Experiment 17. X-rays

Updated MD July 15, 2016

1 Safety First

During this experiment we are using radioactive sources. All sources are well shielded or are oflow intensity, nevertheless you should avoid any unnecessary exposure by keeping away fromthe sources (r−2 dependence) and limit the time of being in proximity to them.If not in use,radioactive sources should stay in a lead container provided.

Another safety concern is the high voltage power supply usedto power on detector. Underany circumstances do not switch on the high voltage power supply if high voltage cables arenot connected to the detector. Do not disconnect high voltage cables if the high voltage powersupply is active.

If you notice any exposed or damaged electrical wires, please notify laboratory staff immedi-ately.

2 Objectives

This experiment first examines various line spectra of knownenergy in order to calibrate theapparatus. X-rays resulting from nuclear processes are then observed and discussed. Finally,

17–2 SENIOR PHYSICS LABORATORY

the absorption characteristics of X-rays as a function of energy and medium traversed are in-vestigated. These characteristics are of considerable importance in fields such as medicine andengineering where X-rays are used as probes.

3 Introduction

X-radiation (composed of X-rays) is a form of electromagnetic radiation. X-rays have a wave-length in the range of 0.01 nm to 10 nm, corresponding to energies in the range 120 eV to120 keV 1. Although γ-rays may have energy in the same range, the difference is that γ-radiation comes from an exited nucleus and x-rays are alwaysproduced by changing electron’senergy outside nucleus. However, there is no physical difference betweenγ-ray and x-rayphotons of the same energy.

3.1 X-rays production in an x-ray tube or medical linear accelerator

High energy photons are given off when a solid target is bombarded with electrons of energyin the range from tens to hundreds keV. To produce high intensity x-ray beams, (as for medicaland x-ray diffraction applications) an x-ray tube or medical linear accelerator are commonlyused. Two types of emission are observed. The first, known asbremsstrahlung(literally brakeradiation in German), is a broadband or polychromatic radiation produced when the electronshave their velocities changed in magnitude or direction near the nuclei of the atoms of thetarget. These inelastic collisions with the Coulomb fields of nuclei involve the loss of all ofthe electron’s kinetic energy in one extreme case, and the loss of infinitesimal amounts ofenergy in the other extreme case. In the first case, a photon isemitted with the same energyas the incident electron. In the second case, the photon’s energy is vanishingly small. Thebremsstrahlung spectrum extends over a wide range of energies ending at the maximum energyof the incident electron.

The term x-ray is properly used to describe a line emission which can accompany bremsstrahlung.The electron bombardment can eject inner electrons from thetarget atoms leaving a vacantspace. Outer electrons then jump into the vacancy producingphotons of unique energy - a lineemission. X-rays are also produced when a target is bombarded with photons of sufficientlyhigh energy (these could beγ-ray or even x-ray photons). It is only necessary for these pho-tons to be able to eject inner electrons from the target atomsfor these so called ’secondaryx-ray’ to be produced. The combined spectrum has the characteristic peaks superimposed onthe bremsstrahlung base. The energy of the characteristic photons does not depend on the en-ergy of the incident electrons. However, the intensities ofthe different lines do change withelectron’s energy. The exact shape of the spectrum of the emitted x-ray radiation depends onthe energy of the incident electrons, material and thickness of the target, and absorption of theproduced x-rays inside the target and by the filter usually used at x-ray tube output. Measuredx-ray spectra for tungsten target are shown in Fig. 17-1.

According to Bohr’s theory, electrons with principal quantum numbern have a binding energyin the atom of

1This energy range is corresponding to the binding energy of electrons in K shell. Bremsstrahlung X-ray radia-tion can reach energy much higher, for example, 6 MeV x-rays are commonly used in medical applications.

X-RAYS 17–3

Fig. 17-1 X-ray radiation spectra for electrons of various energies bombarding tungsten target.

En = −

Z2RE

n2(1)

whereZ is the atomic number andRE = 13.6eV is the Rydberg energy constant.

’X-ray people’ calln = 1 the K shell,n = 2 the L shell,n = 3 the M shell etc.

The energies of x-rays are thus roughly proportional toZ2, although shielding of the nucleusby other electrons (which happen to be closer to the nucleus at the time) often results2 in theproportionality being closer to(Z − σ)2 whereσ ≈ 1.2 for n = 1. The energy gained by anelectron dropping from the second shell to the first gives Moseley’s law forKα lines:

E = RE(Z − 1)2(1

12−

1

22) (2)

We use x-ray tube to produce copperKα monochromatic spectrum in “X-ray Diffraction”experiment, but this kind of x-ray source will not be investigated in this experiment.

3.2 X-rays resulting from nuclear processes

3.2.1 Orbital electron capture

Nuclei with too many protons or neutrons are unstable. A nucleus with too many protons needsto reduce its charge, and this can be achieved in two ways:

• By positron emission; this occurs, for example, for22Na and is observed in the “GammaRadiation” experiment. In this case we have22Na→22Ne + e+ + νeorp→ n + e+ + νe

2This can be calculated using Hartree-Fock method.

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• By orbital electron capture; here the nucleus ’gobbles up’an orbiting atomic electron(mostly K shell, of course) and the reaction isp + e− → n + νeThis process is energetically easier by an amount2mec

2 = 1022 keV, as we are absorb-ing an existing electron rather than having to create a new positron.Such is the case for55Fe which electron captures to give55Mne− + 55Fe→55Mn + νeAs the resulting manganese atom has a missing K shell electron, we would expect Mnx-rays to ensue, and we can indeed observe these with our apparatus.

3.2.2 X-ray emission after internal conversion

There is another nuclear process which can produce x-rays. When gamma emission is possible,the nucleus also has the option of losing energy by the emission of one of its orbital electrons.This cannot be considered as a gamma emission followed by theatomic photoelectric effect inthe same atom. In fact it is really an extra mode of decay whichincreases the probability ofnuclear decay. Orbital electrons (especially K shell electrons) have a reasonable probability ofbeing in the vicinity of the nucleus. When this occurs, the excited nucleus can lower its energyby transferring the excitation energy directly to the electron, thus ejecting it right out of theatom. This process is calledinternal conversion. This additional decay channel is obviouslyonly possible for nuclei ’clothed’ in atomic electrons.

The first nuclide to be studied which exhibits this behaviouris 137Ba. It is also looked at in the“Gamma Radiation” and “Nuclear Lifetimes” experiments. Itis produced from the decay of137Cs.

137Cs→137Bam + e− + ν̃e

This is a straightforward beta decay with a half-life of 30 years. The superscript,m, indicatesthat137Ba is created in an excited state which can subsequently de-excite via the reaction

137Bam →137Ba +γ (with Eγ = 662 keV)

This nuclide also decays by internal conversion, the 662 keVbeing used to eject an orbitalelectron, usually from the K shell. The electron leaves the atom with 662 keV - 37 keV =625 keV, 37 keV being the energy needed to remove the K shell electron from the atom againstthe Coulomb attraction from the nucleus. X-rays result because the vacancy left by the ejectedelectron is filled by an outer electron.

Another case of internal conversion occurs in241Am, a 433 year half-life alpha emitter whichis studied in the “Alpha Radiation” experiment. Its decay scheme is shown in Fig. 17-2. Thestrong 60 keVγ-ray is used in the variable energy x-ray source3 to excite the targets. Since theprobability of internal conversion is high for the 60 keVγ-ray, we should expect strong x-rayemission from the source; however, the 60 keV is not enough energy to eject K shell electronsfrom the237Np atom produced after theα decay. Although the L shell electron wave functionsare smaller at the nucleus, we have considerable conversionof the L shell electrons as this isenergetically possible.

We will investigate spectra of x-rays produced from above mentioned nuclear sources later in

3One of the sources used in this experiment.

X-RAYS 17–5

241

95Am

146

237

93Np

144

432.6 a

α 100 %

5/2- 0 keV

7/2- 103.959 keV

13.23 %

0.38 %

0 keV5/2+

80 ps

2.144 Ma

67 ns 84.45 %

5/2- 59.54092 keV

9/2- 158.497 keV

1.66 %

0.23 %

33.19629 keV7/2+54 ps

0.12

15

35.9

2

2.31

0.06

69

0.01

95

0.01

81

0.02

03

Fig. 17-2 Decay scheme of241Am (only the most prominent energy levels andγ transitions are shown).

this experiment.

3.3 Absorption of x-ray photons in matter

The three main processes by which photons interact with matter are photoelectric absorptionwhich dominates at low energies, incoherent (Compton) scattering which is most importantbetween about 0.2 MeV and 5 MeV, and pair production which dominates at high energies.For x-ray photons the dominant absorption process is the atomic photoelectric effect; Comptonscattering is small. Under these conditions we expect an exponential absorption of the quantaso that the intensity of the radiation transmitted by an absorber of thicknessx is I(x) = I0e

−µx

whereI0 is the incident intensity.

It is easy to show that exponential absorption results from the ’all or nothing’ nature of theabsorption process: in a short distancedx the probabilitydp of the photon being ’lost’ byabsorption is given bydp = µdx.

Thus we may writedII = −µdx

Integration yields:I = I0e

−µx (3)

The absorption coefficientµ, depends on the density of the medium in a simple way. If wechange the state of the medium, say by vaporising it,µ drops by the ratio of the densities of thetwo states. The density dependence can be removed by using the mass absorption coefficientµ/ρ.

There is a general tendency forµ/ρ to drop with increasing quantum energy - except at the socalledabsorption edges. If energy is sufficiently large, all the orbital electrons of the absorbercan be ejected in the atomic photoelectric effect. As energyis reduced, one eventually reaches

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Fig. 17-3 Mass absorption coefficient as function of photon’s energy.

the point where energy is less than the binding energy of a shell, or sub-shell of orbital electrons,and because these electrons are no longer available for ejecting, the absorption ’suddenly’ drops- i.e. we have an absorption edge. The general behaviour ofµ/ρ is shown in the figure Fig. 17-3which shows both K and L edges. Notice that there are three L edges due to the 2S1/2, 2P1/2,and 2P3/2 possible states of electrons. The M edge (not shown here) has5 breaks for similarreasons.

Thecross-section, σ is another measure of absorption. We imagine each atom to be representedby an areaσ and that the photon is absorbed if it hits this area.

Thus we have for a thin absorber withN atoms per unit volume

dII = −σNdx

Soµ = σN or σ = µ/N

Also N = ρNA

A whereA is the mass number andNA is Avogadro’s number

∴ σ =µ

ρ

A

NA(4)

Thusµ/ρ gives us an idea of the cross-section for absorption of the x-rays as they traverse agiven material.

4 Apparatus

The apparatus consists of a detector (a xenon-filled proportional counter), a pre-amplifier, and amultichannel pulse height analyser (often called MCA, in this experiment it is a sound recorderplaced inside a computer and operated using the “PRA” [1] software). Various sources of x-raysare used in the experiment including a variable energy x-raysource (where characteristic x-rayfrom Cu, Rb, Mo, Ag, Ba, and Tb can be selected), a55Fe→55Mn (low energy 5.9 keV x-raysource), and a137Cs→137Ba (popular 662 keVγ-ray source). To investigate absorption of x-rays by media, different absorbers are also provided. Schematic block diagram of the apparatus

X-RAYS 17–7

is shown in Fig. 17-4.

Xenon detector Computer

X-ray

source Absorber Colimator Preamplifier

Fig. 17-4 Schematic of the apparatus used in the x-ray experiment.

4.1 Gas-filled proportional counter

The detector used in this experiment is a proportional counter. The height of the pulse producedat the anode of this type of detector is proportional to the energy of the detected particle. Xenonis a gas of high atomic number and thus has a high cross-section for the capture of low energyphotons by the photoelectric effect. The efficiency of the counter as a function of photon energyis shown in the figure Fig. 17-5.

Fig. 17-5 Proportional counter efficiency as function of photon’s energy.

Notice how the efficiency drops above 10 keV; the counter gas is becoming more and moretransparent to photons as the quantum energy increases. Thereduction in efficiency below9 keV is mostly due to the increasing absorption of photons bythe beryllium window. Beryl-lium is the lowest atomic number material which can be used asa counter window and thusis the most transparent practical window. Despite it being ametal some thousand or so timesmore dense than the xenon gas it encloses, it manifests an absorption for x-ray photons muchless than the gas.

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Efficiency of the detector suddenly increases when x-ray energy exceeds≈ 34.5 keV. At thisphoton’s energy it is possible to remove electrons from K shell in the photoelectric effect. It ismanifestation of an absorption edge and it was discussed in Section 3.3 and will be investigatedlater experimentally.

When a photon is caught in the counter gas some of its energy isgiven to a photo-electron4 (therest of the energy is used to ’drag’ the electron out of the atom against the attractive Coulombfield of the nucleus). Ionisation of the xenon gas occurs along the track of the photo-electron.The energy used to eject the photo-electron may also finally appear as ionisation: an x-ray willbe emitted by the xenon atom which has had its electron removed and this x-ray can be trappedin another part of the counter. If this latter x-ray escapes then we have an escape peak formed.If escaped x-ray is produced by filling electron vacancy in the K shell of the xenon atom, thenits energy can be 29.67 keV forKα or 33.74 keV forKβ transition. As you can see at theseenergies our detector is not very efficient, so probability of escape is large.

The counter separates the ionisation electrons from the positive ions and multiplies them up byproportional amplification; an avalanche occurs in the counter’s gas near its centre wire anode.A pulse of a few millivolts is produced at the centre wire. Themultichannel pulse heightanalyser (in this experiment the “PRA” [1] application) shows the amplified counter pulses as aspectrum, the pulse height being proportional to the quantum energies of the photons. Photonsof identical energy produces a peak in the spectrum. These peaks are relatively broad, aneffect due to the Poisson fluctuations in the finite number of ion pairs produced by the photo-electrons and by the loss of some of the original energy of thephotons at the various stagesin the counter’s processes. A photo-electron hitting the counter wall is an example of such aprocess (’surprisingly’ calledwall effect).

Some details concerning the construction and operation of the LND 45432 counter are in thetable 17-1.

4.2 Preamplifier

The preamplifier is used to match high output impedance of thedetector to low input impedanceof the audio recorder of the computer and to amplify the low level signal to the line level. Thegain of this preamplifier is≈ 250. See schematic Fig. 17-6 for details.

4.3 Variable energy x-ray source

One of the radioactive sources used in this experiment is variable energy x-ray source codeAMC2084. It is constructed as a compact assembly containinga sealed ceramic primary sourcewhich excites characteristic x-rays from six different targets in turn. The annular primarysource surrounds the x-ray emission aperture in the fixed part of the stainless steel assemblyand the targets are mounted on a rotary holder. Each target can be presented to the primarysource in turn and the characteristic x-rays from the targetare emitted through the 4 mm diam-eter aperture. The primary source is a241Am source (10 mCi), consisting of a ceramic activecomponent in a welded stainless steel capsule, with integral tungsten alloy rear shielding. Con-struction of the AMC2084 is shown in Fig. 17-7.

4An electron which gains energy from photon in photoelectriceffect.

X-RAYS 17–9

GENERAL SPECIFICATIONSGas filling XenonGas pressure 800 torrPath length 47.8 mmCathode material AluminiumMaximum length 203.5 mmEffective length 141.7 mmMaximum diameter 50.8 mmEffective diameter 47.8 mmConnector MHVOperating temperature range (-40 to +75)◦CWINDOW SPECIFICATIONSMaterial BerylliumAreal density 23 mg/cm2

Thickness 0.127 mmDimensions 25.4 mm x 50.8 mmELECTRICAL SPECIFICATIONSRecommended operating voltage2000 VOperating voltage range 1900 V to 2150 VTypical resolution (fwhm Cd109) 10Capacitance 3 pF

Table 17-1 Technical details of proportional gas counter.

Fig. 17-6 Schematic of the preamplifier. Batteries power supply not shown on the drawing.

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37 mm

23 m

m

Sealed annular

primary source

X-ray aperture

Target

Rotary target holder

Section of lid

Fig. 17-7 Construction of the variable energy x-ray source.

Characteristics of x-rays emitted from different targets are listed in the table 17-2.

Target selected Energy/keV Energy/keV Photon yieldKα Kβ photons/s/sr

Cu 8.04 8.91 2500Rb 13.37 14.97 8800Mo 17.44 19.63 24000Ag 22.10 24.99 38000Ba 32.06 36.55 46000Tb 44.23 50.65 76000

Table 17-2 X-ray emission from different targets in AMC2048.

4.4 Collimator

A collimator is a lead block with a hole in the centre. It can beplaced between the source andthe detector. By moving the collimator towards the detectorwe can decrease a solid angle ofthe x-ray beam and thus decrease counting rate of the detector. It is important to keep countingrate not to exceed≈600 counts/s, to avoid pile up of the pulses and minimise deadtime of thecounter. From x-ray sources used in this experiment only thevariable energy source with theterbium target selected and the manganese source needs the collimator to be used.

X-RAYS 17–11

5 Data Acquisition

In this experiment a lot of similar measurements are to be taken. It is important that conditions(including high voltage on the detector and its temperature) during all measurements are notchanging. For this reason we recommend to do all necessary (for the whole experiment) dataacquisition first and then concentrate on analysis and interpretation of the data.

Prepare your apparatus for data acquisition:

1. Place variable x-ray source in the mount and select Ag.

2. Switch on the pre-amplifier (remember to switch it off after all data is collected).

3. Run the “PRA” (Pulse Recorder-Analyser) [1] application.

4. Open the “Audio Input” window (use menuV iew → Audio Input).

5. Start data acquisition (use menuAction → StartDataAcquisition or just press theAkey). You should see negative pulses coming from the detector.

6. Open the “Data Acquisition and Analysis” window (choose the menuSettings →

DataAcquisition andAnalysis). Check if settings for pulse trigger are consistent withwhat you observed in the “Audio Input”. Make sure the polarity is right (for negativepulses use negative threshold). The “Shape tolerance method” should be checked.

7. Open the “Pulse Height Histogram” window (use menuV iew → PulseHeightHistogram).You should see a large peak around 20 arb.u corresponding toKα x-ray from silver(22.1 keV).

8. After 120 s data acquisition should stop. Save the data (use menuFile → SaveData)in your folder (create it with your name) at “My Documents” location under “Ag.pls”name.

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Below is procedure which you have to repeat for each set of x-ray source and absorber listed inthe table 17-3.

1. Change x-ray source and absorber to the next specified in the table.

2. For the variable energy source with the Tb target selectedand the55Fe source (withoutusing any absorber), adjust position of the collimator to achieve counting rate≈600 counts/s.Do not change this position for the same source and differentabsorbers. In case of the137Cs source, place it directly close to the detector.

3. Acquire data for 120 s.

4. Save data in your folder (created earlier) under the name:“[Source] [Absorber1][Thickness1][Absorber2][Thickness2].pls”.For example: “MnCr0.04CrBacking0.15.pls” is a file name for the data if the x-raysource was manganese (from55Fe) and the absorber was 0.04 mm thick chromium layeron 0.15 mm thick plastic backing. Using this naming system allows easy finding requiredfile later.

Please, switch the amplifier off when not in use, to save the batteries and place back allsources into the lead shielding, to avoid unnecessary irradiation.

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X-ray source Absorber Thickness [mm]

Ag - -Ag Al 0.75Ag Al 1.50Ag Al 2.25Ag Al 3.00Ag Al 3.75Ag polyethylene 28.00

137Cs wood 19.00Ba - -Ba Al 7.60Tb - -Tb Al 9.50Mo - -Mo Al 0.75Mo polyethylene 28.00Rb - -Rb Al 0.75Rb polyethylene 28.00Cu - -55Fe - -55Fe Al 0.0555Fe Cr on backing 0.0455Fe backing for Cr 0.1555Fe Fe 0.02555Fe Mn on backing 0.01555Fe backing for Mn 0.8655Fe polyethylene 3.8055Fe Ti 0.0255Fe V 0.015

Table 17-3 Table of all x-ray source and absorber configurations in the experiment.

X-RAYS 17–13

6 Data Analysis

6.1 Calibration of the apparatus

All measurements of pulse height in this experiment are in arbitrary units (arb.u). The pulseheight depends on an photon’s energy deposited in the detector which produces the pulse. In ourcase of proportional counter detector, dependence betweenphoton’s energy and pulse heightis approximately linear (with a good accuracy). This linearfunction (energy of photon in keVversus pulse height in arb.u) we call a calibration of the detector. To calibrate the detector wewill use previously obtained x-ray spectra (without using absorber) of Ag, Ba, Cu, Mo, Rb, andTb from variable energy x-ray source and energy ofKα. If energy ofKα andKβ are so closethat they form one peak (Cu, Mo, and Rb), you should use an weighted average of 100% ofKα with 20% ofKβ lines from table 17-2. Some of the spectra are quite complicated and isnot easy to tell which peak representsKα line, but if you start from Mo and Ag (which largestpeak isKα) to do a rough calibration (arbitrary units should be close to keV), it should beeasy to find required peak in other spectra. For each mentioned above x-ray sources follow theprocedure listed below:

1. Open previously saved data file in “PRA” [1] using theFile → OpenData menu.

2. View the “Pulse Height Histogram” window usingV iew → PulseHeightHistogram.

3. Select ’Region Of Interest’ (ROI) containing required peak5. Selected ROI is displayedin distinctive colour and information about peak’s parameters is listed. Write down meanvalue and standard deviation for each peak.

After exploring all required spectra:

1. Open the “QtiPlot” [2] application and in the table write in the first column values ofpeak’s mean in arb.u and in the second column corresponding energy in keV.

2. Add new column and set it as X-error. Fill it with standard deviation of each peak.

3. Select columns X, Y, and X-error and choosePlot → Scatter. This should displayyour data points.

4. ChooseAnalysis → Fit Linear. Make a proper labels and print the graph.

Now, after the calibration was done ‘by hand’ you can use a PRA’s calibration feature to makeyour live easier. Open “Calibration” dialogue box and put the same data points (mean pulseheight of the peak in arbitrary units, standard deviation ofthe peak in arbitrary units, andcorresponding energy in keV) into the appropriate edit boxes. Choose a linear calibration modeand click over “Apply” button. Next open the “Data Acquisition and Analysis” dialogue boxand check “Use calibration” box. Your pulse height histograms becomes calibrated in energyunits. Save settings in your folder using “Setting→ Save Settings As. . . ” menu. You can loadall your settings including calibration by using “Setting→ Load Settings. . . ” menu if needed6.

Remember, save your projects frequently!5Use “B” and “E” keys to mark the beginning and the end of ROI or press “F” key to select ROI automatically

using “Gaussian correlation” curve.6From now you should open PRA files usingFile → LoadData menu rather thanFile → Open. This way

you preserve all your current settings including calibration and ROIs.

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6.2 Analysis of the55Mn spectrum

Similarly as described in the previous section, using your calibration find the energy of thex-ray peak of the Mn. Compare your result with the value listed in Kaye and Laby [3, p. 4.2.1table] and comment.

Question 1: Can you observeKα andKβ peaks separately?Hint: What is the width of theobserved peak?

6.3 Analysis of the x-ray spectra of Ba

There are two different sources which will produce x-ray spectra of Ba: variable energy x-raysource with Ba target selected and137Cs. Both sources were described earlier.

1. Open the data file from the137Cs source and find positions of all peaks.

2. Repeat previous procedure with the data file of the Ba target from the variable energyx-ray source.

3. Carefully compare both spectra and comment on results.

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6.4 Investigation of x-ray absorption versus absorber thickness

In this part of experiment we will investigate exponential nature of absorption as has beendescribed in section 3.3. We will use data obtained from Ag x-ray source with Al absorber ofthickness (0, 0.75, 1.5, 2.25, 3.0, and 3.75) mm.

1. Open Ag.pls data file in “PRA” [1].

2. View the “Pulse Height Histogram” window.

3. Select the ROI over the main peak. This should be just a few bins around the 22,1 keVselected. This selection should stay the same for all silverdata files.

4. Read the number ofGrosspulses in the selected ROI and write it down.

5. Repeat points 1 and 4 for each data file obtained from Ag source and Al absorbers ofdifferent thickness.

6. Use the “QtiPlot” [2] application to plot number of pulsesversus absorber thickness.

7. Open “Fit Wizard” using the menuAnalysis → FitWizard . . . and then select theExpAbsorptionfunction from theUser definedcategory to fit exponential function toyour data. Make sure that theFit with selected user functioncheck box is checked. Goto Fitting Sessionand press theFit and then theClosebuttons to finish “Fit Wizard”.

8. Calculate mass absorption coefficientµ/ρ assuming aluminium densityρ = 2700 kg m−3

and compare result with value from Kaye & Laby [3, p. 4.2.2 graph].

X-RAYS 17–15

6.5 Aluminium mass absorption coefficient versus photon’s energy

It is instructive to see howµ/ρ depends upon quantum energy. Aluminium absorbers are usedbecause its K absorption edge is at a much lower energy than the photons used in this test.

X-ray source Al thickness/mm

Mn 0.05Rb 0.75Mo 0.75Ag 3.00Ba 7.60Tb 9.50

In energy range which is investigated, the major interaction of photon with matter is the pho-toelectric effect. According to Kaye & Laby [3, p. 4.2.2], the equation bellow describes thephotoelectric effect cross-section:

σphotoelectric(m2) ≈ 6× 10−37 Z4.5/E3

γ (5)

WhereZ is the atomic number of the attenuating material andEγ is the energy of the photonin MeV.

1. For each of the specified sources and absorbers measure theK peak gross number ofcounts with and without absorber. Use the same method as in the previous section.

2. AssumeI0 in (3) is equal to number of counts in each peak without absorber and calculateµ/ρ for each energy.

3. Obtain a graph oflog(µ/ρ) as a function oflog(E).

4. Fit a straight line to the data points. Compare the slope tothe value expected fromequation for photoelectric effect cross-section (5).

6.6 Carbon mass absorption coefficient versus energy

This section is very similar to the previous. We will use now acarbon absorber. Polyethylene isused for convenience; it is chemically (CH2)n, but the hydrogen, only having one orbital elec-tron, causes negligible absorption and can be ignored. The density of carbon in polyethylene is790 kg m−3.

1. Use data files where polyethylene absorber was used (Mn, Rb, Mo, and Ag sources) andcorresponding data without any absorber to calculateµ/ρ for each energy. The procedureis identical to the procedure used in the previous section.

2. Obtain a graph oflog(µ/ρ) as a function oflog(E).

3. Fit a straight line to the data points. Compare the slope tothe value expected fromequation for the photoelectric effect cross-section (5). It should be close to -3. It isinstructive to print data for aluminium and carbon absorbers on the same graph.

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4. Calculate ratio ofµ/ρ values for the same photon’s energy which you obtained for carbonand aluminium absorbers and compare it with the same ratio calculated using equations(4) and (5).

6.7 Observation of absorption edges

As it was discussed earlierµ/ρ falls as photon’s energy increases, except for the region ofabsorption edges.

In this experiment you will examine the K edge. The obvious way to do this would be to use atarget of a single element, vary energy over a small energy range and plotµ/ρ as we proceed.This cannot be done with our x-ray source so we use an alternative procedure. We fix photon’senergy (manganese x-rays) and vary the absorbers. The absorbers are chosen from consecutiveelements in periodic table: titanium, vanadium, chromium,manganese, and iron. The tablebelow is listing property of used absorbers:

Absorber Density/(kg m−3) Thickness/mm

22Ti 4508 0.02023V 6090 0.01524Cr 7194 0.04025Mn 7473 0.015

26Fe 7873 0.025

1. Similarly as you did in the previous section, open desireddata files in “PRA” [1] andcalculateµ/ρ for each absorber. Note that the Mn and Cr absorbers are placed on theplastic backing, and in those casesI0 should be number of counts when photons arepassing through the backing (not air).

2. Plot a graph ofµ/ρ as a function ofZ. The graph should closely resemble a similargraph in Kaye & Laby [3, p. 4.2.2 graph] with the K edge clearlyvisible.

3. Recall that the Mn source emitsKα andKβ rays. Look up their energies in Kaye &Laby [3, p. 4.2.1 table] to see whether they are larger or smaller than the energies of theK edges of the absorber elements.

Question 2: Can you explain from the above data why the K edge occurs whereit does? Bylooking at your plot - particularly in the region of chromium- can you draw any conclusion asto the relative importance of theKβ x-rays being emitted by manganese?

Question 3: In the “X-ray Diffraction” experiment a thin nickel foil is used to reduce theintensity of theKβ lines from the copper x-ray target. TheKα copper x-rays are relativelyunaffected. Using the tabulated data in Kaye & Laby [3, p. 4.2.1 table] for copper and nickel,can you explain why this works?

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X-RAYS 17–17

7 Supplementary investigation

These are additional investigations which may be made with the apparatus. They do not formpart of the experiment as such but if you have the time you may like to try them.

Hints to all tasks listed below:Peaks of certain energy which occurs in all spectra from differenttargets of the variable energy x-ray source, can be on account of the primary radiation from thissource or produced inside the detector (escape peaks). In the first case, a relative intensity ofpeaks with different energies should change when using an absorber (recall your investigationof µ/ρ versus photon’s energy dependence Section 6.5).

1. Determine the energy of the primary radiation in the variable energy x-ray source.

2. The low energy peaks observed for terbium and barium have been interpreted as ’escapepeaks’. Another possible explanation of these peaks is thatthey are due to lower energyx-rays coming from the target. Make measurements to check the relative merits of thetwo explanations.

3. Choose any of the variable energy x-ray source target and try to identify all peaks ob-served in its spectrum. If needed take an extra measurement of its spectrum for longertime (10 min), to achieve better accuracy.

C 6 ⊲

References

[1] M. Dolleiser.PRA, version 15, 2016.http://www.physics.usyd.edu.au/ ˜ marek/pra/

[2] I. Vasilief. QtiPlot, version 0.9.9, 2016.http://soft.proindependent.com/qtiplot.html

[3] G. W. C. Kaye and T. H. Laby.Tables of Physical & Chemical Constants. Longman GroupLimited, Essex CM20 2JE, England, 1995.http://www.kayelaby.npl.co.uk/