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Advanced Laboratory

by: Nichole Keebler

Advanced Laboratory PHYSICS 407

Nichole Keebler
GPA 3.95

Robert McDermott

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Robert McDermott
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This 13 page Class Notes was uploaded by Nichole Keebler on Thursday September 17, 2015. The Class Notes belongs to PHYSICS 407 at University of Wisconsin - Madison taught by Robert McDermott in Fall. Since its upload, it has received 65 views. For similar materials see /class/205211/physics-407-university-of-wisconsin-madison in Physics 2 at University of Wisconsin - Madison.


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Date Created: 09/17/15
revised 41806 RANGE OF ALPHAS Advanced Laboratory7 Physics 407 University of Wisconsin Madison7 Wisconsin 53706 Abstract A silicon solid state detector is used to measure the energy of alphas which have passed through air from an Amz41 source The air pressure may be varied and so the alpha particle Bethe Bloch formula for dEdz may be veri ed and the alpha particle range and straggling can be measured Theory A charged particle moving through a neutral medium will interact electro magnetically with both the electrons and nucleii ofthe material The electro magnetic interactions with the nucleii cause Rutherford Scattering and are seen as small and occasionally large changes in directions The interactions with the electrons are far more frequent and are seen as a fairly steady loss of kinetic energy There are7 of course7 statistical uctuations in the rate of the interactions and this is seen as straggling of the range of monoenergetic particles For example7 alphas with a mean range of 20 cm will have range uctuations straggling of about i1 The rate of loss of energy can be calculated see Reflll7 pg 637 and Refl27 pp 155 162 dE i 1 47Te422 NB E T 747T602 mgr2 mks where e charge on electron coulombs z Atomic number of moving particle N the number of atomsunit volume meter g m5 mass of electron kg 1 velocity of the moving particle metersec E kinetic energy of the moving particle joules z distance travelled by the particle meter 60 permittivity of free space 147T60 8988 gtlt 109 Newton meterZcoulombz B Atomic stopping number dimensionless The factor B is not constant but varies slowly with energy in a logarithmic manner The theoretical calculations for B become dif cult when allowance is made for the partial screening of the nuclear charge by the inner electrons The best formula for B is probably that of Refll7 pg 638 2m 112 B Z 1114 71111 732 in 7 OK I where CK the correction term for the K shielding The equations and a plot of CK are shown on pg 639 of Ref1 B the usual relativity factor veloc particleveloc light I average77 ionization potential of the stopping medium Z average atomic number of the stopping medium If we assume that the velocity is non relativistic7 then E mvz and so dE i 1 42 E774W60227f z Nlt MgtB E We where M is the mass of the particle 62 is also small so that ln1 7 62 m 732 and so 4mE 321 5 70 nltMIgt K Fortunately in our experiment with alpha particles in air7 the calculated value of CK is nearly constant near 090 The particle range can be determined by integrating over the particle energy E dE RltEgt 0 11 Statistical uctuations lead to a distribution of ranges about the mean R0 with a straggling parameter 04 de ned by the probability distribution for the ranges R 7 R02 PltRgt a explia l 1 000 800 600 400 300 833888 cf MevKg cm z to ma GINO Shin by o150 P 1 01 02 03 1 10 100 1o3 104 Kinetic energy MeV FIGURE 84 Energyloss curves for different charged particles in air and in lead Note how all the curves are related to each other Figure 1 Energy Loss Curves for Different Particles in Air and Lead Numerical values for as a function of energy are shown in Fig 1 for various particles A 5 Mev alpha particle has a value of about 1000 MeV gm cm2 has minimum for all particles at a kinetic emergy of about twice the rest mass For singly charged particles this value is about 2 MeVgm cm2 Fig 2 shows differential and integral probability distributions for heavy particles ranges The extrapolated range Rem is related to the straggling parameter oz as explained later in the text Fig 3 shows range vs energy for alpha particled in air at standard con ditions The range for a 5486 keV alpha in dry air at 15 and 760 Torr is 4051 cm 10 PU 05 l LLgt a Re R 0 R0 Rex R FIGURE 203 a Distribution of ranges for charged particles 6 Probability of a particle having a range larger than R Figure 2 The differential and integral probability distributions for heavy Charged particle range Mean range cm of air at 15 C upper curve curve N o g H O a Ray energy in Mev 2 cc Ray energy in Mev lower curve 0 15 7 10 13 14 Mean range cm uf air at 15 C lower curve Fig 32 Rangeenergy relationship for a rays in dry air at 15 C and 760 mm Hg The curves agree with those of Bethe B44 and with the tables by Jesse and Sadauskis J12 Two low energy calibration points J12 are provided by the a rays emitted in the thermal neutron reactions B1 naLiquot and Li naH Figure 3 Alpha Range Energy in air Apparatus 1 Vacuum Chamber The vacuum chamber is made of pyreX glass and is mounted inside a dark wooden box The Silicon detector must be pro tected from room light since photons cause a noise background which spoils the resolution of the detector Do not open the glassware The alpha source could7 over a long time7 shed some radioactive dust The system has been designed to ensure that any dust is trapped inside the glass system vacuum The source to detector surface was remeasured in 2005 and determined to be 665 i 005 cm 3 Filter An automobile oil lter is used to check for possible source leak age The lter is periodically tested to check for activity The lter has an internal rubber gasket which blocks the gas ow at low pressure differentials 10 Torr A copper wire has been inserted to hold the internal rubber gasket open Do not open or disconnect the lter 00 Pressure GaugeiMKS Baratron type 122A The pressure gauge is an absolute pressure transducer based on measuring the capacitance of a sample chamber The accuracy is rated at 05 of reading from 0 7 50 C The readout is in Torr 4 Vacuum Pump The pump is a 2 stage rotary pump enclosed in the standard cart to reduce acoustic noise Notice that a ow of warm air is exhausted from the cart by an electric fan to prevent the pump and motor from overheating 241 Cf Alpha Source The decay scheme of Am is shown in Fig 4 This source is not sealed and so must remain inside the vacuum enclosure Usually sources are sealed with very thin metal skins In this experiment7 a skin would slow the alphas slightly As the skin could not have a perfectly uniform thickness7 the alphas would emerge with a broader range of energies The 5486 and 5443 keV alphas will not be resolved due to the nite thickness of the source A 5486 keV alpha has a range in dry air at 15 C and 760 Torr of 4051 cm and so the source alphas cannot reach the detector until the chamber pressure has been reduced CT Solid State Detector Ortec A 040 200 3007 Serial 9 129B The detec tor is a surface barrier detector consisting of an extremely thin p type layer on the face of a high purity n type Si wafer The rated energy I 241 95 458 years 127 860 Oi 0c 5443 keV 5486 keV 241 Figure 4 Decay Scheme of Am resolution of the detector is 40 keV and the active thickness when fully depleted is 300p The p type surface of the detector is gold plated with a layer approximately 40 Mg cm z thick The detector has a sensitive diameter of about 16 mm and is mounted on a BNC connector within the vacuum system Although the detector can operate with a bias of 100V in a very good vacuum7 we will use the detector in the danger ous 10 2 Torr to 10 Torr region Set the bias to 30 V but do not use a bias greater than 30 V Some useful properties of Si are listed in Fig 6 Pre ampli er Ortec model A576 This is a charge sensitive pre ampli er which also supplies the bias voltage for the Si detector The pre ampli er is designed to have a large effective input capacitance Ca so that most of the charge drains from the detector and cable into the pre ampli er and is ampli ed If the capacitances of the detector and cable are Cd and Cc then Ca Qa QM ml 7 where QM is the total charge collected by the detector7 and Qa is the charge delivered to the charge sensitive pre ampli er 8 10 09 39 AMPLIFIER Figure 5 Apparatus Schematic Diagram Although Cu is large7 the charge seen by the pre ampli er depends upon 00 and so the same short cable should be used to connect the detector and pre ampli er for all measurements Ampli er ORTEC Model 570 Use the input set to P08 and the unipolar output The ampli er gain is adjustable so that the gain can be matched to the full scale range of the PC MCA System The ampli er also shortens the pulses so that a typical alpha pulse out is N 2 866 Pulse Height Analyze Ortec 916A board inside the PC using the Maestro MCA software Usually set for 512 channels full scale Scaler Ortec Model 484 Procedure 1 2 CO Read Refl27 pp 208 2177 and the theory in Re ll Chapt 22 Pump down the vacuum chamber The lter has a low pumping speed and so the time to reach 10 Torr is several minutes Practice using the air inlet valve or the vacuum pump valve to obtain and hold any pressure you wish Connect the detector to the FET pre ampli er with a short 1 foot cable The TEST OFF switch should be set to the center position Connect the rear pre ampli er output to the input of the pulse ampli er Connect the pulse ampli er output to the pulse height analyzer input and scope Do not terminate the cable to the scope7 since the pulse height analyzer input has a relatively low input impedance The schematic is shown in Fig 5 4 The ampli er should be set for POS input pulses Lower the pressure to less than 5 Torr and look for positive pulses 5 psec at the MCA and scope inputs Adjust the gain of the ampli er so that the pulses are being counted near the upper end of the 512 channel MHA The MCA requires positive pulses and full scale corresponds to 10 Volt input pulses Record all parameters so that you can later reproduce the same gain The Si detector output will be pulses whose amplitude is proportional to the alpha particle energy less the energy lost in the air Since these pulses are fed to the MCA we have Energy constantgtltpulse height constantgtlt channel numberconstant Cf Compare the pulse height channel of pulses produced with a bias of 20 V with those produced with a bias of 30 V Estimate the error in the channel due to your error in setting the bias at 30 V 03 Use the ampli er attenuator to measure the linearity and zero offset of the MCA 1 Measure the full width half maximum resolution of the alpha particle peak and compare to the intrinsic resolution of the Si detector 00 Measure the count rate and the mean energy E and energy straggling full width at half max of the alphas as a function of the air pressure P Take ne steps near the end of the range so you can determine the range accurately The count rate can be determined from the sum of the counts in the MCA peaks However it is much better to measure the count rate using a scaler to avoid the MCA dead time correction Plot count rate against P Determine the mean range R0 and the ex trapolated range Rex of the alpha particles as shown in Fig 2 Compare your result to the predicted value based on Fig 3 Remember that you have to correct the range predicted value for the temperature and at mospheric pressure of your data From the quantity RexiRO determine the effective straggling parameter a The quantity 04 is de ned by the probability distribution for the ranges exp7 R 7 R0 PR a M l and Rex 7 R0 04 Measure the source detector distance and cal culate the expected pressure for the range using the one atmosphere range given above Compare the measured straggling parameter to the value given in Fig 7 below and the measured resolution of the alpha peak 9 Now use the MCA to measure the alpha particle energy as a function of air pressure Plot E against P From this data compute dEdx and plot dEdx against 1E If the factor B in the formula for dEdx were perfectly constant7 then the dEdx versus 1E plot would be a straight line through the origin SigmaPlot has a nice Spline tool to determine the derivatives of a set of x y numbers 10 Plot E ltgt against ln E to verify that the ln term is energy dependent From the dEdx vs ln E data determine the average lonization Potential 1 of dry air Compare to the expected value 11 Both the source and the detector have nite widths and so some par ticles will travel slightly different path lengths to the detector Discuss this contribution to the observed energy resolution 12 From the count rate and by estimating the source and detector dimen sions without opening the chamber7 estimate the source strength in microcuries MCi 13 Use the range energy data sheet in Fig 8 to check that the solid state detector has a depletion depth greater than the range of 55 MeV alphas References 1 RD Evans7 The Atomic Nucleus77 McGrawiHill7 1955 2 AC Melissinos7 Experiments in Modern Physics 7 Academic Press7 1966 2nd Ed 2003 21 Selected Physical Properties of Silicon TABLE 1 Selected Physical Properties of Silicon Atomic Density 50 x 10 atomscm393 Density 233 gmcm39 Dielectric Coefficient 12 Energy Gap 11 eV Energy per ElectronHole Pair 36 eVpair Mobility Electron 1350 cm2 volt sec 1 21x 109 Tquot5 cm2 volt l sec Hole 480 cm2 volt39l sec391 23 x 109 T392397 cm2 volt l secquot Thermal Expansion linear coefficient 42 x 108 PCquot Unless otherwise indicated above quantities correspond to 25 C Figure 6 Silicon Properties 11 012 I I 1 010 008 004 002 Range straggling parameter one 0 O 01 I l O I I i l 0 2 4 6 8 10 R mean range aircm 15 C 760 mm Hg Fig 53 Rangestraggling parameter am for natural x rays in air L25 Figure 7 Alpha Particle Straggling Parameter in Air 12 PARTICLE ENERGY IN MIV 6 a e um tnken rum BI Williamsnn LP Bnujnl Ill MI cn nram July I956 Iu RANGE IN MICRONS OF SILICON Figuve 6A RangeEnergy Curves for Chargad Panicles in Silicon Figure 8 Alpha Range Energy in Silicon 13


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