 8 10 12 14 16 18 200

005

01

015

02

025

03

035

04

occuring event n

prob

abili

ty P

n

average event N=1

N=4

N=10

Figure 2 Plot of several Poissonians for dierent average values N (own design)

24 Interaction of radiation with matter

Briey the γ detector which is used in this experiment is based on the photoelectriceect Once it has been performed an electron causes multiple ionization (which in turnis dependent upon the photons and thus the electrons kinetic energy) The Comptoneect as well as pair production are not desired in this experiment (ie they add noiseand thereby deteriorate the measurement) Yet all of these eects actually are possiblewithin the energy range of the photons in this experiment (about 40keV to several MeV also see gure 4 for a graphical representation) Therefore all of the eects need to beconsidered

Photoelectric eect3

Let the frequency of a γ particle be ν Then its energy is E = hν (h being Plancksconstant) The most important presumption of the photoelectric eect is that the photonis absorbed entirely by a metal object (this diers from eg the Compton scatteringwhere the energy of the photon is only partly absorbed) The photons energy is thentransferred to a delocalized electron from the surface of the metal A part of the energyis used to make the electron escape the potential barrier of the metal object This part iscalled the work function ϕ = hν0 where ν0 is the threshold frequency which enables theelectron to escape the potential barrier Naturally the kinetic energy of the photon mustbe Ekin ge ϕ for the photoelectric eect to occur The remaining energy transferred tothe electrons kinetic energy E = hν minus ϕ See gure 3 (a) for a graphical representationof the energies

3The photoelectric eect has been correctly interpreted by Einstein in 1905 The Nobel Prize hasbeen awarded to him in 1921 especially for his discovery of the law of the photoelectric eect (not forthe Theory of Relativity which was very disputed even at that time)

5

(a) kinetic energy of the electron in dependenceof incident photons energy

(b) momentum before and after Compton scat-tering

Figure 3 photoelectric eect and Compton eect (own design)

Compton eect (also referred to as Compton scattering)

The Compton eect occurs when only a part of the photons energy is absorbed by anatom In this case the photon performs an inelastic scattering process with one of theatom shells electrons The total (relativistic) energy as well as the momentum areconserved (see gure 3 (b)) Using the equation of momentum conservation pγ = pprimeγ + pe(where pγ is the photons momentum before the scattering process pprimeγ its momentum afterscattering and pe = pprimee the electrons momentum after scattering) combined with energyconservation Eγ = E primeγ + Eekin

(Eγ and E primeγ being the photons energies before and afterscattering and Eekin

being the electrons kinetic energy after scattering) and combiningthese with de Broglies relation the relativistic energy momentum invariance equationand several other relations one obtains the Compton scattering formula4

λprimeγ = λγ +h

mec(1minus cos θ)

λγ and λprimeγ being the photons wavelengths before and after scattering and θ being thescattering angle

Pair production

A photon is transformed into an electron and a positron The positron has the same massas the electron but the inverse (that is positive) charge This process only occurs withphoton energies greater than 102MeV Also for the process to happen the electric eldof a nucleus is required

See gure 4 for a comparison of cross sections at dierent energies It helps to distinguishwhich of the eects (photoelectric eect Compton scattering pair production) is mostprobable at a given energy

4See httpenwikipediaorgwikiCompton_effect for a good derivation of Comptons scatter-ing formula

6

(a) kinetic energy of the electron in dependenceof incident photons energy

(b) momentum before and after Compton scat-tering

Figure 3 photoelectric eect and Compton eect (own design)

Compton eect (also referred to as Compton scattering)

The Compton eect occurs when only a part of the photons energy is absorbed by anatom In this case the photon performs an inelastic scattering process with one of theatom shells electrons The total (relativistic) energy as well as the momentum areconserved (see gure 3 (b)) Using the equation of momentum conservation pγ = pprimeγ + pe(where pγ is the photons momentum before the scattering process pprimeγ its momentum afterscattering and pe = pprimee the electrons momentum after scattering) combined with energyconservation Eγ = E primeγ + Eekin

(Eγ and E primeγ being the photons energies before and afterscattering and Eekin

being the electrons kinetic energy after scattering) and combiningthese with de Broglies relation the relativistic energy momentum invariance equationand several other relations one obtains the Compton scattering formula4

λprimeγ = λγ +h

mec(1minus cos θ)

λγ and λprimeγ being the photons wavelengths before and after scattering and θ being thescattering angle

Pair production

A photon is transformed into an electron and a positron The positron has the same massas the electron but the inverse (that is positive) charge This process only occurs withphoton energies greater than 102MeV Also for the process to happen the electric eldof a nucleus is required

See gure 4 for a comparison of cross sections at dierent energies It helps to distinguishwhich of the eects (photoelectric eect Compton scattering pair production) is mostprobable at a given energy

4See httpenwikipediaorgwikiCompton_effect for a good derivation of Comptons scatter-ing formula

6

Figure 4 Cross sections compared for dierent energies(from [8] p 89 translated from German)

25 Exponential radioactive decay

A (activity) is the number of disintegrations per second measured in Bq (Becquerel)which is one disintegration per second Another unit is Ci (Curie) 1Ci = 37 middot 1010Bq

Activity ie disintegrations per time is a statistical process Activity experiences expo-nential decay Let t be the time and A0 be the initial activity (ie t = 0) Then theactivity at time t is A = A (t) It is given by

dA

dt= minusλArArr A (t) = A0e

minusλt (1)

The latter result was obtained via separation of variables The parameter λ [λ] = 1sis

a specic decay constant of which the half life is dependent The half life T12 is theamount of time after the activity has bisected

A(T12

)=

A0

2= A0 e

minusλT12 harr ln (2) = λT12 harr λ =ln (2)

T12

rarr A (t) = A0eminus ln(2)

T12middott

(2)

If only the time t has some error or uncertainty tplusmn∆t error propagation yields

∆A =A0 ln (2) ∆t

T12

eminus ln(2)

T12middott

(3)

After the occurrence of α or β decay corresponding daughter nuclides are formedFrequently the daughters are too radioactive and disintegrate Thus a decay chainis formed As radioactive decay is statistical certain probabilities can be assigned todierent kinds of decay For example Cs-137 may have Ba-137 (β decay) in the groundstate as its daughter It may also have (Ba-137) in an elevated energy state as itsdaughter The probability for the rst event is 6 and for the latter is 94 Thereforea decay process can be assigned a branching ratio (in this case f = 094 for Ba-137)

7

3 Experimental Setup

31 High Purity Germanium detector

Basic idea underlying HPGe detectors

A High Purity Germanium (HPGe) detector is used to obtain γ spectra of dierent sam-ples in this experiment In this type of detector photons perform a photoelectric eectwith the HPGe semiconductor detector Thus they cause a separation between an elec-tron and a hole The electron is thereby put into the conductor band and causes multipleionizations The kinetic energy of the electron is dependent on the incident photonsenergy The more kinetic energy the photon transfers to the electron the higher is thenumber of ionizations the electron causes Those ionized electrons cause ionizations them-selves and the current which results is very representative for the incident photons kineticenergy

This principle is actually very similar to an ionization chamber But as the mediumfor ionization in a HPGe detector is solid (not gaseous) its density is much greater andthus a much larger number of ionizations occur (consequently the measured output signalis relatively large) That is why the output signal is relatively easy to amplify and veryrepresentative for the incident photons energy Therefore HPGe semiconductor detectorsachieve a very good resolution However compared to scintillation detectors like the NaIdetector the HPGe detectors eciency is rather small

Brief comparison with NaI scintillation detectors

NaI detectors consist of special crystals which cause uorescence when hit by γ particlesDynodes in a photomultiplier are used for the amplication of the signal The eciencyadvantage is due to the fact that the crystals can easily be built in large shapes eg(almost) completely surrounding a small sample But unfortunately the resolution islow compared to HPGe detectors As this experiment is about the investigation of lowenergy samples (the energy spectrum is about 40keV to several MeV ) HPGe detectorsare a better choice Also their eciency can be improved by providing favorable samplegeometry (a Marinelli beaker is helpful for this purpose)

More on this experiments HPGe detector Cooling and MCA

The HPGe detector must be cooled in order to reduce the thermal charge carrier gen-eration (noise) to an acceptable level So cooling reduces Compton scattering Liquidnitrogen cooling was employed in the detector used for this experiment

The HPGe γ spectrometer used for this experiment was connected to an analog dig-ital converter (ADC) where the signal was digitalized after linear preamplication Thedigital signal was then conducted to a multichannel analyzer (MCA) The MCA has aninternal memory of 8kbits (8096 bits) It can be visualized like a sorting device channelnumbers are assigned to certain pulse height intervals If an impulse of a height whichis part of that interval is measured the counts number of the corresponding channel isincreased by one As the preamplication is linear only two points are required to builda relationship between between channel numbers and energies (energy calibration) TheHPGe detector in use used a step width of approximately two channels for one keV

8

The MCA had a built-in display for live observation of the spectrum but also collectedthe counts data internally and transferred them to a computer This data was obtainedfor the analysis of the experiment

Both the sample and the detector were locked in a cabinet of lead in order to isolatethem from background radiation

32 Evaluation of γ spectra

The MCAs amplier can be assumed as linear Thus the relationship between channelnumber and energy are linear E (n) = a middot n+ b

What is also very important is the relationship between eciency ξ and activity A

ξ (E) =N

t middot f middot A(4)

This relationship is required for obtaining the eciency in dependence of the activity (asin section 53) and vice versa (section 55) In simple terms it is the fraction betweenthe amount of γ particles registered by the detector and the amount of γ particles whichwere actually emitted from the source (within a certain time frame)

After registering a particle the detector is unable to respond for a certain dead timeso its life time is slightly shorter than the time which actually passed (real time)

When a spectrum is measured it is partially buried in a background This is why it isrequired to subtract the background from the net peak The idea of how this is done inthis experiment is shown in gure 5 First of all it is necessary to decide which channelsactually belong to the peak Suppose these are channels 5176 to 5190 that is n = 15channels The content of these channels (which is the sum of all counts in channel 5176

Figure 5 Visualization of background subtraction procedure used in the experimentsanalysis (own design)

9

to 5190) is Ntot Then with a constant distance d to the left and to the right preservedthe same amount of channels n used for summing up its count contents Let the sum ofcounts within the n channels to the left of the peak be NBGL and the one to the right beNBGR The average of them is NBG = (NBGL +NBGR) 2 Consequently the net numberof counts in the peak Nnet can be obtained

Nnet = Ntot minusNBG

σnet =radicσ2tot + σ2

BG =radicNtot +NBG

The latter result has been obtained assuming that both the peak and the background canbe adequately represented by a Poisson distribution

4 Experimental Procedure

For the experiment it was necessary to collect a soil sample A Marinelli beaker wasused for this purpose Its shape is very well adapted to the shape of the detector therebyimproving the eciency of the measurement The time date and location of the samplescollection are given in gure 6 It is a digitally modied Google Map5

5The original unmodied picture can be recreated via httpmapsgoogledemapsf=qampsource=

s_qamphl=deampq=Waller+Feldmarksee+Walle+28237+Bremenampsll=5115178610415039ampsspn=

1745592638979492ampie=UTF8ampcd=1ampgeocode=FZSmKgMdWheGAAampsplit=0amphq=amphnear=Waller+

Feldmarkseeampll=531266258788526ampspn=00068370015235ampt=hampz=16

Figure 6 Sample collected in this location at 0030 PM on October 8th 2009

10

3 Experimental Setup

31 High Purity Germanium detector

Basic idea underlying HPGe detectors

A High Purity Germanium (HPGe) detector is used to obtain γ spectra of dierent sam-ples in this experiment In this type of detector photons perform a photoelectric eectwith the HPGe semiconductor detector Thus they cause a separation between an elec-tron and a hole The electron is thereby put into the conductor band and causes multipleionizations The kinetic energy of the electron is dependent on the incident photonsenergy The more kinetic energy the photon transfers to the electron the higher is thenumber of ionizations the electron causes Those ionized electrons cause ionizations them-selves and the current which results is very representative for the incident photons kineticenergy

This principle is actually very similar to an ionization chamber But as the mediumfor ionization in a HPGe detector is solid (not gaseous) its density is much greater andthus a much larger number of ionizations occur (consequently the measured output signalis relatively large) That is why the output signal is relatively easy to amplify and veryrepresentative for the incident photons energy Therefore HPGe semiconductor detectorsachieve a very good resolution However compared to scintillation detectors like the NaIdetector the HPGe detectors eciency is rather small

Brief comparison with NaI scintillation detectors

NaI detectors consist of special crystals which cause uorescence when hit by γ particlesDynodes in a photomultiplier are used for the amplication of the signal The eciencyadvantage is due to the fact that the crystals can easily be built in large shapes eg(almost) completely surrounding a small sample But unfortunately the resolution islow compared to HPGe detectors As this experiment is about the investigation of lowenergy samples (the energy spectrum is about 40keV to several MeV ) HPGe detectorsare a better choice Also their eciency can be improved by providing favorable samplegeometry (a Marinelli beaker is helpful for this purpose)

More on this experiments HPGe detector Cooling and MCA

The HPGe detector must be cooled in order to reduce the thermal charge carrier gen-eration (noise) to an acceptable level So cooling reduces Compton scattering Liquidnitrogen cooling was employed in the detector used for this experiment

The HPGe γ spectrometer used for this experiment was connected to an analog dig-ital converter (ADC) where the signal was digitalized after linear preamplication Thedigital signal was then conducted to a multichannel analyzer (MCA) The MCA has aninternal memory of 8kbits (8096 bits) It can be visualized like a sorting device channelnumbers are assigned to certain pulse height intervals If an impulse of a height whichis part of that interval is measured the counts number of the corresponding channel isincreased by one As the preamplication is linear only two points are required to builda relationship between between channel numbers and energies (energy calibration) TheHPGe detector in use used a step width of approximately two channels for one keV

8

The MCA had a built-in display for live observation of the spectrum but also collectedthe counts data internally and transferred them to a computer This data was obtainedfor the analysis of the experiment

Both the sample and the detector were locked in a cabinet of lead in order to isolatethem from background radiation

32 Evaluation of γ spectra

The MCAs amplier can be assumed as linear Thus the relationship between channelnumber and energy are linear E (n) = a middot n+ b

What is also very important is the relationship between eciency ξ and activity A

ξ (E) =N

t middot f middot A(4)

This relationship is required for obtaining the eciency in dependence of the activity (asin section 53) and vice versa (section 55) In simple terms it is the fraction betweenthe amount of γ particles registered by the detector and the amount of γ particles whichwere actually emitted from the source (within a certain time frame)

After registering a particle the detector is unable to respond for a certain dead timeso its life time is slightly shorter than the time which actually passed (real time)

When a spectrum is measured it is partially buried in a background This is why it isrequired to subtract the background from the net peak The idea of how this is done inthis experiment is shown in gure 5 First of all it is necessary to decide which channelsactually belong to the peak Suppose these are channels 5176 to 5190 that is n = 15channels The content of these channels (which is the sum of all counts in channel 5176

Figure 5 Visualization of background subtraction procedure used in the experimentsanalysis (own design)

9

to 5190) is Ntot Then with a constant distance d to the left and to the right preservedthe same amount of channels n used for summing up its count contents Let the sum ofcounts within the n channels to the left of the peak be NBGL and the one to the right beNBGR The average of them is NBG = (NBGL +NBGR) 2 Consequently the net numberof counts in the peak Nnet can be obtained

Nnet = Ntot minusNBG

σnet =radicσ2tot + σ2

BG =radicNtot +NBG

The latter result has been obtained assuming that both the peak and the background canbe adequately represented by a Poisson distribution

4 Experimental Procedure

For the experiment it was necessary to collect a soil sample A Marinelli beaker wasused for this purpose Its shape is very well adapted to the shape of the detector therebyimproving the eciency of the measurement The time date and location of the samplescollection are given in gure 6 It is a digitally modied Google Map5

5The original unmodied picture can be recreated via httpmapsgoogledemapsf=qampsource=

s_qamphl=deampq=Waller+Feldmarksee+Walle+28237+Bremenampsll=5115178610415039ampsspn=

1745592638979492ampie=UTF8ampcd=1ampgeocode=FZSmKgMdWheGAAampsplit=0amphq=amphnear=Waller+

Feldmarkseeampll=531266258788526ampspn=00068370015235ampt=hampz=16

Figure 6 Sample collected in this location at 0030 PM on October 8th 2009

10

The MCA had a built-in display for live observation of the spectrum but also collectedthe counts data internally and transferred them to a computer This data was obtainedfor the analysis of the experiment

Both the sample and the detector were locked in a cabinet of lead in order to isolatethem from background radiation

32 Evaluation of γ spectra

The MCAs amplier can be assumed as linear Thus the relationship between channelnumber and energy are linear E (n) = a middot n+ b

What is also very important is the relationship between eciency ξ and activity A

ξ (E) =N

t middot f middot A(4)

This relationship is required for obtaining the eciency in dependence of the activity (asin section 53) and vice versa (section 55) In simple terms it is the fraction betweenthe amount of γ particles registered by the detector and the amount of γ particles whichwere actually emitted from the source (within a certain time frame)

After registering a particle the detector is unable to respond for a certain dead timeso its life time is slightly shorter than the time which actually passed (real time)

When a spectrum is measured it is partially buried in a background This is why it isrequired to subtract the background from the net peak The idea of how this is done inthis experiment is shown in gure 5 First of all it is necessary to decide which channelsactually belong to the peak Suppose these are channels 5176 to 5190 that is n = 15channels The content of these channels (which is the sum of all counts in channel 5176

Figure 5 Visualization of background subtraction procedure used in the experimentsanalysis (own design)

9

to 5190) is Ntot Then with a constant distance d to the left and to the right preservedthe same amount of channels n used for summing up its count contents Let the sum ofcounts within the n channels to the left of the peak be NBGL and the one to the right beNBGR The average of them is NBG = (NBGL +NBGR) 2 Consequently the net numberof counts in the peak Nnet can be obtained

Nnet = Ntot minusNBG

σnet =radicσ2tot + σ2

BG =radicNtot +NBG

The latter result has been obtained assuming that both the peak and the background canbe adequately represented by a Poisson distribution

4 Experimental Procedure

For the experiment it was necessary to collect a soil sample A Marinelli beaker wasused for this purpose Its shape is very well adapted to the shape of the detector therebyimproving the eciency of the measurement The time date and location of the samplescollection are given in gure 6 It is a digitally modied Google Map5

5The original unmodied picture can be recreated via httpmapsgoogledemapsf=qampsource=

s_qamphl=deampq=Waller+Feldmarksee+Walle+28237+Bremenampsll=5115178610415039ampsspn=

1745592638979492ampie=UTF8ampcd=1ampgeocode=FZSmKgMdWheGAAampsplit=0amphq=amphnear=Waller+

Feldmarkseeampll=531266258788526ampspn=00068370015235ampt=hampz=16

Figure 6 Sample collected in this location at 0030 PM on October 8th 2009

10

to 5190) is Ntot Then with a constant distance d to the left and to the right preservedthe same amount of channels n used for summing up its count contents Let the sum ofcounts within the n channels to the left of the peak be NBGL and the one to the right beNBGR The average of them is NBG = (NBGL +NBGR) 2 Consequently the net numberof counts in the peak Nnet can be obtained

Nnet = Ntot minusNBG

σnet =radicσ2tot + σ2

BG =radicNtot +NBG

The latter result has been obtained assuming that both the peak and the background canbe adequately represented by a Poisson distribution

4 Experimental Procedure

For the experiment it was necessary to collect a soil sample A Marinelli beaker wasused for this purpose Its shape is very well adapted to the shape of the detector therebyimproving the eciency of the measurement The time date and location of the samplescollection are given in gure 6 It is a digitally modied Google Map5

5The original unmodied picture can be recreated via httpmapsgoogledemapsf=qampsource=

s_qamphl=deampq=Waller+Feldmarksee+Walle+28237+Bremenampsll=5115178610415039ampsspn=

1745592638979492ampie=UTF8ampcd=1ampgeocode=FZSmKgMdWheGAAampsplit=0amphq=amphnear=Waller+

Feldmarkseeampll=531266258788526ampspn=00068370015235ampt=hampz=16

Figure 6 Sample collected in this location at 0030 PM on October 8th 2009

10

The samples weight is given below

weigth of Marinelli beaker (empty) 1802g

beaker lled with soil sample 13487g

soil sample itself 11685g

41 Test source with one γ line

The spectrum of a Cs-137 point source sample is recorded from dierent locations eachtime for 20 seconds In one case a lead plate is put in between the sample and the detectorThe Germanium detector has a cylindrical shape The goal is to nd a dependencybetween the samples location and the number of registered counts and also to givereasons for this dependency

42 Test sources with multiple lines - energy calibration

Co-60 and Cs-137 test sources are placed on top of the detector The spectrum is recordedfor 200 seconds with closed shielding door Cs-137 has one distinct distinct peak whereasCo-60 hast two An energy calibration is performed using two peaks

43 Eciency calibration

A Cs-137 test source was placed on top of the detector The spectrum was recorded for400s with closed shielding door An eciency calibration was performed based on giveninformation about the Cs-137 (age activity half life)

44 Soil sample spectrum measurement calculating activities

After a new energy calibration the spectrum of the soil sample was recorded for 5864s(which is about 98 minutes) Using an energy table it was possible to identify manypeaks Three prominent peaks were chosen for calculating the current activity of thecorresponding radionuclide in the soil sample

5 Analysis

51 Test source with one gamma line

For each of the below situations (1 to 4) a characteristic peak is measured in the spectrumIn every situation the shielding doors were closed The number of recorded counts in thecentral channel is given in table 2 A graphical representation of the situations is givenin gure 7

1 Sample on top of detector centered

2 Sample on top of the detector as far away from the center as possible

3 Sample on top of the detector centered A lead plate (about 25mm thickness) isput between the sample and the detector

4 Sample as far away from the detector as possible within the detector chamber

11

Figure 7 Numbers of counts in the central channel in dierent positions (own design)

situation no location (short) measured t counts (central channel)

1 on top of detector (center) t = 20s N = 24002 on top of the detector (edge) t = 20s N = 14523 on top with lead plate t = 20s N = 13214 as far away as possible t = 20s N = 48

Table 2 Counts N in the central channel obtained in dierent situations

Obviously the further away the sample is from the detector (and also the more resis-tance like lead shielding or lead plates is in the way of the photons) the fewer countsare registered This is due to the fact that the emission of photons is isotropic ie thephotons are distributed to all directions In situation no 1 about one half of all photonshit the detector In situation no 2 less than one fourth of the photons hit the detec-tor and in no 4 it is even less The very low number of registered counts in case no 4is also due to the fact that the photons actually ionize the air on their way to the detector

In situation no 3 although the position of the radionuclide is favorable the lead plateabsorbs lots of photons The higher the thickness of the lead plate the fewer photonsreach the detector with sucient energy to perform a photoelectric eect (and thus arecorrectly detected by the HPGe detector) This is due to the fact that the γ rays lose someof their kinetic energy through scattering (esp Compton) and ionization and thereforehave less remaining energy to perform a photoelectric eect in the detector

52 Test sources with multiple lines - energy calibration

With the HPGe γ spectrometer in use linear ampliers can be assumed Thus channelnumbers are proportional impulse heights which in turn are proportional to energiesEnergy calibration is all about assigning energies E to channel numbers n The energiesof the photons emitted by radioactive nuclides in use here can be looked up in literature([3] was used for this purpose) Table 3 combines the literature energy values and thecorresponding channel numbers

For the energy calibrations the two outer points (n1 E1) and (n3 E3) were usedUsing these points combined with the linear equation E (n) = a middot n+ b yields a set of twolinear equations The solution yields the unknown parameters a and b

E (n) = 049582keV middot n+ 024052keV E energy in keV n channel number

12

large peak energy nuclide channel number

E1 = 66166keV Csminus 137 n1 = 1334E2 = 117324keV Cominus 60 n2 = 2366E3 = 133250keV Cominus 60 n3 = 2687

Table 3 Data points for energy calibration

53 Eciency calibration

The properties of the used Csminus 137 sample were these

activity on 19750929 A0 = 132microCi 48840Bq half life T12 = 3017y

error of initial activity ∆A0 = A0 middot 5 = 2442Bq

In order to calculate the eciency ξ = N (t middot f middot A) the current activity needs to beobtained rst The date of the experiment was the 15th of October 2009 The timedierence is tnow = 3407y Thus the current activity is

A (tnow) = A0 middot eminus ln(2)tnow

T12 = 22327Bq (5)

∆A (tnow) = ∆A0 middot eminus ln(2)tnow

T12 = 1116Bq (6)

For the eciency 14 channel of the Csminus 137 peak were considered Another 14 channelswere considered for the background radiance to the left and another 14 channels for thebackground radiance to the right of the peak Among these channels all the counts weresummed up This resulted in Ntot = 5191 NBGL = 1 and NBGR = 31 The average countsof the background channels are

NBG =NBGL +NBGR

2= 16 σBG =

radicNBG

Thus the net counts of the peak (without the background radiation) are

Nnet = Ntot minusNBG = 5175 σnet =radicNtot +NBG = 7215rarr Nnet = 5175plusmn 72

Note that the MCA-built-in display had an internal routine for calculating Ntot andNnet The values it yielded for the very same channels were Ntot MCA = 5188 andNnet MCA = 3893 Consequently NBG MCA = 1259 16 = NBG However Ntot MCA

and Ntot are very close to each other

The branching ratio being f = 085 and the time of the experiment being texp = 400sthe eciency can now be obtained

ξ = Nnet

t f A(tnow)= 681 ∆ξ = σnet

t f A(tnow)+ Nnet ∆A(tnow)

t f [A(tnow)]2= 044rarr ξ = 684plusmn 044

For the above error calculation several assumptions had to be made ∆Nnet 6= 0∆A (tnow) ∆texp = 0 ∆f = 0 These assumption actually make sense because texpand f and have either been measured very precisely or have been taken from literature

13

the MCA was congured to measure for a real time interval of texp = 400s Asanalyzed in the soil sample section the dierence between real and life time onlycauses an error of lt 05

f was looked up in [3]

concerning A (tnow) = A0 middot exp(minus ln (2) tnowT12

) the value for T12 was inscribed

on the sample tnow has been computed as described above The computation wasperformed in Mathematica based on seconds For this reason the exp() term itself

is assumed to have practically no error at all However an error of 5 for A0 wasinscribed on the sample This has been considered in the computation of ∆A (tnow)according to equation 6

It is now possible to compare the results for the eciency ξ with the the laboratorysown eciency calibration curve (see Appendix B) It results from measurements withmany radionuclides and is a good source for comparison The laboratorys calibrationcurve yields an expected eciency of ξlab = 43 whereas ξexp = 684 plusmn 044 Theauthor presumes that the principal source of error is the background radiation (as statedabove the other variables have very small error ranges and also Ntot MCA and Ntot arevery close) The background radiation value was much more appropriately given by theinternal MCA routine (its result could be read o the internal display) Performing theeciency calculation with Nnet MCA yields ξnet MCA = 512 which is much closer toξlab However an obvious error source can not be made out The author was carefullyinstructed in the usage of the MCA and entered nearly all of the commands himself(under supervision) Still the only reasonable cause for error seems to be software basedPerhaps an automatic and undesired re-scaling or normalization was performed by theoscilloscope

54 Data analysis of soil sample measurement

For the analysis of the soil sample spectrum another energy calibration was requiredThe Cs-137 peak as well as the K-40 peak were used for this purpose Both peaks arevery characteristic for the spectrum (the Cs-137 peak is the largest peak of the spectrumwhereas the K-40 peak is by far the largest peak with energies above 1000keV ) TheCs-137 peak at E1 = 6616keV was found at channel number n1 = 2651 and the K-40peak at E2 = 14608keV was found at n2 = 5846 The linear energy calibration yieldedE (n) = 0250141keV middot nminus 152338keV With the energy calibration performed it is possible to identify radionuclides from thesoil samples spectrum The energies to which the peaks correspond as well as thecorresponding nuclide information can be found in table 4 An overall plot of the spectrumis given in gure 8 It provides a good view on the proportions of the peak heights (Thethree peaks which are annotated in this plot are important for section 55) A large plotof the spectrum with annotated peaks can be looked up in 9

14

0 200 400 600 800 1000 1200 1400 1600 1800 20000

50

100

150

200

E [keV]

coun

ts p

er c

hann

el

Kminus40Csminus137Pbminus214

(3520keV)

Figure 8 spectrum recorded from soil sample (overall view)

energy [keV] radionuclide f [] half life origin

771 (x-ray) Pb-214 107 long U-238926 Th-234 56 long U-2381856 U-235 540 71e7y natural2095 Ac-228 41 long Th-2322386 Pb-212 450 long Th-2322702 Ac-228 38 long Th-2322952 Pb-214 187 long U-2383385 Ac-228 123 long Th-2323520 Pb-214 366 long U-2385110 annihilation peak 5831 Tl-208 300 long Th-2326094 Bi-214 450 long U-2386616 Cs-137 852 302y fallout7272 Bi-212 70 long Th-2327684 Bi-214 50 long U-2387949 Ac-228 49 long Th-2329111 Ac-228 290 long Th-2329689 Ac-228 175 long Th-23211204 Bi-214 152 U-238 U-23814608 K-40 107 13e9y natural15095 Bi-214 22 long U-23815881 Ac-228 46 long Th-23216310 Ac-228 34 long Th-23217647 Bi-214 154 long U-238

Table 4 Nuclides identied in the soil sample (individual nuclide information from [3])

15

020

040

060

080

010

0012

0014

0016

0018

0020

000102030405060708090

Ene

rgy

[keV

]

counts per channel

Kminus

40

Biminus

214

Biminus

214

Acminus

228

Csminus

137

Biminus

214

Acminus

228

Pbminus

214

Pbminus

212

Acminus

228

Biminus

214

Acminus

228

Acminus

228

Biminus

214

Biminus

212

Pbminus

214

(Xminus

ray)

Thminus

234

Uminus

235

Tlminus

208

anni

hila

tion

peak

at

511k

eV

Acminus

228

Figure 9 annotated spectrum (recorded from soil sample in Marinelli beaker)

16

A characteristic property of natural radionuclides is their half life which is usuallyvery long Also it is much more probable to encounter a radionuclide with a smallbranching ration (eg 5) and a very long half life than to encounter a nuclide witha short half life (eg 10 days) even though if its branching ratio may be great (eg85) This consideration was helpful in many decisions when close energy values madethe distinction of dierent radionuclides possible Also it is important to remark thatmany of the encountered radionuclides originate from either Th-232 or U-238 which areboth natural radionuclides

55 Calculating activities of three prominent lines

The nal task was to calculate the activities of three prominent lines The time of theexperiment t as well as the branching ratio for each radionuclide f being known theactivity A the eciency ξ and the net number of counts in the peak Nnet need to befound

For Nnet the same procedure as in section 53 is employed (summing up the totalnumber of counts N tot in the peak doing the same for the background radiationNBGL left of the peak and NBGR right of the peak and then averaging them andnally subtracting Nnet = Ntot minus NBG) For a more detailed description of thisprocess see section 22

For the eciency ξ another calibration curve is obtained from the laboratorys long-termed measurements (see Appendix C) The required eciency can easily be reado the graph as indicated in the Appendix

The real time of the experiment was 5864s but the time in which the detector wasresponsive (life time) was slightly smaller t = 5861s Note that the dierence is onlyabout 005 so ∆t is regarded as practically non-existent With this information it ispossible to calculate the activity A of the investigated radionuclides Note that this timeerror propagation (according to Gauss) was necessary to employ

A =Nnet

t f ξ∆A =

radic(σNnet

t f ξ

)2

+

(Nnet ∆ξ

t f ξ2

)2

and σNnet=radicNnet

The error of the eciency was appropriately set to ξ = 0001 The investigated radionu-clides were K-40 Cs-137 and Pb-214 (at 3520keV) also see gure 8 The results for theactivities as well as their errors and other details of the calculation process are given intable 5 All of the data given in this table was calculated using the self-written MATLABfunctionpeak_counter Its source code is given in Appendix A

Surprisingly the activity of Cs-137 is comparatively small Even though its peak isabout three times larger than the Pb-214 peak it is also narrower so their activitiesare very close The activity of K-40 (which like Pb-214 has a natural origin) is muchgreater Having in mind that the Cs-137 peak is the largest peak in the spectrum it isstill a somewhat comforting result that the activity of the articial isotope Cs-137 is notoutrageously great (any more)

17

variable K-40 Cs-137 Pb-214

t[s] 5861 5861 5861f 0107 0852 0366ξ 0010plusmn 0001 0018plusmn 0001 0024plusmn 0001Ntot 1399plusmn 37 1234plusmn 35 726plusmn 26NBGL 25plusmn 5 294plusmn 17 191plusmn 13NBGR 14plusmn 3 270plusmn 16 181plusmn 13NBG 195plusmn 4 282plusmn 16 186plusmn 13Nnet 13795plusmn 37 952plusmn 30 540plusmn 23

A [Bq] 21997plusmn 2278 1059plusmn 068 1049plusmn 063

Table 5 Detailed information on activity calculation

6 Conclusion

The results of the experiment Natural and Man-Made Radioactivity are Soil are absolutelysatisfactory and do not leave many questions unanswered

The linear energy calibration (which was performed twice with a dataset of only twopoints) of the Canberra MCA was precise and allowed investigating even very distinctpeaks Although the calculation of the eciency in section 53 yielded a rather unreal-istic result it was possible to narrow down the error source to a disharmony in softwarecalculations

In the soil sample as many as 24 radionuclides were identied Among them Cs-137(which originates in global fallout after atmospheric nuclear bomb tests and also in the1986 Chernobyl accident) has the most distinct peak The digital data which resultedfrom the soil sample measurement was easy to handle and had a very good resolution (aswas to be expected from a HPGe detector) The activity calculation of the radionuclidesPb-214 (at 3520keV ) Cs-137 and K-40 clearly illustrated the independence between peakheight and activity

18

References

[1] Helmut Fischer Natural and Man-Made Radioactivity in Soil April 5 2004httpwwwpraktikumphysikuni-bremendeimagespdffpfp21_

radioactivitypdf

[2] Helmut Fischer Radioisotopes in Soil June 2003httpwwwmsc-epuni-bremendeserviceslecturespracticalsmeas_

tech_radioactivity_hf_rev3pdf

[3] Gamma Rays in the Environment with Intensities greater than 1 August 1980Nuclear Data Sheets 15 203 (1975) Part of a collection of tables on radioactivityobtained at the laboratory

[4] Basic Counting Systems copy 2006 Canberra IndustrieshttpwwwcanberracompdfLiteraturebasic20counting20sys20sfpdf

[5] Gamma and X-Ray Detectioncopy 2006 Canberra IndustrieshttpwwwcanberracompdfLiteratureGamma20Xray20Det20SFpdf

[6] Spectrum Analysis copy 2006 Canberra IndustrieshttpwwwcanberracompdfLiteratureSpectrum20Analysis20SFpdf

[7] D A Gedecke How Counting Statistics Controls Detection Limits and Peak Preci-sion copy Ortec (no date given)httpwwwortec-onlinecomapplication-notesan59pdf

[8] Wolfgang Demtroumlder Experimentalphysik 4 Second edition Springer 2005

19

Figure 7 Numbers of counts in the central channel in dierent positions (own design)

situation no location (short) measured t counts (central channel)

1 on top of detector (center) t = 20s N = 24002 on top of the detector (edge) t = 20s N = 14523 on top with lead plate t = 20s N = 13214 as far away as possible t = 20s N = 48

Table 2 Counts N in the central channel obtained in dierent situations

Obviously the further away the sample is from the detector (and also the more resis-tance like lead shielding or lead plates is in the way of the photons) the fewer countsare registered This is due to the fact that the emission of photons is isotropic ie thephotons are distributed to all directions In situation no 1 about one half of all photonshit the detector In situation no 2 less than one fourth of the photons hit the detec-tor and in no 4 it is even less The very low number of registered counts in case no 4is also due to the fact that the photons actually ionize the air on their way to the detector

In situation no 3 although the position of the radionuclide is favorable the lead plateabsorbs lots of photons The higher the thickness of the lead plate the fewer photonsreach the detector with sucient energy to perform a photoelectric eect (and thus arecorrectly detected by the HPGe detector) This is due to the fact that the γ rays lose someof their kinetic energy through scattering (esp Compton) and ionization and thereforehave less remaining energy to perform a photoelectric eect in the detector

52 Test sources with multiple lines - energy calibration

With the HPGe γ spectrometer in use linear ampliers can be assumed Thus channelnumbers are proportional impulse heights which in turn are proportional to energiesEnergy calibration is all about assigning energies E to channel numbers n The energiesof the photons emitted by radioactive nuclides in use here can be looked up in literature([3] was used for this purpose) Table 3 combines the literature energy values and thecorresponding channel numbers

For the energy calibrations the two outer points (n1 E1) and (n3 E3) were usedUsing these points combined with the linear equation E (n) = a middot n+ b yields a set of twolinear equations The solution yields the unknown parameters a and b

E (n) = 049582keV middot n+ 024052keV E energy in keV n channel number

12

large peak energy nuclide channel number

E1 = 66166keV Csminus 137 n1 = 1334E2 = 117324keV Cominus 60 n2 = 2366E3 = 133250keV Cominus 60 n3 = 2687

Table 3 Data points for energy calibration

53 Eciency calibration

The properties of the used Csminus 137 sample were these

activity on 19750929 A0 = 132microCi 48840Bq half life T12 = 3017y

error of initial activity ∆A0 = A0 middot 5 = 2442Bq

In order to calculate the eciency ξ = N (t middot f middot A) the current activity needs to beobtained rst The date of the experiment was the 15th of October 2009 The timedierence is tnow = 3407y Thus the current activity is

A (tnow) = A0 middot eminus ln(2)tnow

T12 = 22327Bq (5)

∆A (tnow) = ∆A0 middot eminus ln(2)tnow

T12 = 1116Bq (6)

For the eciency 14 channel of the Csminus 137 peak were considered Another 14 channelswere considered for the background radiance to the left and another 14 channels for thebackground radiance to the right of the peak Among these channels all the counts weresummed up This resulted in Ntot = 5191 NBGL = 1 and NBGR = 31 The average countsof the background channels are

NBG =NBGL +NBGR

2= 16 σBG =

radicNBG

Thus the net counts of the peak (without the background radiation) are

Nnet = Ntot minusNBG = 5175 σnet =radicNtot +NBG = 7215rarr Nnet = 5175plusmn 72

Note that the MCA-built-in display had an internal routine for calculating Ntot andNnet The values it yielded for the very same channels were Ntot MCA = 5188 andNnet MCA = 3893 Consequently NBG MCA = 1259 16 = NBG However Ntot MCA

and Ntot are very close to each other

The branching ratio being f = 085 and the time of the experiment being texp = 400sthe eciency can now be obtained

ξ = Nnet

t f A(tnow)= 681 ∆ξ = σnet

t f A(tnow)+ Nnet ∆A(tnow)

t f [A(tnow)]2= 044rarr ξ = 684plusmn 044

For the above error calculation several assumptions had to be made ∆Nnet 6= 0∆A (tnow) ∆texp = 0 ∆f = 0 These assumption actually make sense because texpand f and have either been measured very precisely or have been taken from literature

13

the MCA was congured to measure for a real time interval of texp = 400s Asanalyzed in the soil sample section the dierence between real and life time onlycauses an error of lt 05

f was looked up in [3]

concerning A (tnow) = A0 middot exp(minus ln (2) tnowT12

) the value for T12 was inscribed

on the sample tnow has been computed as described above The computation wasperformed in Mathematica based on seconds For this reason the exp() term itself

is assumed to have practically no error at all However an error of 5 for A0 wasinscribed on the sample This has been considered in the computation of ∆A (tnow)according to equation 6

It is now possible to compare the results for the eciency ξ with the the laboratorysown eciency calibration curve (see Appendix B) It results from measurements withmany radionuclides and is a good source for comparison The laboratorys calibrationcurve yields an expected eciency of ξlab = 43 whereas ξexp = 684 plusmn 044 Theauthor presumes that the principal source of error is the background radiation (as statedabove the other variables have very small error ranges and also Ntot MCA and Ntot arevery close) The background radiation value was much more appropriately given by theinternal MCA routine (its result could be read o the internal display) Performing theeciency calculation with Nnet MCA yields ξnet MCA = 512 which is much closer toξlab However an obvious error source can not be made out The author was carefullyinstructed in the usage of the MCA and entered nearly all of the commands himself(under supervision) Still the only reasonable cause for error seems to be software basedPerhaps an automatic and undesired re-scaling or normalization was performed by theoscilloscope

54 Data analysis of soil sample measurement

For the analysis of the soil sample spectrum another energy calibration was requiredThe Cs-137 peak as well as the K-40 peak were used for this purpose Both peaks arevery characteristic for the spectrum (the Cs-137 peak is the largest peak of the spectrumwhereas the K-40 peak is by far the largest peak with energies above 1000keV ) TheCs-137 peak at E1 = 6616keV was found at channel number n1 = 2651 and the K-40peak at E2 = 14608keV was found at n2 = 5846 The linear energy calibration yieldedE (n) = 0250141keV middot nminus 152338keV With the energy calibration performed it is possible to identify radionuclides from thesoil samples spectrum The energies to which the peaks correspond as well as thecorresponding nuclide information can be found in table 4 An overall plot of the spectrumis given in gure 8 It provides a good view on the proportions of the peak heights (Thethree peaks which are annotated in this plot are important for section 55) A large plotof the spectrum with annotated peaks can be looked up in 9

14

0 200 400 600 800 1000 1200 1400 1600 1800 20000

50

100

150

200

E [keV]

coun

ts p

er c

hann

el

Kminus40Csminus137Pbminus214

(3520keV)

Figure 8 spectrum recorded from soil sample (overall view)

energy [keV] radionuclide f [] half life origin

771 (x-ray) Pb-214 107 long U-238926 Th-234 56 long U-2381856 U-235 540 71e7y natural2095 Ac-228 41 long Th-2322386 Pb-212 450 long Th-2322702 Ac-228 38 long Th-2322952 Pb-214 187 long U-2383385 Ac-228 123 long Th-2323520 Pb-214 366 long U-2385110 annihilation peak 5831 Tl-208 300 long Th-2326094 Bi-214 450 long U-2386616 Cs-137 852 302y fallout7272 Bi-212 70 long Th-2327684 Bi-214 50 long U-2387949 Ac-228 49 long Th-2329111 Ac-228 290 long Th-2329689 Ac-228 175 long Th-23211204 Bi-214 152 U-238 U-23814608 K-40 107 13e9y natural15095 Bi-214 22 long U-23815881 Ac-228 46 long Th-23216310 Ac-228 34 long Th-23217647 Bi-214 154 long U-238

Table 4 Nuclides identied in the soil sample (individual nuclide information from [3])

15

020

040

060

080

010

0012

0014

0016

0018

0020

000102030405060708090

Ene

rgy

[keV

]

counts per channel

Kminus

40

Biminus

214

Biminus

214

Acminus

228

Csminus

137

Biminus

214

Acminus

228

Pbminus

214

Pbminus

212

Acminus

228

Biminus

214

Acminus

228

Acminus

228

Biminus

214

Biminus

212

Pbminus

214

(Xminus

ray)

Thminus

234

Uminus

235

Tlminus

208

anni

hila

tion

peak

at

511k

eV

Acminus

228

Figure 9 annotated spectrum (recorded from soil sample in Marinelli beaker)

16

A characteristic property of natural radionuclides is their half life which is usuallyvery long Also it is much more probable to encounter a radionuclide with a smallbranching ration (eg 5) and a very long half life than to encounter a nuclide witha short half life (eg 10 days) even though if its branching ratio may be great (eg85) This consideration was helpful in many decisions when close energy values madethe distinction of dierent radionuclides possible Also it is important to remark thatmany of the encountered radionuclides originate from either Th-232 or U-238 which areboth natural radionuclides

55 Calculating activities of three prominent lines

The nal task was to calculate the activities of three prominent lines The time of theexperiment t as well as the branching ratio for each radionuclide f being known theactivity A the eciency ξ and the net number of counts in the peak Nnet need to befound

For Nnet the same procedure as in section 53 is employed (summing up the totalnumber of counts N tot in the peak doing the same for the background radiationNBGL left of the peak and NBGR right of the peak and then averaging them andnally subtracting Nnet = Ntot minus NBG) For a more detailed description of thisprocess see section 22

For the eciency ξ another calibration curve is obtained from the laboratorys long-termed measurements (see Appendix C) The required eciency can easily be reado the graph as indicated in the Appendix

The real time of the experiment was 5864s but the time in which the detector wasresponsive (life time) was slightly smaller t = 5861s Note that the dierence is onlyabout 005 so ∆t is regarded as practically non-existent With this information it ispossible to calculate the activity A of the investigated radionuclides Note that this timeerror propagation (according to Gauss) was necessary to employ

A =Nnet

t f ξ∆A =

radic(σNnet

t f ξ

)2

+

(Nnet ∆ξ

t f ξ2

)2

and σNnet=radicNnet

The error of the eciency was appropriately set to ξ = 0001 The investigated radionu-clides were K-40 Cs-137 and Pb-214 (at 3520keV) also see gure 8 The results for theactivities as well as their errors and other details of the calculation process are given intable 5 All of the data given in this table was calculated using the self-written MATLABfunctionpeak_counter Its source code is given in Appendix A

Surprisingly the activity of Cs-137 is comparatively small Even though its peak isabout three times larger than the Pb-214 peak it is also narrower so their activitiesare very close The activity of K-40 (which like Pb-214 has a natural origin) is muchgreater Having in mind that the Cs-137 peak is the largest peak in the spectrum it isstill a somewhat comforting result that the activity of the articial isotope Cs-137 is notoutrageously great (any more)

17

variable K-40 Cs-137 Pb-214

t[s] 5861 5861 5861f 0107 0852 0366ξ 0010plusmn 0001 0018plusmn 0001 0024plusmn 0001Ntot 1399plusmn 37 1234plusmn 35 726plusmn 26NBGL 25plusmn 5 294plusmn 17 191plusmn 13NBGR 14plusmn 3 270plusmn 16 181plusmn 13NBG 195plusmn 4 282plusmn 16 186plusmn 13Nnet 13795plusmn 37 952plusmn 30 540plusmn 23

A [Bq] 21997plusmn 2278 1059plusmn 068 1049plusmn 063

Table 5 Detailed information on activity calculation

6 Conclusion

The results of the experiment Natural and Man-Made Radioactivity are Soil are absolutelysatisfactory and do not leave many questions unanswered

The linear energy calibration (which was performed twice with a dataset of only twopoints) of the Canberra MCA was precise and allowed investigating even very distinctpeaks Although the calculation of the eciency in section 53 yielded a rather unreal-istic result it was possible to narrow down the error source to a disharmony in softwarecalculations

In the soil sample as many as 24 radionuclides were identied Among them Cs-137(which originates in global fallout after atmospheric nuclear bomb tests and also in the1986 Chernobyl accident) has the most distinct peak The digital data which resultedfrom the soil sample measurement was easy to handle and had a very good resolution (aswas to be expected from a HPGe detector) The activity calculation of the radionuclidesPb-214 (at 3520keV ) Cs-137 and K-40 clearly illustrated the independence between peakheight and activity

18

References

[1] Helmut Fischer Natural and Man-Made Radioactivity in Soil April 5 2004httpwwwpraktikumphysikuni-bremendeimagespdffpfp21_

radioactivitypdf

[2] Helmut Fischer Radioisotopes in Soil June 2003httpwwwmsc-epuni-bremendeserviceslecturespracticalsmeas_

tech_radioactivity_hf_rev3pdf

[3] Gamma Rays in the Environment with Intensities greater than 1 August 1980Nuclear Data Sheets 15 203 (1975) Part of a collection of tables on radioactivityobtained at the laboratory

[4] Basic Counting Systems copy 2006 Canberra IndustrieshttpwwwcanberracompdfLiteraturebasic20counting20sys20sfpdf

[5] Gamma and X-Ray Detectioncopy 2006 Canberra IndustrieshttpwwwcanberracompdfLiteratureGamma20Xray20Det20SFpdf

[6] Spectrum Analysis copy 2006 Canberra IndustrieshttpwwwcanberracompdfLiteratureSpectrum20Analysis20SFpdf

[7] D A Gedecke How Counting Statistics Controls Detection Limits and Peak Preci-sion copy Ortec (no date given)httpwwwortec-onlinecomapplication-notesan59pdf

[8] Wolfgang Demtroumlder Experimentalphysik 4 Second edition Springer 2005

19

large peak energy nuclide channel number

E1 = 66166keV Csminus 137 n1 = 1334E2 = 117324keV Cominus 60 n2 = 2366E3 = 133250keV Cominus 60 n3 = 2687

Table 3 Data points for energy calibration

53 Eciency calibration

The properties of the used Csminus 137 sample were these

activity on 19750929 A0 = 132microCi 48840Bq half life T12 = 3017y

error of initial activity ∆A0 = A0 middot 5 = 2442Bq

In order to calculate the eciency ξ = N (t middot f middot A) the current activity needs to beobtained rst The date of the experiment was the 15th of October 2009 The timedierence is tnow = 3407y Thus the current activity is

A (tnow) = A0 middot eminus ln(2)tnow

T12 = 22327Bq (5)

∆A (tnow) = ∆A0 middot eminus ln(2)tnow

T12 = 1116Bq (6)

For the eciency 14 channel of the Csminus 137 peak were considered Another 14 channelswere considered for the background radiance to the left and another 14 channels for thebackground radiance to the right of the peak Among these channels all the counts weresummed up This resulted in Ntot = 5191 NBGL = 1 and NBGR = 31 The average countsof the background channels are

NBG =NBGL +NBGR

2= 16 σBG =

radicNBG

Thus the net counts of the peak (without the background radiation) are

Nnet = Ntot minusNBG = 5175 σnet =radicNtot +NBG = 7215rarr Nnet = 5175plusmn 72

Note that the MCA-built-in display had an internal routine for calculating Ntot andNnet The values it yielded for the very same channels were Ntot MCA = 5188 andNnet MCA = 3893 Consequently NBG MCA = 1259 16 = NBG However Ntot MCA

and Ntot are very close to each other

The branching ratio being f = 085 and the time of the experiment being texp = 400sthe eciency can now be obtained

ξ = Nnet

t f A(tnow)= 681 ∆ξ = σnet

t f A(tnow)+ Nnet ∆A(tnow)

t f [A(tnow)]2= 044rarr ξ = 684plusmn 044

For the above error calculation several assumptions had to be made ∆Nnet 6= 0∆A (tnow) ∆texp = 0 ∆f = 0 These assumption actually make sense because texpand f and have either been measured very precisely or have been taken from literature

13

the MCA was congured to measure for a real time interval of texp = 400s Asanalyzed in the soil sample section the dierence between real and life time onlycauses an error of lt 05

f was looked up in [3]

concerning A (tnow) = A0 middot exp(minus ln (2) tnowT12

) the value for T12 was inscribed

on the sample tnow has been computed as described above The computation wasperformed in Mathematica based on seconds For this reason the exp() term itself

is assumed to have practically no error at all However an error of 5 for A0 wasinscribed on the sample This has been considered in the computation of ∆A (tnow)according to equation 6

It is now possible to compare the results for the eciency ξ with the the laboratorysown eciency calibration curve (see Appendix B) It results from measurements withmany radionuclides and is a good source for comparison The laboratorys calibrationcurve yields an expected eciency of ξlab = 43 whereas ξexp = 684 plusmn 044 Theauthor presumes that the principal source of error is the background radiation (as statedabove the other variables have very small error ranges and also Ntot MCA and Ntot arevery close) The background radiation value was much more appropriately given by theinternal MCA routine (its result could be read o the internal display) Performing theeciency calculation with Nnet MCA yields ξnet MCA = 512 which is much closer toξlab However an obvious error source can not be made out The author was carefullyinstructed in the usage of the MCA and entered nearly all of the commands himself(under supervision) Still the only reasonable cause for error seems to be software basedPerhaps an automatic and undesired re-scaling or normalization was performed by theoscilloscope

54 Data analysis of soil sample measurement

For the analysis of the soil sample spectrum another energy calibration was requiredThe Cs-137 peak as well as the K-40 peak were used for this purpose Both peaks arevery characteristic for the spectrum (the Cs-137 peak is the largest peak of the spectrumwhereas the K-40 peak is by far the largest peak with energies above 1000keV ) TheCs-137 peak at E1 = 6616keV was found at channel number n1 = 2651 and the K-40peak at E2 = 14608keV was found at n2 = 5846 The linear energy calibration yieldedE (n) = 0250141keV middot nminus 152338keV With the energy calibration performed it is possible to identify radionuclides from thesoil samples spectrum The energies to which the peaks correspond as well as thecorresponding nuclide information can be found in table 4 An overall plot of the spectrumis given in gure 8 It provides a good view on the proportions of the peak heights (Thethree peaks which are annotated in this plot are important for section 55) A large plotof the spectrum with annotated peaks can be looked up in 9

14

0 200 400 600 800 1000 1200 1400 1600 1800 20000

50

100

150

200

E [keV]

coun

ts p

er c

hann

el

Kminus40Csminus137Pbminus214

(3520keV)

Figure 8 spectrum recorded from soil sample (overall view)

energy [keV] radionuclide f [] half life origin

771 (x-ray) Pb-214 107 long U-238926 Th-234 56 long U-2381856 U-235 540 71e7y natural2095 Ac-228 41 long Th-2322386 Pb-212 450 long Th-2322702 Ac-228 38 long Th-2322952 Pb-214 187 long U-2383385 Ac-228 123 long Th-2323520 Pb-214 366 long U-2385110 annihilation peak 5831 Tl-208 300 long Th-2326094 Bi-214 450 long U-2386616 Cs-137 852 302y fallout7272 Bi-212 70 long Th-2327684 Bi-214 50 long U-2387949 Ac-228 49 long Th-2329111 Ac-228 290 long Th-2329689 Ac-228 175 long Th-23211204 Bi-214 152 U-238 U-23814608 K-40 107 13e9y natural15095 Bi-214 22 long U-23815881 Ac-228 46 long Th-23216310 Ac-228 34 long Th-23217647 Bi-214 154 long U-238

Table 4 Nuclides identied in the soil sample (individual nuclide information from [3])

15

020

040

060

080

010

0012

0014

0016

0018

0020

000102030405060708090

Ene

rgy

[keV

]

counts per channel

Kminus

40

Biminus

214

Biminus

214

Acminus

228

Csminus

137

Biminus

214

Acminus

228

Pbminus

214

Pbminus

212

Acminus

228

Biminus

214

Acminus

228

Acminus

228

Biminus

214

Biminus

212

Pbminus

214

(Xminus

ray)

Thminus

234

Uminus

235

Tlminus

208

anni

hila

tion

peak

at

511k

eV

Acminus

228

Figure 9 annotated spectrum (recorded from soil sample in Marinelli beaker)

16

A characteristic property of natural radionuclides is their half life which is usuallyvery long Also it is much more probable to encounter a radionuclide with a smallbranching ration (eg 5) and a very long half life than to encounter a nuclide witha short half life (eg 10 days) even though if its branching ratio may be great (eg85) This consideration was helpful in many decisions when close energy values madethe distinction of dierent radionuclides possible Also it is important to remark thatmany of the encountered radionuclides originate from either Th-232 or U-238 which areboth natural radionuclides

55 Calculating activities of three prominent lines

The nal task was to calculate the activities of three prominent lines The time of theexperiment t as well as the branching ratio for each radionuclide f being known theactivity A the eciency ξ and the net number of counts in the peak Nnet need to befound

For Nnet the same procedure as in section 53 is employed (summing up the totalnumber of counts N tot in the peak doing the same for the background radiationNBGL left of the peak and NBGR right of the peak and then averaging them andnally subtracting Nnet = Ntot minus NBG) For a more detailed description of thisprocess see section 22

For the eciency ξ another calibration curve is obtained from the laboratorys long-termed measurements (see Appendix C) The required eciency can easily be reado the graph as indicated in the Appendix

The real time of the experiment was 5864s but the time in which the detector wasresponsive (life time) was slightly smaller t = 5861s Note that the dierence is onlyabout 005 so ∆t is regarded as practically non-existent With this information it ispossible to calculate the activity A of the investigated radionuclides Note that this timeerror propagation (according to Gauss) was necessary to employ

A =Nnet

t f ξ∆A =

radic(σNnet

t f ξ

)2

+

(Nnet ∆ξ

t f ξ2

)2

and σNnet=radicNnet

The error of the eciency was appropriately set to ξ = 0001 The investigated radionu-clides were K-40 Cs-137 and Pb-214 (at 3520keV) also see gure 8 The results for theactivities as well as their errors and other details of the calculation process are given intable 5 All of the data given in this table was calculated using the self-written MATLABfunctionpeak_counter Its source code is given in Appendix A

Surprisingly the activity of Cs-137 is comparatively small Even though its peak isabout three times larger than the Pb-214 peak it is also narrower so their activitiesare very close The activity of K-40 (which like Pb-214 has a natural origin) is muchgreater Having in mind that the Cs-137 peak is the largest peak in the spectrum it isstill a somewhat comforting result that the activity of the articial isotope Cs-137 is notoutrageously great (any more)

17

variable K-40 Cs-137 Pb-214

t[s] 5861 5861 5861f 0107 0852 0366ξ 0010plusmn 0001 0018plusmn 0001 0024plusmn 0001Ntot 1399plusmn 37 1234plusmn 35 726plusmn 26NBGL 25plusmn 5 294plusmn 17 191plusmn 13NBGR 14plusmn 3 270plusmn 16 181plusmn 13NBG 195plusmn 4 282plusmn 16 186plusmn 13Nnet 13795plusmn 37 952plusmn 30 540plusmn 23

A [Bq] 21997plusmn 2278 1059plusmn 068 1049plusmn 063

Table 5 Detailed information on activity calculation

6 Conclusion

The results of the experiment Natural and Man-Made Radioactivity are Soil are absolutelysatisfactory and do not leave many questions unanswered

The linear energy calibration (which was performed twice with a dataset of only twopoints) of the Canberra MCA was precise and allowed investigating even very distinctpeaks Although the calculation of the eciency in section 53 yielded a rather unreal-istic result it was possible to narrow down the error source to a disharmony in softwarecalculations

In the soil sample as many as 24 radionuclides were identied Among them Cs-137(which originates in global fallout after atmospheric nuclear bomb tests and also in the1986 Chernobyl accident) has the most distinct peak The digital data which resultedfrom the soil sample measurement was easy to handle and had a very good resolution (aswas to be expected from a HPGe detector) The activity calculation of the radionuclidesPb-214 (at 3520keV ) Cs-137 and K-40 clearly illustrated the independence between peakheight and activity

18

References

[1] Helmut Fischer Natural and Man-Made Radioactivity in Soil April 5 2004httpwwwpraktikumphysikuni-bremendeimagespdffpfp21_

radioactivitypdf

[2] Helmut Fischer Radioisotopes in Soil June 2003httpwwwmsc-epuni-bremendeserviceslecturespracticalsmeas_

tech_radioactivity_hf_rev3pdf

[3] Gamma Rays in the Environment with Intensities greater than 1 August 1980Nuclear Data Sheets 15 203 (1975) Part of a collection of tables on radioactivityobtained at the laboratory

[4] Basic Counting Systems copy 2006 Canberra IndustrieshttpwwwcanberracompdfLiteraturebasic20counting20sys20sfpdf

[5] Gamma and X-Ray Detectioncopy 2006 Canberra IndustrieshttpwwwcanberracompdfLiteratureGamma20Xray20Det20SFpdf

[6] Spectrum Analysis copy 2006 Canberra IndustrieshttpwwwcanberracompdfLiteratureSpectrum20Analysis20SFpdf

[7] D A Gedecke How Counting Statistics Controls Detection Limits and Peak Preci-sion copy Ortec (no date given)httpwwwortec-onlinecomapplication-notesan59pdf

[8] Wolfgang Demtroumlder Experimentalphysik 4 Second edition Springer 2005

19

the MCA was congured to measure for a real time interval of texp = 400s Asanalyzed in the soil sample section the dierence between real and life time onlycauses an error of lt 05

f was looked up in [3]

concerning A (tnow) = A0 middot exp(minus ln (2) tnowT12

) the value for T12 was inscribed

on the sample tnow has been computed as described above The computation wasperformed in Mathematica based on seconds For this reason the exp() term itself

is assumed to have practically no error at all However an error of 5 for A0 wasinscribed on the sample This has been considered in the computation of ∆A (tnow)according to equation 6

It is now possible to compare the results for the eciency ξ with the the laboratorysown eciency calibration curve (see Appendix B) It results from measurements withmany radionuclides and is a good source for comparison The laboratorys calibrationcurve yields an expected eciency of ξlab = 43 whereas ξexp = 684 plusmn 044 Theauthor presumes that the principal source of error is the background radiation (as statedabove the other variables have very small error ranges and also Ntot MCA and Ntot arevery close) The background radiation value was much more appropriately given by theinternal MCA routine (its result could be read o the internal display) Performing theeciency calculation with Nnet MCA yields ξnet MCA = 512 which is much closer toξlab However an obvious error source can not be made out The author was carefullyinstructed in the usage of the MCA and entered nearly all of the commands himself(under supervision) Still the only reasonable cause for error seems to be software basedPerhaps an automatic and undesired re-scaling or normalization was performed by theoscilloscope

54 Data analysis of soil sample measurement

For the analysis of the soil sample spectrum another energy calibration was requiredThe Cs-137 peak as well as the K-40 peak were used for this purpose Both peaks arevery characteristic for the spectrum (the Cs-137 peak is the largest peak of the spectrumwhereas the K-40 peak is by far the largest peak with energies above 1000keV ) TheCs-137 peak at E1 = 6616keV was found at channel number n1 = 2651 and the K-40peak at E2 = 14608keV was found at n2 = 5846 The linear energy calibration yieldedE (n) = 0250141keV middot nminus 152338keV With the energy calibration performed it is possible to identify radionuclides from thesoil samples spectrum The energies to which the peaks correspond as well as thecorresponding nuclide information can be found in table 4 An overall plot of the spectrumis given in gure 8 It provides a good view on the proportions of the peak heights (Thethree peaks which are annotated in this plot are important for section 55) A large plotof the spectrum with annotated peaks can be looked up in 9

14

0 200 400 600 800 1000 1200 1400 1600 1800 20000

50

100

150

200

E [keV]

coun

ts p

er c

hann

el

Kminus40Csminus137Pbminus214

(3520keV)

Figure 8 spectrum recorded from soil sample (overall view)

energy [keV] radionuclide f [] half life origin

771 (x-ray) Pb-214 107 long U-238926 Th-234 56 long U-2381856 U-235 540 71e7y natural2095 Ac-228 41 long Th-2322386 Pb-212 450 long Th-2322702 Ac-228 38 long Th-2322952 Pb-214 187 long U-2383385 Ac-228 123 long Th-2323520 Pb-214 366 long U-2385110 annihilation peak 5831 Tl-208 300 long Th-2326094 Bi-214 450 long U-2386616 Cs-137 852 302y fallout7272 Bi-212 70 long Th-2327684 Bi-214 50 long U-2387949 Ac-228 49 long Th-2329111 Ac-228 290 long Th-2329689 Ac-228 175 long Th-23211204 Bi-214 152 U-238 U-23814608 K-40 107 13e9y natural15095 Bi-214 22 long U-23815881 Ac-228 46 long Th-23216310 Ac-228 34 long Th-23217647 Bi-214 154 long U-238

Table 4 Nuclides identied in the soil sample (individual nuclide information from [3])

15

020

040

060

080

010

0012

0014

0016

0018

0020

000102030405060708090

Ene

rgy

[keV

]

counts per channel

Kminus

40

Biminus

214

Biminus

214

Acminus

228

Csminus

137

Biminus

214

Acminus

228

Pbminus

214

Pbminus

212

Acminus

228

Biminus

214

Acminus

228

Acminus

228

Biminus

214

Biminus

212

Pbminus

214

(Xminus

ray)

Thminus

234

Uminus

235

Tlminus

208

anni

hila

tion

peak

at

511k

eV

Acminus

228

Figure 9 annotated spectrum (recorded from soil sample in Marinelli beaker)

16

A characteristic property of natural radionuclides is their half life which is usuallyvery long Also it is much more probable to encounter a radionuclide with a smallbranching ration (eg 5) and a very long half life than to encounter a nuclide witha short half life (eg 10 days) even though if its branching ratio may be great (eg85) This consideration was helpful in many decisions when close energy values madethe distinction of dierent radionuclides possible Also it is important to remark thatmany of the encountered radionuclides originate from either Th-232 or U-238 which areboth natural radionuclides

55 Calculating activities of three prominent lines

The nal task was to calculate the activities of three prominent lines The time of theexperiment t as well as the branching ratio for each radionuclide f being known theactivity A the eciency ξ and the net number of counts in the peak Nnet need to befound

For Nnet the same procedure as in section 53 is employed (summing up the totalnumber of counts N tot in the peak doing the same for the background radiationNBGL left of the peak and NBGR right of the peak and then averaging them andnally subtracting Nnet = Ntot minus NBG) For a more detailed description of thisprocess see section 22

For the eciency ξ another calibration curve is obtained from the laboratorys long-termed measurements (see Appendix C) The required eciency can easily be reado the graph as indicated in the Appendix

The real time of the experiment was 5864s but the time in which the detector wasresponsive (life time) was slightly smaller t = 5861s Note that the dierence is onlyabout 005 so ∆t is regarded as practically non-existent With this information it ispossible to calculate the activity A of the investigated radionuclides Note that this timeerror propagation (according to Gauss) was necessary to employ

A =Nnet

t f ξ∆A =

radic(σNnet

t f ξ

)2

+

(Nnet ∆ξ

t f ξ2

)2

and σNnet=radicNnet

The error of the eciency was appropriately set to ξ = 0001 The investigated radionu-clides were K-40 Cs-137 and Pb-214 (at 3520keV) also see gure 8 The results for theactivities as well as their errors and other details of the calculation process are given intable 5 All of the data given in this table was calculated using the self-written MATLABfunctionpeak_counter Its source code is given in Appendix A

Surprisingly the activity of Cs-137 is comparatively small Even though its peak isabout three times larger than the Pb-214 peak it is also narrower so their activitiesare very close The activity of K-40 (which like Pb-214 has a natural origin) is muchgreater Having in mind that the Cs-137 peak is the largest peak in the spectrum it isstill a somewhat comforting result that the activity of the articial isotope Cs-137 is notoutrageously great (any more)

17

variable K-40 Cs-137 Pb-214

t[s] 5861 5861 5861f 0107 0852 0366ξ 0010plusmn 0001 0018plusmn 0001 0024plusmn 0001Ntot 1399plusmn 37 1234plusmn 35 726plusmn 26NBGL 25plusmn 5 294plusmn 17 191plusmn 13NBGR 14plusmn 3 270plusmn 16 181plusmn 13NBG 195plusmn 4 282plusmn 16 186plusmn 13Nnet 13795plusmn 37 952plusmn 30 540plusmn 23

A [Bq] 21997plusmn 2278 1059plusmn 068 1049plusmn 063

Table 5 Detailed information on activity calculation

6 Conclusion

The results of the experiment Natural and Man-Made Radioactivity are Soil are absolutelysatisfactory and do not leave many questions unanswered

The linear energy calibration (which was performed twice with a dataset of only twopoints) of the Canberra MCA was precise and allowed investigating even very distinctpeaks Although the calculation of the eciency in section 53 yielded a rather unreal-istic result it was possible to narrow down the error source to a disharmony in softwarecalculations

In the soil sample as many as 24 radionuclides were identied Among them Cs-137(which originates in global fallout after atmospheric nuclear bomb tests and also in the1986 Chernobyl accident) has the most distinct peak The digital data which resultedfrom the soil sample measurement was easy to handle and had a very good resolution (aswas to be expected from a HPGe detector) The activity calculation of the radionuclidesPb-214 (at 3520keV ) Cs-137 and K-40 clearly illustrated the independence between peakheight and activity

18

References

[1] Helmut Fischer Natural and Man-Made Radioactivity in Soil April 5 2004httpwwwpraktikumphysikuni-bremendeimagespdffpfp21_

radioactivitypdf

[2] Helmut Fischer Radioisotopes in Soil June 2003httpwwwmsc-epuni-bremendeserviceslecturespracticalsmeas_

tech_radioactivity_hf_rev3pdf

[3] Gamma Rays in the Environment with Intensities greater than 1 August 1980Nuclear Data Sheets 15 203 (1975) Part of a collection of tables on radioactivityobtained at the laboratory

[4] Basic Counting Systems copy 2006 Canberra IndustrieshttpwwwcanberracompdfLiteraturebasic20counting20sys20sfpdf

[5] Gamma and X-Ray Detectioncopy 2006 Canberra IndustrieshttpwwwcanberracompdfLiteratureGamma20Xray20Det20SFpdf

[6] Spectrum Analysis copy 2006 Canberra IndustrieshttpwwwcanberracompdfLiteratureSpectrum20Analysis20SFpdf

[7] D A Gedecke How Counting Statistics Controls Detection Limits and Peak Preci-sion copy Ortec (no date given)httpwwwortec-onlinecomapplication-notesan59pdf

[8] Wolfgang Demtroumlder Experimentalphysik 4 Second edition Springer 2005

19

0 200 400 600 800 1000 1200 1400 1600 1800 20000

50

100

150

200

E [keV]

coun

ts p

er c

hann

el

Kminus40Csminus137Pbminus214

(3520keV)

Figure 8 spectrum recorded from soil sample (overall view)

energy [keV] radionuclide f [] half life origin

771 (x-ray) Pb-214 107 long U-238926 Th-234 56 long U-2381856 U-235 540 71e7y natural2095 Ac-228 41 long Th-2322386 Pb-212 450 long Th-2322702 Ac-228 38 long Th-2322952 Pb-214 187 long U-2383385 Ac-228 123 long Th-2323520 Pb-214 366 long U-2385110 annihilation peak 5831 Tl-208 300 long Th-2326094 Bi-214 450 long U-2386616 Cs-137 852 302y fallout7272 Bi-212 70 long Th-2327684 Bi-214 50 long U-2387949 Ac-228 49 long Th-2329111 Ac-228 290 long Th-2329689 Ac-228 175 long Th-23211204 Bi-214 152 U-238 U-23814608 K-40 107 13e9y natural15095 Bi-214 22 long U-23815881 Ac-228 46 long Th-23216310 Ac-228 34 long Th-23217647 Bi-214 154 long U-238

Table 4 Nuclides identied in the soil sample (individual nuclide information from [3])

15

020

040

060

080

010

0012

0014

0016

0018

0020

000102030405060708090

Ene

rgy

[keV

]

counts per channel

Kminus

40

Biminus

214

Biminus

214

Acminus

228

Csminus

137

Biminus

214

Acminus

228

Pbminus

214

Pbminus

212

Acminus

228

Biminus

214

Acminus

228

Acminus

228

Biminus

214

Biminus

212

Pbminus

214

(Xminus

ray)

Thminus

234

Uminus

235

Tlminus

208

anni

hila

tion

peak

at

511k

eV

Acminus

228

Figure 9 annotated spectrum (recorded from soil sample in Marinelli beaker)

16

A characteristic property of natural radionuclides is their half life which is usuallyvery long Also it is much more probable to encounter a radionuclide with a smallbranching ration (eg 5) and a very long half life than to encounter a nuclide witha short half life (eg 10 days) even though if its branching ratio may be great (eg85) This consideration was helpful in many decisions when close energy values madethe distinction of dierent radionuclides possible Also it is important to remark thatmany of the encountered radionuclides originate from either Th-232 or U-238 which areboth natural radionuclides

55 Calculating activities of three prominent lines

The nal task was to calculate the activities of three prominent lines The time of theexperiment t as well as the branching ratio for each radionuclide f being known theactivity A the eciency ξ and the net number of counts in the peak Nnet need to befound

For Nnet the same procedure as in section 53 is employed (summing up the totalnumber of counts N tot in the peak doing the same for the background radiationNBGL left of the peak and NBGR right of the peak and then averaging them andnally subtracting Nnet = Ntot minus NBG) For a more detailed description of thisprocess see section 22

For the eciency ξ another calibration curve is obtained from the laboratorys long-termed measurements (see Appendix C) The required eciency can easily be reado the graph as indicated in the Appendix

The real time of the experiment was 5864s but the time in which the detector wasresponsive (life time) was slightly smaller t = 5861s Note that the dierence is onlyabout 005 so ∆t is regarded as practically non-existent With this information it ispossible to calculate the activity A of the investigated radionuclides Note that this timeerror propagation (according to Gauss) was necessary to employ

A =Nnet

t f ξ∆A =

radic(σNnet

t f ξ

)2

+

(Nnet ∆ξ

t f ξ2

)2

and σNnet=radicNnet

The error of the eciency was appropriately set to ξ = 0001 The investigated radionu-clides were K-40 Cs-137 and Pb-214 (at 3520keV) also see gure 8 The results for theactivities as well as their errors and other details of the calculation process are given intable 5 All of the data given in this table was calculated using the self-written MATLABfunctionpeak_counter Its source code is given in Appendix A

Surprisingly the activity of Cs-137 is comparatively small Even though its peak isabout three times larger than the Pb-214 peak it is also narrower so their activitiesare very close The activity of K-40 (which like Pb-214 has a natural origin) is muchgreater Having in mind that the Cs-137 peak is the largest peak in the spectrum it isstill a somewhat comforting result that the activity of the articial isotope Cs-137 is notoutrageously great (any more)

17

variable K-40 Cs-137 Pb-214

t[s] 5861 5861 5861f 0107 0852 0366ξ 0010plusmn 0001 0018plusmn 0001 0024plusmn 0001Ntot 1399plusmn 37 1234plusmn 35 726plusmn 26NBGL 25plusmn 5 294plusmn 17 191plusmn 13NBGR 14plusmn 3 270plusmn 16 181plusmn 13NBG 195plusmn 4 282plusmn 16 186plusmn 13Nnet 13795plusmn 37 952plusmn 30 540plusmn 23

A [Bq] 21997plusmn 2278 1059plusmn 068 1049plusmn 063

Table 5 Detailed information on activity calculation

6 Conclusion

The results of the experiment Natural and Man-Made Radioactivity are Soil are absolutelysatisfactory and do not leave many questions unanswered

The linear energy calibration (which was performed twice with a dataset of only twopoints) of the Canberra MCA was precise and allowed investigating even very distinctpeaks Although the calculation of the eciency in section 53 yielded a rather unreal-istic result it was possible to narrow down the error source to a disharmony in softwarecalculations

In the soil sample as many as 24 radionuclides were identied Among them Cs-137(which originates in global fallout after atmospheric nuclear bomb tests and also in the1986 Chernobyl accident) has the most distinct peak The digital data which resultedfrom the soil sample measurement was easy to handle and had a very good resolution (aswas to be expected from a HPGe detector) The activity calculation of the radionuclidesPb-214 (at 3520keV ) Cs-137 and K-40 clearly illustrated the independence between peakheight and activity

18

References

[1] Helmut Fischer Natural and Man-Made Radioactivity in Soil April 5 2004httpwwwpraktikumphysikuni-bremendeimagespdffpfp21_

radioactivitypdf

[2] Helmut Fischer Radioisotopes in Soil June 2003httpwwwmsc-epuni-bremendeserviceslecturespracticalsmeas_

tech_radioactivity_hf_rev3pdf

[3] Gamma Rays in the Environment with Intensities greater than 1 August 1980Nuclear Data Sheets 15 203 (1975) Part of a collection of tables on radioactivityobtained at the laboratory

[4] Basic Counting Systems copy 2006 Canberra IndustrieshttpwwwcanberracompdfLiteraturebasic20counting20sys20sfpdf

[5] Gamma and X-Ray Detectioncopy 2006 Canberra IndustrieshttpwwwcanberracompdfLiteratureGamma20Xray20Det20SFpdf

[6] Spectrum Analysis copy 2006 Canberra IndustrieshttpwwwcanberracompdfLiteratureSpectrum20Analysis20SFpdf

[7] D A Gedecke How Counting Statistics Controls Detection Limits and Peak Preci-sion copy Ortec (no date given)httpwwwortec-onlinecomapplication-notesan59pdf

[8] Wolfgang Demtroumlder Experimentalphysik 4 Second edition Springer 2005

19

020

040

060

080

010

0012

0014

0016

0018

0020

000102030405060708090

Ene

rgy

[keV

]

counts per channel

Kminus

40

Biminus

214

Biminus

214

Acminus

228

Csminus

137

Biminus

214

Acminus

228

Pbminus

214

Pbminus

212

Acminus

228

Biminus

214

Acminus

228

Acminus

228

Biminus

214

Biminus

212

Pbminus

214

(Xminus

ray)

Thminus

234

Uminus

235

Tlminus

208

anni

hila

tion

peak

at

511k

eV

Acminus

228

Figure 9 annotated spectrum (recorded from soil sample in Marinelli beaker)

16

A characteristic property of natural radionuclides is their half life which is usuallyvery long Also it is much more probable to encounter a radionuclide with a smallbranching ration (eg 5) and a very long half life than to encounter a nuclide witha short half life (eg 10 days) even though if its branching ratio may be great (eg85) This consideration was helpful in many decisions when close energy values madethe distinction of dierent radionuclides possible Also it is important to remark thatmany of the encountered radionuclides originate from either Th-232 or U-238 which areboth natural radionuclides

55 Calculating activities of three prominent lines

The nal task was to calculate the activities of three prominent lines The time of theexperiment t as well as the branching ratio for each radionuclide f being known theactivity A the eciency ξ and the net number of counts in the peak Nnet need to befound

For Nnet the same procedure as in section 53 is employed (summing up the totalnumber of counts N tot in the peak doing the same for the background radiationNBGL left of the peak and NBGR right of the peak and then averaging them andnally subtracting Nnet = Ntot minus NBG) For a more detailed description of thisprocess see section 22

For the eciency ξ another calibration curve is obtained from the laboratorys long-termed measurements (see Appendix C) The required eciency can easily be reado the graph as indicated in the Appendix

The real time of the experiment was 5864s but the time in which the detector wasresponsive (life time) was slightly smaller t = 5861s Note that the dierence is onlyabout 005 so ∆t is regarded as practically non-existent With this information it ispossible to calculate the activity A of the investigated radionuclides Note that this timeerror propagation (according to Gauss) was necessary to employ

A =Nnet

t f ξ∆A =

radic(σNnet

t f ξ

)2

+

(Nnet ∆ξ

t f ξ2

)2

and σNnet=radicNnet

The error of the eciency was appropriately set to ξ = 0001 The investigated radionu-clides were K-40 Cs-137 and Pb-214 (at 3520keV) also see gure 8 The results for theactivities as well as their errors and other details of the calculation process are given intable 5 All of the data given in this table was calculated using the self-written MATLABfunctionpeak_counter Its source code is given in Appendix A

Surprisingly the activity of Cs-137 is comparatively small Even though its peak isabout three times larger than the Pb-214 peak it is also narrower so their activitiesare very close The activity of K-40 (which like Pb-214 has a natural origin) is muchgreater Having in mind that the Cs-137 peak is the largest peak in the spectrum it isstill a somewhat comforting result that the activity of the articial isotope Cs-137 is notoutrageously great (any more)

17

variable K-40 Cs-137 Pb-214

t[s] 5861 5861 5861f 0107 0852 0366ξ 0010plusmn 0001 0018plusmn 0001 0024plusmn 0001Ntot 1399plusmn 37 1234plusmn 35 726plusmn 26NBGL 25plusmn 5 294plusmn 17 191plusmn 13NBGR 14plusmn 3 270plusmn 16 181plusmn 13NBG 195plusmn 4 282plusmn 16 186plusmn 13Nnet 13795plusmn 37 952plusmn 30 540plusmn 23

A [Bq] 21997plusmn 2278 1059plusmn 068 1049plusmn 063

Table 5 Detailed information on activity calculation

6 Conclusion

The results of the experiment Natural and Man-Made Radioactivity are Soil are absolutelysatisfactory and do not leave many questions unanswered

The linear energy calibration (which was performed twice with a dataset of only twopoints) of the Canberra MCA was precise and allowed investigating even very distinctpeaks Although the calculation of the eciency in section 53 yielded a rather unreal-istic result it was possible to narrow down the error source to a disharmony in softwarecalculations

In the soil sample as many as 24 radionuclides were identied Among them Cs-137(which originates in global fallout after atmospheric nuclear bomb tests and also in the1986 Chernobyl accident) has the most distinct peak The digital data which resultedfrom the soil sample measurement was easy to handle and had a very good resolution (aswas to be expected from a HPGe detector) The activity calculation of the radionuclidesPb-214 (at 3520keV ) Cs-137 and K-40 clearly illustrated the independence between peakheight and activity

18

References

[1] Helmut Fischer Natural and Man-Made Radioactivity in Soil April 5 2004httpwwwpraktikumphysikuni-bremendeimagespdffpfp21_

radioactivitypdf

[2] Helmut Fischer Radioisotopes in Soil June 2003httpwwwmsc-epuni-bremendeserviceslecturespracticalsmeas_

tech_radioactivity_hf_rev3pdf

[3] Gamma Rays in the Environment with Intensities greater than 1 August 1980Nuclear Data Sheets 15 203 (1975) Part of a collection of tables on radioactivityobtained at the laboratory

[4] Basic Counting Systems copy 2006 Canberra IndustrieshttpwwwcanberracompdfLiteraturebasic20counting20sys20sfpdf

[5] Gamma and X-Ray Detectioncopy 2006 Canberra IndustrieshttpwwwcanberracompdfLiteratureGamma20Xray20Det20SFpdf

[6] Spectrum Analysis copy 2006 Canberra IndustrieshttpwwwcanberracompdfLiteratureSpectrum20Analysis20SFpdf

[7] D A Gedecke How Counting Statistics Controls Detection Limits and Peak Preci-sion copy Ortec (no date given)httpwwwortec-onlinecomapplication-notesan59pdf

[8] Wolfgang Demtroumlder Experimentalphysik 4 Second edition Springer 2005

19

A characteristic property of natural radionuclides is their half life which is usuallyvery long Also it is much more probable to encounter a radionuclide with a smallbranching ration (eg 5) and a very long half life than to encounter a nuclide witha short half life (eg 10 days) even though if its branching ratio may be great (eg85) This consideration was helpful in many decisions when close energy values madethe distinction of dierent radionuclides possible Also it is important to remark thatmany of the encountered radionuclides originate from either Th-232 or U-238 which areboth natural radionuclides

55 Calculating activities of three prominent lines

The nal task was to calculate the activities of three prominent lines The time of theexperiment t as well as the branching ratio for each radionuclide f being known theactivity A the eciency ξ and the net number of counts in the peak Nnet need to befound

For Nnet the same procedure as in section 53 is employed (summing up the totalnumber of counts N tot in the peak doing the same for the background radiationNBGL left of the peak and NBGR right of the peak and then averaging them andnally subtracting Nnet = Ntot minus NBG) For a more detailed description of thisprocess see section 22

For the eciency ξ another calibration curve is obtained from the laboratorys long-termed measurements (see Appendix C) The required eciency can easily be reado the graph as indicated in the Appendix

The real time of the experiment was 5864s but the time in which the detector wasresponsive (life time) was slightly smaller t = 5861s Note that the dierence is onlyabout 005 so ∆t is regarded as practically non-existent With this information it ispossible to calculate the activity A of the investigated radionuclides Note that this timeerror propagation (according to Gauss) was necessary to employ

A =Nnet

t f ξ∆A =

radic(σNnet

t f ξ

)2

+

(Nnet ∆ξ

t f ξ2

)2

and σNnet=radicNnet

The error of the eciency was appropriately set to ξ = 0001 The investigated radionu-clides were K-40 Cs-137 and Pb-214 (at 3520keV) also see gure 8 The results for theactivities as well as their errors and other details of the calculation process are given intable 5 All of the data given in this table was calculated using the self-written MATLABfunctionpeak_counter Its source code is given in Appendix A

Surprisingly the activity of Cs-137 is comparatively small Even though its peak isabout three times larger than the Pb-214 peak it is also narrower so their activitiesare very close The activity of K-40 (which like Pb-214 has a natural origin) is muchgreater Having in mind that the Cs-137 peak is the largest peak in the spectrum it isstill a somewhat comforting result that the activity of the articial isotope Cs-137 is notoutrageously great (any more)

17

variable K-40 Cs-137 Pb-214

t[s] 5861 5861 5861f 0107 0852 0366ξ 0010plusmn 0001 0018plusmn 0001 0024plusmn 0001Ntot 1399plusmn 37 1234plusmn 35 726plusmn 26NBGL 25plusmn 5 294plusmn 17 191plusmn 13NBGR 14plusmn 3 270plusmn 16 181plusmn 13NBG 195plusmn 4 282plusmn 16 186plusmn 13Nnet 13795plusmn 37 952plusmn 30 540plusmn 23

A [Bq] 21997plusmn 2278 1059plusmn 068 1049plusmn 063

Table 5 Detailed information on activity calculation

6 Conclusion

The results of the experiment Natural and Man-Made Radioactivity are Soil are absolutelysatisfactory and do not leave many questions unanswered

The linear energy calibration (which was performed twice with a dataset of only twopoints) of the Canberra MCA was precise and allowed investigating even very distinctpeaks Although the calculation of the eciency in section 53 yielded a rather unreal-istic result it was possible to narrow down the error source to a disharmony in softwarecalculations

In the soil sample as many as 24 radionuclides were identied Among them Cs-137(which originates in global fallout after atmospheric nuclear bomb tests and also in the1986 Chernobyl accident) has the most distinct peak The digital data which resultedfrom the soil sample measurement was easy to handle and had a very good resolution (aswas to be expected from a HPGe detector) The activity calculation of the radionuclidesPb-214 (at 3520keV ) Cs-137 and K-40 clearly illustrated the independence between peakheight and activity

18

References

[1] Helmut Fischer Natural and Man-Made Radioactivity in Soil April 5 2004httpwwwpraktikumphysikuni-bremendeimagespdffpfp21_

radioactivitypdf

[2] Helmut Fischer Radioisotopes in Soil June 2003httpwwwmsc-epuni-bremendeserviceslecturespracticalsmeas_

tech_radioactivity_hf_rev3pdf

[3] Gamma Rays in the Environment with Intensities greater than 1 August 1980Nuclear Data Sheets 15 203 (1975) Part of a collection of tables on radioactivityobtained at the laboratory

[4] Basic Counting Systems copy 2006 Canberra IndustrieshttpwwwcanberracompdfLiteraturebasic20counting20sys20sfpdf

[5] Gamma and X-Ray Detectioncopy 2006 Canberra IndustrieshttpwwwcanberracompdfLiteratureGamma20Xray20Det20SFpdf

[6] Spectrum Analysis copy 2006 Canberra IndustrieshttpwwwcanberracompdfLiteratureSpectrum20Analysis20SFpdf

[7] D A Gedecke How Counting Statistics Controls Detection Limits and Peak Preci-sion copy Ortec (no date given)httpwwwortec-onlinecomapplication-notesan59pdf

[8] Wolfgang Demtroumlder Experimentalphysik 4 Second edition Springer 2005

19

variable K-40 Cs-137 Pb-214

t[s] 5861 5861 5861f 0107 0852 0366ξ 0010plusmn 0001 0018plusmn 0001 0024plusmn 0001Ntot 1399plusmn 37 1234plusmn 35 726plusmn 26NBGL 25plusmn 5 294plusmn 17 191plusmn 13NBGR 14plusmn 3 270plusmn 16 181plusmn 13NBG 195plusmn 4 282plusmn 16 186plusmn 13Nnet 13795plusmn 37 952plusmn 30 540plusmn 23

A [Bq] 21997plusmn 2278 1059plusmn 068 1049plusmn 063

Table 5 Detailed information on activity calculation

6 Conclusion

The results of the experiment Natural and Man-Made Radioactivity are Soil are absolutelysatisfactory and do not leave many questions unanswered

The linear energy calibration (which was performed twice with a dataset of only twopoints) of the Canberra MCA was precise and allowed investigating even very distinctpeaks Although the calculation of the eciency in section 53 yielded a rather unreal-istic result it was possible to narrow down the error source to a disharmony in softwarecalculations

In the soil sample as many as 24 radionuclides were identied Among them Cs-137(which originates in global fallout after atmospheric nuclear bomb tests and also in the1986 Chernobyl accident) has the most distinct peak The digital data which resultedfrom the soil sample measurement was easy to handle and had a very good resolution (aswas to be expected from a HPGe detector) The activity calculation of the radionuclidesPb-214 (at 3520keV ) Cs-137 and K-40 clearly illustrated the independence between peakheight and activity

18

References

[1] Helmut Fischer Natural and Man-Made Radioactivity in Soil April 5 2004httpwwwpraktikumphysikuni-bremendeimagespdffpfp21_

radioactivitypdf

[2] Helmut Fischer Radioisotopes in Soil June 2003httpwwwmsc-epuni-bremendeserviceslecturespracticalsmeas_

tech_radioactivity_hf_rev3pdf

[3] Gamma Rays in the Environment with Intensities greater than 1 August 1980Nuclear Data Sheets 15 203 (1975) Part of a collection of tables on radioactivityobtained at the laboratory

[4] Basic Counting Systems copy 2006 Canberra IndustrieshttpwwwcanberracompdfLiteraturebasic20counting20sys20sfpdf

[5] Gamma and X-Ray Detectioncopy 2006 Canberra IndustrieshttpwwwcanberracompdfLiteratureGamma20Xray20Det20SFpdf

[6] Spectrum Analysis copy 2006 Canberra IndustrieshttpwwwcanberracompdfLiteratureSpectrum20Analysis20SFpdf

[7] D A Gedecke How Counting Statistics Controls Detection Limits and Peak Preci-sion copy Ortec (no date given)httpwwwortec-onlinecomapplication-notesan59pdf

[8] Wolfgang Demtroumlder Experimentalphysik 4 Second edition Springer 2005

19

References

[1] Helmut Fischer Natural and Man-Made Radioactivity in Soil April 5 2004httpwwwpraktikumphysikuni-bremendeimagespdffpfp21_

radioactivitypdf

[2] Helmut Fischer Radioisotopes in Soil June 2003httpwwwmsc-epuni-bremendeserviceslecturespracticalsmeas_

tech_radioactivity_hf_rev3pdf

[3] Gamma Rays in the Environment with Intensities greater than 1 August 1980Nuclear Data Sheets 15 203 (1975) Part of a collection of tables on radioactivityobtained at the laboratory

[4] Basic Counting Systems copy 2006 Canberra IndustrieshttpwwwcanberracompdfLiteraturebasic20counting20sys20sfpdf

[5] Gamma and X-Ray Detectioncopy 2006 Canberra IndustrieshttpwwwcanberracompdfLiteratureGamma20Xray20Det20SFpdf

[6] Spectrum Analysis copy 2006 Canberra IndustrieshttpwwwcanberracompdfLiteratureSpectrum20Analysis20SFpdf

[7] D A Gedecke How Counting Statistics Controls Detection Limits and Peak Preci-sion copy Ortec (no date given)httpwwwortec-onlinecomapplication-notesan59pdf

[8] Wolfgang Demtroumlder Experimentalphysik 4 Second edition Springer 2005

19

A function peak_counter for calculating activities

This MATLAB function was written by the author in order to calculate the values fortable 5

function peak_counter(BGL1 BGL2 peak1 peak2 BGR1 BGR2f epsilon counts)

PEAK_COUNTER Calculates the activity of a prominent line from the

spectrum

counts array holding the counts per channel Its index number minus

one corresponds to the channel number

The other variables are quite obvious The following calls of this

program have been used in order to compute the data given in the

labreport

Cs-137

peak_counter(931944952965973986 08520018counts)

K-40

peak_counter(5804583258335860586158880107001counts)

Pb-214

peak_counter(13871403140414201421143703660024counts)

depsilon=0001

tlife=5861

NBGL=sum(counts(BGL1-1BGL2-1))

NBGR=sum(counts(BGR1-1BGR2-1))

Ntot=sum(counts(peak1-1peak2-1))

NBG=(NBGL+NBGR)2

Nnet=Ntot-NBG

dNnet=sqrt(Nnet)

Ak=Nnet(tlifefepsilon)

dAk=sqrt((dNnet(tlifefepsilon))^2+(Nnetdepsilon(tlifefepsilon^2))^2)

fprintf(1t[s]tgntlife)

fprintf(1ft13fnf)

fprintf(1$xi$t$13f pm 13f$nepsilondepsilon)

fprintf(1Ntott$g pm g$nNtotfloor(sqrt(Ntot)))

fprintf(1NBGLt$g pm g$nNBGLfloor(sqrt(NBGL)))

fprintf(1NBGRt$g pm g$nNBGRfloor(sqrt(NBGR)))

fprintf(1NBGt$g pm g$nNBGfloor(sqrt(NBG)))

fprintf(1Nnett$g pm g$nNnetfloor(sqrt(Nnet)))

fprintf(1A [Bq]t$2f pm 2f$nAkdAk)

B Laboratorys eciency calibration curve for point

source geometry

C Laboratorys eciency calibration curve for Marinelli

beaker geometry

D Measurement Report

See following pages

• Introduction
• Theory
• • Modes of Decay
  • Several Basics of Probability Theory
  • The Poisson Distribution
  • Interaction of radiation with matter
  • Exponential radioactive decay
  • • Experimental Setup
    • • High Purity Germanium detector
      • Evaluation of spectra
      • • Experimental Procedure
        • • Test source with one line
          • Test sources with multiple lines - energy calibration
          • Efficiency calibration
          • Soil sample spectrum measurement calculating activities
          • • Analysis
            • • Test source with one gamma line
              • Test sources with multiple lines - energy calibration
              • Efficiency calibration
              • Data analysis of soil sample measurement
              • Calculating activities of three prominent lines
              • • Conclusion
                • function peak_counter for calculating activities
                • Laboratorys efficiency calibration curve for point source geometry
                • Laboratorys efficiency calibration curve for Marinelli beaker geometry
                • Measurement Report

B Laboratorys eciency calibration curve for point

source geometry

C Laboratorys eciency calibration curve for Marinelli

beaker geometry

D Measurement Report

See following pages

• Introduction
• Theory
• • Modes of Decay
  • Several Basics of Probability Theory
  • The Poisson Distribution
  • Interaction of radiation with matter
  • Exponential radioactive decay
  • • Experimental Setup
    • • High Purity Germanium detector
      • Evaluation of spectra
      • • Experimental Procedure
        • • Test source with one line
          • Test sources with multiple lines - energy calibration
          • Efficiency calibration
          • Soil sample spectrum measurement calculating activities
          • • Analysis
            • • Test source with one gamma line
              • Test sources with multiple lines - energy calibration
              • Efficiency calibration
              • Data analysis of soil sample measurement
              • Calculating activities of three prominent lines
              • • Conclusion
                • function peak_counter for calculating activities
                • Laboratorys efficiency calibration curve for point source geometry
                • Laboratorys efficiency calibration curve for Marinelli beaker geometry
                • Measurement Report