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DETERMINATION OF ern FOR ELECTRONS Physics 302 DL Humphrey 1 Introduction The em vacuum tube has been designed for detennining the ration of charge to mass of an electron The beam of electrons in the tube is produced by an electron gun mounted with its center line coincident with the vertical axis of the tube The gun consists of an indirectly heated cathode which supplies the electrons a grid charged to a positive potential with respect to the cathode which serves to focus the electron beam and a circular plate which is held at a high positive potential and thus accelerates the electrons The electron stream is projected vertically through a small hole at the center ofthe disk The bulb and disk are coated with a material which fluoresces when struck by electrons The tube contains a trace ofinert gas that aids in focusing the electron beam as well as to cause the beam to make a visible trace The tube is immersed in a unifonn magnetic field produced by a set ofHelmholtz coils which causes the stream of electrons to move in a circular path the radius of which decreases as the magnetic eld increases By proper control ofthe magnetic eld the beam can be made to coincide with any one ofthe four circles on the disk 2 Theory When a charged particle such as an electron moves in a magnetic eld in a direction at right angles to the eld it is acted on by a force the value of which is given by FBev l where B is the magnetic ux density 2 is the charge on the electron and v is the velocity ofthe electron This force causes the particle to move in a circle in a plane perpendicular to the magnetic eld The radius of this circle is such that the required centripetal force is furnished by the force exerted on the particle by the magnetic eld 2 HIV Bev 2 r where m is the mass of an electron and r is the radius of the circle If the velocity of the electron is due to its being accelerated though a potential difference V it has a kinetic energy 1 7 mv39 6V 3 2 Substituting the value v from Eq 3 to Eq 2 2 2V m le39l 4 Thus when the accelerating potential the ux density ofthe magnetic eld and the radius of the circular path described by the electron beam are known the value of em can be computed The magnetic eld which causes the electron beam to move in a circular path has the magnetic ux density B which in terms ofcurrent through the Helmholtz coils and certain constants ofthe coil is 810N1 125a B Where N is the number ot tums on each coil 1 is the mean radius ofthe coil and l is the current through the coils Substituting Eq 5 in Eq 4 gives 329x10quot 6 m 139quot Eq 6 is the working equation for this apparatus The value of r the radius of the electron beam can be varied by changing either the accelerating potential or the Helmholtz coils cuiTent For any given set ofvalues the value of em can be computed 3 Experimental Procedure Make certain the potentiometers on all power supplies are fully counterclockwise before you plug them in Ix Place 30V accelerating potential on the anode and 2th on the focusing grid Raise slowly the heating lament voltage take about 1 minute to 59V Do not exceed this value There should be now a visible blue beam exiting through the hole in the plate and striking the glass wall Iv La Increase the Helmholtz coils current until the electron beam describes a circle Adjust its value until the sharp outside edge ofthe beam strikes the smallest circle 4 Record this value I in your data table Determine and record the eld current required to cause the electron beam to strike other circles This is the value of the current to be used in computing em Since there will be some uncertainty in determining when the beam strikes the circles take several readings for each circle 5 Compute the em for each value of I Put your data in a spreadsheet 53 Repeat the above and detemrine em using another value for accelerating voltage Compare your results with the published value of em which is 176 x 10quot Ckg Suppose your error in I is 2 your error in V is 1 and your error in r is 005cm How much variation do you expect in your value of em for the largest and smallest circle Since the whole em tube is in a magnetic eld the beam is travelling in the magnetic eld before it passes through the center hole in the top plate How does this tend to affect your results 1 We jet 7 i3 w as my equot femea im St 535 a e W The Gamma Spectrometry System The components of the multichannel analyzer based gamma spectrometry system include the NalTl Scintillation crystal a photomultiplier tube a wellregulated high voltage supply a linear amplifier and optional data output devices in addition to a PCabased data acquisition system DASl orquot Dnlnler uv an Supply spamcue Amnilltquot lln Ind Forquot SMFI39Y Figure 1 Gamma Spectrometry System Detection The most commonly used inorganic scintillator is sodium iodide containing approximately 01 thallium iodide impurity which acts as an activator center for the scintillation process NalTl Sodium iodide has a high density 367 glcm and a high effective atomic number Z 53 for iodine These two factors result in a high probability of gamma interaction in the crystal The light output from NalTl is the largestfor any of the scintillators in common use The emitted light has an average wavelength of 410 mp 4i1x10397m and a decay time of 025 psacl The crystal is transparent to the scintillations The scintillation spectrum matches the photo cathode response of the coupled photomultiplier tube This provides a high efficiency of conversion from light output in the crystal to electrical output from the PM tube The resolution of a sodium iodide gamma detector is defined as the full width at half maximum FWHM of the total absorption peak at one half its maximum height divided by the pulse height at the center of the total absorption peak mm P 1 1 I 0 0 Resolution FWHM n PP This is shown in Figure 2 s The smaller the numerical value obtained for resolution the better is the detector and associated electronic system To report a resolution figure the energy with which it was measured should also be Pr indicated If no energy is indicated with a Nquot quot m resolution figure it is understood that this resolution was measured using 705 or an energy of 662 keV AVERAGE 3 1 Figure 2 Resolution Determination The observed resolution of a spectrometer system is a combination of the effective resolution of the sodium iodide crystal the photomultiplier tube and the associated electronic components A large variety of shapes and sizes is available for NalTl crystals A typical shape is the right circular cylinder detector Another common shape is the well crystal The crystal has a well drilled into it to accommodate sample holders in order to increase detection efficiency r Llneor I Ampllfle Sclntlllcrtion Detgcfo Figure 3 Components ofa Gamma Spectrometry System Counll Effect of Crystal Size The purpose of having large size crystals is to produce a greater number of total absorption events and therefore more counts in the total absorption peak and less in the Compton region of the spectrum Figure 4 below shows the effect of three crystal sizes Each of the spectra have been normalized to the same total absorption peak count From this figure it is observed that the larger the crystal the greater will be the percentage of counts that will fall in the total absorption peak The high voltage power supply shown in the component diagram of Figure 3 provides the accelerating potential for the dynodes of the photomultiplier tube The HV supply provides a positive voltage between 500 and 1500 volts The high voltage is applied to the resistor divider string of the photomultiplier tube as shown in Figure 5 V BACKSCAT TER 5 PEAK 1 12 I 1quot 2x2 313quot PulIoHelght Units PHOTOCATHODE Figure 4 Typical photomultiplier tube and resistor divider string Figure 5 Comparison ofmCs spectra using different size crystals The 410 mp light output of the Nal l crystal is optically coupled to the photocathode which has a thin layer of photosensitive substance typically antimonycesium or silver magnesium alloys The photocathode will emit a number of electrons proportional to the intensity number of 410mp photons of the scintillation from the crystal Since the intensity of light output from the crystal is proportional to the energy deposited in the crystal by the gamma ray the number of electrons emitted from the photocathode is proportional to the energy of the gamma ray These photoelectrodes are called dynodes A typical photomultiplier tube will contain 10 dynodes The rst dynode is maintained at a positive potential with respect to the photocathode Each succeeding dynode is kept at about the same potential difference with respect to the preceding one The electrons that are emitted from the photocathode are attracted to the rst dynode and acquire enough kinetic energy to free additional electrons as they collide with the dynode secondary emission This charge multiplication process occurs at each dynode After the last dynode stage the electrons are collected at the anode of the tube Processing the Signal The amplifier provides both appropriate pulse shaping and linear amplification A voltage sensitive input at the amplifier accepts the current pulse from the detector The ampli er differentiates and ampli es the detector pulse and produces a fast rising positive voltage pulse that has approximately a gaussian shape with about a Zps width The amplification is linear and the output pulse from the ampli er has a height that is proportional to the energy deposited in the crystal by the gamma ray AnalogtoDigital Conversion This positive pulse from the amplifier is directed to the input of the analogto digital converter ADC of the multichannel analyzer When this occurs a rundown circuit is activated which linearly reduces the peak voltage to baseline value This takes a period of time number of cycles of the oscillator which is proportional to the peak height The number of oscillations is counted by the scaler At the end of this process the memory location channel appropriate for the sealer count is addressed and the count in that location of the semiconductor memory is increased by one While this pulse height analysis is taking place the input to the amplifier is closed so that no ads ditional pulses can begin the process This deadlttime is automatically corrected for by the livetime clock so that the time set for counting a sample is live time I The memory accumulates and stores this pulse height information in digital form When the readout operation is requested the memory information is read and put in suitable format for scope display or other forms of data output printer plotter Teletype etc FIGURE 6 Pulse Height Analysis Gamma Spectrum Analysis The general form of gamma ray spectra is shown in Figure 7 below The total absorption peak represents those detector pulses arising from a total energy absorption process within the crystal in order to interpret the spectra obtained Touuasowno mm with a NalTl gamma ray spectrometry sys tern you must understand the three principal interactions of gamma rays with the crystal They are 1 photoelectric effect 2 Compton scattering and 3 pair production They are discussed in the following paragraphs COMPTON EDGE DISTRIBUTION Pull pu Unll Fulu Hltqht cannon VALLEY FIGURE 7 Typical shape at gammaray spectra Putquot might Photoelectric Effect In the photoelectric effect a gamma ray interacts with a bound electron in the structure of an atom The gamma ray energy is completely absorbed and the electron is ejected from the atom with a kinetic energy equal to the gamma energy minus the binding energy of the electron Since the electron leaves the atom a vacancy results usually the K shell An outer shell electron will tall down to fill the K shell vacancy This results in an X Flay characteristic of the atom This resulting XRay can interact with a valence electron of the atom causing it to be ejected When this occurs it is called an Auger electron Following the photoelectric interaction the resulting electrons and any XRays are easily absorbed in the crystal so a photoelectric interaction usually results in the absorption of all the gamma ray energy in the crystal The photoelectric effect is more probable for low energy gamma rays and the probability ofthe effect increases rapidly with increasing Z of the absorber in this case the NalTl crystal The photoelectric absorption coefficient varies as Z hv Therefore a NaTl crystal is a good ab sorber of gamma energy due to the high atomic number 2 53 of iodine I ATOMIC ELECTRONS NUCLEUS FIGURE 8 Photoelectric ellect FIGURE 9 Compton scattering Compton Scattering A Compton interaction consists of an incident gamma ray of energy hu colliding with a valence electron and being scattered at some angle relative to its initial direction of incidence The Comp ton scattered photon scatters at angle 9 with reduced energy hy and the electron recoils with kinetic energy T The incident gamma ray has an energy E hu This energy is shared between the Compton scattered photon and the recoiling Compton electron The scattered photon has an energy E hv39 and the electron has an energy T Since the total energy is conserved in the interaction we can write hu hu T 1 Momentum is also conserved in the interaction and from a consideration of this conservation of momentum we can write the two expressions below hu h C cos 0 Pcos 1 x component momentum 2 O 21 sin 5 Psin y component momentum 3 where P represents the momentum of the electron From a simultaneous solution of these three equations we can derive Compton39s well known formula for the energy of the scattered photon in terms of the initial energy hu and scattering angle a 39 hy T 1 1 cos 6 4 quot 06 The kinetic energy of the Compton electron could be written as T hu hu39 5 An examination of the last two equations 4 and 5 indicates that the scattered photon hu39 may go in any direction with respect to the incident gamma ray whereas the electron can be scattered only in a forward direction By using the equations 4 and 5 for scattered photon and electron energies and by substituting different values of scattering angle 6 and different incident gamma energies the following table is obtained Table 1 8 11111 1022 keV hv 652 kaV hv 323 keV hv39 T hv39 T 111139 T O 804 0 662 0 323 0 30 804 215 564 98 298 25 60 511 511 402 260 245 78 90 340 680 288 374 198 125 120 255 765 225 437 166 157 150 215 805 194 468 148 175 180 204 816 184 478 143 180 An inspection of the data shown in Table 1 reveals that the electron receives the maximum kinetic energy when it is projected forward and the Compton photon is scattered backward 39 9 180 The probability of a Compton interaction varies as the ratio of atomic number to mass number ZA of the absorber material and is less dependent on the photon energy than is the photoelectric effect Pair Production Pair production is the process whereby a gamma ray interacts with the strong electric field of a nucleus and an electron positron pair is created as the incident gamma ray disappears For pair production to occur the gamma energy must be greater than 1022 keV or twice the rest mass energy of an electron 511 The energy of 1022 keV is the threshold energy for pair production The probability for pair production rapidly increases as the incident gamma ray energy exceeds the threshold energy Any gamma energy in excess of the 1022 keV necessary to form the e and e is converted into kinetic energy of the pair Both the electron and positron are quickly stopped in NalTl crystal following pair production and the positron combines with an electron to pro duce two 511keV photons called annihilation photons These two 511 keV photons are emitted in opposite directions 180 to one another and may or may not interact with the crystalr In such a case the original gamma is absorbed in the crystal but when the annihila tion process occurs some of the original ener gy either 511 or 1022 keV may escape from the crystal ELECTRON hu gt 1022 kIV POSITRON mrsnss COULOME FIELD FIGURE 10 Pair Production In a NalTl crystal the photoelectric effect is the dominant process for gamma energies less than about 250 keV The Compton effect is predominant from about 300 keV to 5000 keV Above 5000 keV the pair production effect is the most important process This is shown in Figure 11