Experiment No. 9. Absorption of alpha particles and electrons
Contents
1. 0 RR d X In backgr d Fig 4 Scattering of a parallel beam of Mass thickness dp ee electrons beta particles in matter Fig 5 Absorption curve of beta particles in semi logarithmic scale values of thickness d When the logarithm of the particle count is plotted on the vertical axis a linear portion of the absorption curve becomes evident see Fig 5 In this range of d values the absorption curve of beta particles can be approximated by an exponential function N d N exp ud 4 16 The parameter u is called the attenuation coefficient From 4 16 it follows that u 1 d where d is thickness of the material corresponding to decrease of the particle flux by a factor of e x 2 718 As it is evident from Fig 5 the factor Nj is slightly less than the initial value No because the decrease of N at the initial part of the absorption curve is more rapid The attenuation coefficient is approximately proportional to the material density and only weakly dependent on the chemical composition of the material and its aggregation state 1 e solid liquid or gas That is why the so called mass attenuation coefficient 11 is frequently used instead of u The mass attenuation coefficient is obtained by dividing u by the material density p My H p 4 17 The value of 4m is approximately constant for all materials When 4m is used instead of u the relation 4 16 should be replaced by N d No xp Lm2. aluminium absorption curve 1 e click the corresponding option button see Fig 18b Measure the count rate corresponding to zero thickness of the absorber 1 e when there is no absorber between the detector and the radioactive source This is done by clicking the button Start the measurement This action causes opening of the dialog window New measurement where absorber thickness must be entered in this case 0 The measurement will be started after clicking the button OK in the latter dialog window The result of that measurement its standard deviation and the corresponding absorber thickness will be recorded in the Origin worksheet Aluminium Note the measurement is automatically stopped when the total number of particles detected during that measurement exceeds 204 then the relative standard deviation of the average count rate becomes less than 1 204 7 PSs Measurement type m m F Max no of background measurements Stop the measurement Current measurement number one Current measurement time 16 amp Average count rate 0 25 17s Absorber thickness Number of detected particles Standard deviation 0 13 1 s Relative standard deviation standard deviation average 00 O e Measurement type O background C ong glass absorption curve 70 amp Start the measurement Current measurement number DOD ran E Durat
3. 1x0 5mm 1 x 0 1 mm 1 7 mm 1 x 1mm 1x0 5mm 1 x 0 2 mm 1 8 mm 1 x I mm 1x0 5mm 1 x0 2mm 1x 0 1 mm 1 9mm 1 x I mm 1x0 5mm 2 x 0 2 mm 2 0 mm 1 x 2 mm 9 In the same manner measure the absorption curve of beta particles in organic glass Before measuring the organic glass absorption curve the measurement type must be changed to org glass absorption curve by clicking the corresponding option button see Fig 18 The measurement procedure is the same as in Steps 7 and 8 but values of thickness are different from those that were entered in the case of aluminium There are 9 plates of organic glass all of identical thickness 0 47 mm Thus the total thickness d of organic glass must be changed from 0 to 4 23 mm in increments of 0 47 mm 10 After ending the measurements save the measurement data Origin menu command File Save Project or File Save Project As and print the measurement data The printed numbers must not be processed 1 e no background subtracted etc All the printed data must be formatted as a single table and presented in a clear manner this table can be created using a variety of programs such as Origin Excel or Word The list of printers in the Print dialog that pops up after selecting the menu command File Print should include the printer that is present in the laboratory Notes The printer that is currently used in the laboratory i
4. investigation of B particle absorption 1 amplifier 2 high voltage source 3 B particle detector Geiger M ller counter 4 absorbers 5 source of p particles 6 pulse counter Note In this experiment devices 1 2 and 3 are in one case Fig 12 Positions of the radioactive source absorbers and detector inside the UMF device 1 aluminum container with the B radioactive source 2 absorbers aluminum and organic glass plates 3 holder of absorbers 4 entrance window of the GM tube 5 detector shielding 6 handle for pulling the shielding Note The container with the B source 1 must touch the holder of absorbers 3 unlike it is shown in this figure 19 Fig 13 The UMF device with closed shielding case Fig 14 The UMF device with open shielding case Fig 15 The entrance window of the GM tube and the absorber holder in front of it a slide holder is used in its place 20 The aluminum container with the Sr source is shown in Fig 16 Although this material is usually called Sr or Sr 90 it is in fact a mixture of two radioactive nuclides strontium Sr 90 and yttrium Y 90 Y 90 is the product of Sr 90 decay Thus if a sample contains Sr 90 it always contains Y 90 too This mixture is in radioactive equilibrium This means that activities of both its components Sr 90 and Y 90 are equal However beta radiation of Y 90 is more penetrating than beta radiati
5. n The problem of estimating the coefficients A and B is formulated as follows The most likely values of A and B are the values that minimize the expression F A B 9 4 B 12 2 k Expression 12 2 is the sum of squared deviations of theoretical values from the measured ones hence the term least squares That sum is also called the sum of squared errors SSE This expression always has a minimum at certain values of A and B However even if the form of the theoretical function y x correctly reflects the true relationship between the measured quantities y and x those optimal values of A and B which correspond to the minimum SSE do not necessarily coincide with the true values of A and B for example because of measurement errors The method of least squares only allows estimation of the most likely values of A and B Everything that was stated above about the method of least squares also applies to the case when the theoretical function is nonlinear Regardless of the form of that function and of the number of unknown coefficients a SSE expression of the type 12 2 must be minimized However when y x is the linear function 12 1 this problem can be solved analytically 1 e and B can be expressed using elementary functions but when y x is nonlinear this problem can only be solved numerically applying an iterative procedure If y x is the linear function 12 1 then the SSE expression 12 2 can
6. no of background measurements 5 B O Bienes eee Current measurement number mm E Duration of the last measurement 1 s Tis Absorber thickness Number of detected particles Average count rate Standard deviation Relative standard deviation standard deviation average Measurement type C aluminium absorption curve f background j org glass absorption curve Max no of background measurements 5 E Start the measurement Current measurement number mm Duration of the last measurement 1 is Tis pa Absorber thickness Number of detected particles Average count rate Standard deviation Relative standard deviation standard deviation average Fig 17 The main window of Beta EN exe a initial view b when connected with Origin create a new project navigate to a needed folder enter the file name in the field File name that name must be different from the names of all other Origin projects existing in that folder and click the button Open Then the program Beta EN exe will create an empty project whose format is optimized for this experiment Attention If the program Origin was already open when the button Open Origin was clicked then the data will be sent to the open Origin project regardless of the file selected in the Open dialog If several Origin projects are open then the d
7. 204 The computer program which communicates with the pulse counter sends the measurement data in real time to another program Origin 6 produced by OriginLab Corporation The program Origin 6 displays the data tables The experiment must be done as follows 1 Switch on the GM detector emitter follower pulse counter and computer The emitter follower has no separate mains switch it is sufficient to plug in the AC adapter of the emitter follower 2 Open the detector shielding see Fig 14 All measurements will be done with open shielding case Attention The entrance window of the GM tube is very thin and it must not be touched at any circumstances 3 Start the program Beta EN exe Its purpose is to receive data from the pulse counter and to send them to the program Origin 6 1 The shortcut to Beta _EN exe is on Windows desktop The initial view of the main window of that program is shown in Fig 17a Note The Lithuanian version of the same program is named Beta exe a shortcut to it is also on the desktop 4 Ifthe program Origin is open close it Click the button Open Origin In the Open dialog create a new Origin project or select an existing project if you wish to add new data to an unfinished set of measurement results In order to b Measurement type C aluminium absorption curve f background j C org glass absorption curve Max
8. Leave the plastic cap over the fragile window of the G M tube to prevent damage Press SELECT until the control lamp SOUND starts blinking and confirm by pressing ENTER With SELECT you can now start or stop the audible indication of pulses the display shows ON or OFF respectively With the G M tube connected you should now be able to hear the pulses caused by background radiation as short beeps If you want to stop this operating mode press ENTER or simply switch off the instrument 15 2 4 Counting pulses Operating mode MANUAL This section describes different methods to count the number of pulses measured in given time periods For effective demonstrations the pulse rate should be higher than the rate from background radiation An increase in the pulse rate can be achieved by measuring the gamma radiation from the radioactive isotope K 40 All natural potassium compounds contain 0 01 K 40 Just insert the G M tube into the supplied flask of potassium chloride Set the operating mode to MANUAL by pressing the SELECT button until the corresponding control lamp is lit In this particular case it is not necessary to confirm your selection by pressing ENTER a Counting without storing results Press the START STOP button to both start the measurement and reset the counter to zero Press the START STOP button again to stop the measurement the total number of pulses received in the time interval will be displayed b Counting and sto
9. be written as follows F A B A Bu y nA BY x 9 y 2ABY x 2A gt y 2B x y 12 3 k k l k k l k k It is known that partial derivatives of a function with respect to all arguments at a minimum point are zero After equating to zero the partial derivatives of the expression 12 3 with respect to A and B we obtain a system of two linear algebraic equations with unknowns A and B Its solution is Lan Zan BL A y 4 12 5 N k N k The B coefficient is called the slope of the straight line and the 4 coefficient is called the intercept The standard deviations or errors of those two coefficients are calculated according to formulas F X AA min enim 12 6 n n 2 D AB im 12 7 n n 2 D where Finin 18 the minimum value of the SSE 12 3 i e the value of SSE when A and B are equal to their optimal values 12 4 and 12 5 x is the average argument value ya 12 8 N k B 12 4 e and D is the variance of the argument values D F 7 4Y R 12 9 M k n k
10. dependence of the stopping power S on particle energy E is known then it is possible to calculate the particle s path x which corresponds to the decrease of particle energy from the initial value Eo to some smaller value Based on the definition of the stopping power that path is equal to the integral Eo p 4 9 S E By replacing S with its expression 4 6 we obtain E 1 dE l g E E 4 10 E DEA zp J zp where g Eo E1 is a universal function of initial and final energies of the particle Thus if we know the path x that the particle travels in a material we can easily calculate the equivalent path xz in a different material which corresponds to the same decrease of particle energy from o to 1 x fly 4 11 Pa P2 where p and p are densities of the two materials and x is the so called mass path the product of the path x and density of the material Y x 4 12 The mass path is the mass of a column of matter with height equal to the true path length x and with unit cross section area in the above example the mass path must be equal in both materials A similar concept to the mass path is the mass thickness d which is defined as the product of thickness d of a layer of a material and its density d pd 4 13 In general if a particle falls normally to a layer of a material and emerges from its other side the path travelled inside that layer is different from the laye
11. of energy loss What are the differences between interaction of heavy charged particles such as alpha particles with matter and interaction of electrons with matter Explain the concept of particle range and its difference from the average penetration depth How is the range determined from the absorption curve Why is it necessary in this experiment to divide the measured absorption curve by the solid angle Explain the method of calculating air thickness which corresponds to the same energy loss of particles as in the mica window of the detector Recommended reading I Krane K S Introductory Nuclear Physics New York John Wiley amp Sons 1988 p 193 198 217 220 Lilley J Nuclear Physics Principles and Applications New York John Wiley amp Sons 2001 p 129 136 Knoll G F Radiation Detection and Measurement 3rd Edition New York John Wiley amp Sons 2000 p 29 48 118 3 The types of ionizing radiation Ionizing radiation is a flux of subatomic particles e g photons electrons positrons protons neutrons nuclei etc that cause ionization of atoms of the medium through which the particles pass Ionization means the removal of electrons from atoms of the medium In order to remove an electron from an atom a certain amount of energy must be transferred to the atom According to the law of conservation of energy this amount of energy is equal to the decrease of kinetic energy of th
12. 1 eV 1 7 eV Visible light Gamma radiation Table 2 Particle energies corresponding to ionizing radiation composed of particles of matter Radiation type Approximate range of particle energies Alpha a particles He nuclei 4 MeV 9 MeV Beta P particles electrons and positrons 10 keV 10 MeV Nuclear fragments and recoil nuclei The mechanism of interaction of particles with matter depends on the nature of the particles especially on their mass and electric charge According to the manner by which particles interact with matter four distinct groups of particles can be defined 1 heavy charged particles such as alpha particles and nuclei 2 light charged particles such as electrons and positrons 3 photons neutral particles with zero rest mass 4 neutrons neutral heavy particles This experiment concerns only the first two mentioned type of particles alpha particles and electrons 4 Interaction of charged particles with matter 4 1 Interaction of heavy charged particles with matter In nuclear physics the term heavy particles is applied to particles with mass that is much larger than electron mass m 9 1 10 kg Examples of heavy particles are the proton charge e mass My 1 67 10 kg and various nuclei for example He nucleus which is composed of two protons and two neutrons When radiation is composed of charged particles the main quantity characterizing interacti
13. Emas is given in MeV and Rm is obtained in g cm This relationship is valid when 0 lt Emax lt 3 MeV In practice the range of beta particles is measured by extending extrapolating the exponential region of the absorption curve until the intersection with the so called background level 1 e with the horizontal line indicating the counting rate when the investigated beta source is removed see Fig 5 The range measured by this method is called the extrapolated range in Fig 5 it is denoted by Re As evident from Fig 5 the extrapolated range is less than the true range R The relative measurement error is of the order of a few percent a typical value is 5 11 5 Experimental setup for investigation of absorption of alpha particles The experimental equipment that is used for investigation of absorption of alpha particles consists of 1 An open 24l Am a radioactive source activity 3 7 kBq 2 Geiger Muller GM counter entrance window diameter D 9 mm window mass thickness dm 1 8 0 2 mg cm detector s dead time 0 001 s 1 7 10 min 3 Isotrak ratemeter The equipment is shown in Fig 6 nl ye ee ae dee eR EE e ame A A AN TA ee A A OE NS SS ie Fig 6 The experimental equipment The open Am source is shown in Fig 7 The radioactive material is at one end of the source package That end is marked by a groove around the perimeter of the package The open Am source is s
14. GM detector The output resistance of the emitter follower is much less than its input resistance which in turn is greater than the output reistance of the GM detector In addition the emitter follower does not decrease the pulse height Those properties make the emitter follower useful for coupling high output resistance devices such as GM detectors with low input resistance devices such as the pulse counter used in this experiment If the GM detector were directly connected to the pulse counter no pulses would be counted because output resistance of the GM detector is much larger than input resistance of the pulse counter so that only a small fraction of the output voltage would be transferred to the pulse counter and the decreased height of this pulse would be insufficient to register it os 5 k z ee e 3 g Ena a a 7 x 7 G MA 7 E AN a Fig 9 A general view of the equipment for measuring absorption of beta particles The detector device UMF is on the floor beside the table An aluminum container with the radioactive material is placed in front of the detector A box with aluminum and organic glass absorbers is visible on the table as well as a monitor showing the main window of the control program and worksheets of the data analysis program Origin with measurement data 18 Fig 10 The emitter follower on the left and the pulse counter on the right Fig 11 Block diagram of the equipment for
15. Vilnius University Faculty of Physics Department of Solid State Electronics Laboratory of Atomic and Nuclear Physics Experiment No 9 ABSORPTION OF ALPHA PARTICLES AND ELECTRONS by Andrius Poskus e mail andrius poskus ff vu It 2015 09 13 Contents The aim of the experiment 1 Tasks 2 Control questions 3 The types of ionizing radiation 4 Interaction of charged particles with matter 4 1 Interaction of heavy charged particles with matter 4 2 Interaction of electrons with matter 4 3 Mass stopping power 4 4 Estimation of particle path in a material from initial and final energies Particle range 5 Experimental setup for investigation of absorption of alpha particles 6 Measurement procedure for investigation of absorption of alpha particles 7 Ratemeter for investigation of alpha particle absorption User s manual 8 Experimental setup for investigation of absorption of beta particles 9 Measurement procedure for investigation of absorption of beta particles 10 Analysis of alpha particle absorption data 11 Analysis of beta particle absorption data 12 Linear fitting NY A Wn A R 11 12 13 17 21 25 26 Zi The aim of the experiment Measure dependence of alpha and beta radiation intensity on distance traveled by the particles in various materials Determine the range of the particles in those materials Using an empirical range energy relationship determine the energy of alpha part
16. alpha particles and its uncertainty using Eq 4 23 Compare the calculated energy with the true energy of alpha particles emitted by Am 5 48 MeV 26 11 Analysis of beta particle absorption data Adjust results of all measurements taking into account the so called dead time of the detector i e of the GM counter tube This is the time that must pass after each detected particle for the detector to be able to detect the next particle All particles that hit the detector during that interval of time are not detected hence the number of detected particles is always smaller than the actual number of particles that entered the active volume of the detector If the measured count rate N then the corrected count rate 1s N Ny l N T where 71s the dead time The dead time is given in Section 8 This correction is only necessary when the value of the expression N T is greater than 0 01 11 1 Plot the dependences of natural logarithm of count rates on the absorber thickness d those dependences are called absorption curves In another graph plot dependences of the same natural logarithms on the mass thickness pd where p is the material density The curves corresponding to aluminium and organic glass must be plotted in the same graph in order to facilitate their comparison with each other Thus there must be two graphs containing two curves each 1 the graph with functions In M d for aluminum and organic gla
17. ata will be sent to the project that was opened first If the program Beta EN exe successfully establishes connection with Origin then the button Open Origin becomes disabled and the button Start the measurement becomes enabled see Fig 17b Then start measuring background 1 e click the option button background it belongs to the group of three buttons Measurement type and then click the button Start the measurement Then the window of the program Beta _EN exe becomes as shown in Fig 18a and it starts transferring the data to the Origin worksheet Background that worksheet contains particle counts during 1 minute long measurements During the measurement the bottom five text boxes display the sequence number of the current measurement the current number of detected particles the average count rate and its standard deviation see Fig 18a After doing 5 measurements the data transfer will be stopped automatically Place the Sr Y B radioactive source in front of the GM tube entrance window The position of the source container must be as shown in Fig 19 here the source container 1s photographed from the side that is directed towards the GM tube In such position the source container is horizontal and the beam of B particles is incident on the center of the entrance window In the main window of the program Beta _EN exe change the measurement type to
18. cle s trajectory and is always smaller than the range Since interaction with atoms of the material is of random nature different particles will be deflected differently so that their penetration depths will be different even if those particles are identical and have equal initial energies However their ranges in the material will be very similar practically equal to each other The difference between range and penetration depth is especially pronounced in the case of electrons because of their erratic paths see Fig 4 In contrast the range of heavy charged particles is practically equal to their penetration depth 1f the beam of particles is normal to the surface of the material because heavy charged particles move in straight lines N The mentioned difference between the shapes of trajectories of heavy charged particles and N electrons becomes especially evident from comparison of their absorption curves dependences of particle count rate on thickness of the material see Fig 3 and Fig 5 In Fig 3 we see N 2 that the initial part of the absorption curve of heavy charged particles is horizontal This is because heavy charged particles that initially moved towards the detector will be still moving towards it after passing a layer of a material whose thickness is less than the particle range Assuming that the detector is Fig 3 A typical dependence of a particle count rate ideal i e it detects any particle that reaches it o
19. dow see Fig 20 This solid angle is calculated as follows X Q 27 10 2 Jx D 2 where x is the distance between the detector s S entrance window and the radioactive material and D is the diameter of the entrance window The ratio N is the so called angular RAT density of alpha particles The reason of this o transformation of the data is that the source Source ne emits alpha particles in all directions equally An increase of the distance x causes a decrease of Qand a proportional decrease of the number Fig 20 A point radioactive source and a detector The solid of particles that move towards the detector angle is defined as the ratio of the area of the spherical This decrease is of purely geometrical nature segment cut out by the detector window the center of the and is not related to particle absorption Since sphere coinciding with the source and the squared radius of the aim of this experiment is investigation of that sphere the radius is equal to the distance from the source particle absorption in air the mentioned t the edge of the detector At large enough distances x the geometrical dependence must be eliminated mentioned area 1S practically equal to the detector window This is done by replacing the particle counts N area which IS denoted S in this figure not to be confused with by their angular density N Q stopping power which is also denoted Detector 4 Draw the graph s
20. e its direction of motion when it interacts with an atom i e the trajectories of heavy charged particles in matter are almost straight Note The change of the direction of particle motion is called scattering The quantum mechanical calculation of the mentioned interaction gives the following expression of the stopping power due to ionization energy losses incident particle e is the electron charge 2 4 P 2 i ee 4 1 4ntE MU IA p where v is the particle velocity z is its charge in terms of elementary charge e elementary charge e is the absolute value of electron charge n is the electron concentration in the material me is electron mass amp is the electric constant amp 8 854 10 F m is the ratio of particle velocity and velocity of light c i e B v c and the parameter J is the mean excitation energy of the atomic electrons i e the mean value of energies needed to cause all possible types of excitation and ionization of the atom This formula is applicable when v exceeds 10 m s this corresponds to alpha particle energy of 2 MeV The strong dependence of the stopping power 4 1 on particle velocity v its charge z and electron concentration n can be explained as follows The decrease of particle energy during one interaction is directly proportional to the square of the momentum transferred to the atomic electron this follows from the general expression of kinetic energy via the mom
21. e particle that causes ionization Therefore ionization becomes possible only when the energy of incident particles or of the secondary particles that may appear as a result of interactions of incident particles with matter exceeds a certain threshold value the ionization energy of the atom The ionization energy is usually of the order of 10 eV 1 eV 1 6022 10 J Ionizing radiation may be of various nature The directly ionizing radiation is composed of high energy charged particles which ionize atoms of the material due to Coulomb interaction with their electrons Such particles are e g high energy electrons and positrons beta radiation high energy He nuclei alpha radiation various other nuclei Indirectly ionizing radiation is composed of neutral particles which do not directly ionize atoms or do that very infrequently but due to interactions of those particles with matter high energy free charged particles are occasionally emitted The latter particles directly ionize atoms of the medium Examples of indirectly ionizing radiation are high energy photons ultraviolet X ray and gamma radiation and neutrons of any energy Particle energies of various types of ionizing radiation are given in the two tables below Table 1 The scale of wavelengths of electromagnetic radiation Seanco Approximate wavelength Approximate range of range photon energies 100000 km 1 mm 1 1074 eV 0 001 eV Infrared rays 1 mm 0 75 um 0 00
22. ely 100 the number of chemical elements we can conclude that the radiation losses are negligible if kinetic energy of the electrons is of the order of a few MeV or less and then it can be assumed that electrons lose energy only due to ionization energy losses 4 3 Mass stopping power From the expressions of the stopping power for heavy charged particles 4 1 and electrons 4 2 it follows that the main parameter of the material that determines the magnitude of ionization energy losses of charged particles is electron concentration in the material If the material is composed of atoms of one chemical element then n Zn 4 4 where Z is the atomic number of the element 1 e the number of electrons in one atom and n the atom concentration in the material The atom concentration in cm is equal to oN A where p is density of the material in g cm N 6 022 10 mol is the Avogadro number and A is the atomic mass of the material in g mol Therefore electron concentration in cm is equal to n 4P 4 5 The ratio Z A varies from 0 5 for light atoms excluding hydrogen whose Z A 1 to 0 4 for heavy atoms Thus ionization energy losses are directly proportional to density of the material p and the coefficient of proportionality is approximately the same in all materials Summarizing everything that has been said above about ionization energy losses we can conclude that the ionization stopping p
23. ents The set of aluminum absorbers consists of one foil with thickness 0 1 mm two foils with thickness 0 2 mm and three plates with thickness 0 5 mm 1 mm and 2 mm The two foils 0 1 mm and 0 2 mm are in slide frames the values of thickness are written on the frames The three plates 0 5 mm 1 mm and 2 mm are not framed and the values of thickness are not written on them but this should not be a problem because there are no plates of other thickness and those three plates can be quite easily distinguished from each other visually by their thickness If several plates or foils are placed into the holder the effect is the same as though there was a single layer whose thickness is equal to the sum of thicknesses of all those plates and foils Using the various combinations of the mentioned foils and plates any thickness from 0 to 2 mm can be chosen with the minimum increment of 0 1 mm Thus the optimal sequence of absorbers is the following 0 0 mm no absorbers 0 1 mm 1 x 0 1 mm 0 2 mm 1 x 0 2 mm 0 3 mm 1 x 0 2mm 1 x 0 1 mm 0 4 mm 2 x 0 2 mm 0 5 mm 1 x 0 5 mm 0 6mm 1 x 0 5mm 1 x 0 1 mm 0 7mm 1 x 0 5mm 1 x 0 2 mm 0 8mm 1 x 0 5mm 1x0 2mm x 0 1 mm 0 9mm 1 x 0 5mm 2 x 0 2 mm 1 0 mm 1 x 1 mm 1 1 mm 1 x 1mm 1 x 0 1 mm 1 2mm 1 x I mm 1 x 0 2 mm 1 3 mm 1 x 1 mm 1x0 2mm x 0 1 mm 1 4 mm 1 x 1mm 2 x 0 2 mm 1 5 mm 1 x 1mm 1 x 0 5 mm 24 1 6 mm 1 x 1mm
24. entum This momentum is proportional to duration of the interaction this follows from the second Newton s law and the latter duration is inversely proportional to v Therefore the mean decrease of particle energy in one interaction and the stopping power is inversely proportional to v The proportionality of the stopping power to z follows from the fact that the mentioned momentum transfer is directly proportional to Coulomb force which is proportional to z according to the Coulomb s law The proportionality of the stopping power to n follows from the fact that the mean number of collisions per unit path is proportional to n 4 2 Interaction of electrons with matter The physical mechanism of ionization energy losses of fast incident electrons as they slow down in matter is similar to that of heavy charged particles I e the incident electron interacts with atomic electrons due to the Coulomb repulsion and either ionizes the atoms or excites them However there are some differences too First since the mass of incident electrons is the same as the mass of atomic electrons even a single collision with an atomic electron can cause a significant change of electron energy and of the direction in which the electron moves again this follows from the mentioned laws of conservation of energy and momentum As a result an incident electron follows a random erratic path as it slows down in matter This is the main difference between int
25. er Count Period Manual c i amp S 60 s Memory F 100s S i gt Continuous C imersham GSA sound G M Voltage Reg G M Voltage Start Stop Reset Select Enter On Off Front panel of isotrak Ratemeter INPUT terminal for the G M tube Display TTL compatible interface Compartment for 9V battery 9V DC terminal for mains adapter G M tube voltage control START STOP button to start stop the counting process RESET button to clear the display only When the RESET and START STOP buttons are pressed simultaneously the memory will also be cleared 9 SELECT button to choose operating modes and options 10 ENTER button to enter and leave operating modes 11 ON OFF button SSSetgre Control lamps The selected operating mode is indicated by a lamp The MEMORY lamp is lit when data have been stored and starts blinking to indicate a memory overflow During the measurement the GATE lamp blinks rapidly to indicate that the counter is operating 14 2 Operating modes of the G M counter This chapter describes how to operate the G M counter and learn its operating modes by carrying out simple experiments The experiments described in sections 2 4 to 2 6 are also suitable for introducing the subject of radioactivity to students 2 1 Start Up The counter can be operated with the supplied 9V battery or with a mains adapter not supplied with the demonstration set Ensure that the G M tube is disco
26. eraction of fast electrons with matter and interaction of heavy charged particles with matter as mentioned previously the path of heavy charged particles in matter is practically straight Besides there are additional quantum effects related to the fact that it is impossible to distinguish between the incident electron and the electron that has been removed from an atom due to ionization these are the so called exchange effects Taking into account all those effects the following expression of the stopping power due to ionization energy losses of fast electrons 1s obtained 4 2 a o R R 2 pe eE E Vie E n Z 1 1 6 4 2 Mm C Ane2 mv 2 27 where F is the kinetic energy of the electrons and the other notations are the same as in formula 4 1 Comparison of the expression of stopping powers of heavy charged particles formula 4 1 and electrons formula 4 2 shows that they differ only by the factor in braces whose dependence on v and I is weak The factor before the braces 1s the same in both expressions bearing in mind that for electrons z 1 Therefore the main conclusions about dependence of the stopping power on velocity v of the incident particle and on electron concentration n in the material are equally applicable both to heavy charged particles and to electrons As in the case of heavy charged particles scattering of incident electrons by atomic nuclei is much less important than
27. hared with the experiment No 11 Fig 8 shows the GM counter tube with its holder That detector has a protective cap see Fig 9 That cap is only used at the start of the measurements for precise determination of the initial distance between the source and the detector and in order to ensure that under no circumstances the source touches the mica window of the detector in the latter case the detector could sustain irreparable damage As it can be seen in Fig 6 the detector and the source can be moved along an optical bench In this way the distance between the detector and the source is changed Although there is a scale for distance measurements at the bottom of the optical bench it is not used in this experiment In order to measure the distance more precisely Fig 7 The open Am 241 source the radioactive material is at the top a micrometer scale is used that scale is near the micrometer screw that can be seen on the right of Fig 6 The entrance window material of the GM counter tube is mica According to the counter tube s data sheet provided by the manufacturer mass thickness of the entrance window is 1 8 0 2 mg cm Taking into account mica density 1 5 2 g cm we can conclude that the window thickness is approximately 0 01 mm 10 um Thus the window material is extremely thin and fragile Therefore it is strictly forbidden to touch it 12 Geiger Miuller Radioactive material coun
28. howing the dependence of the angular density N on the distance If the measurements were successful its general shape should be as shown in Fig 3 plus random fluctuations related to statistical nature of radioactive decay 5 Determine the value of x corresponding to the decrease of N Q by half in comparison with the initial value In order to decrease random errors it is recommended to replace the initial value by the average of the first five points If there is no point corresponding to exact decrease by half then use the method of linear interpolation The value of x obtained in this way is the so called effective range Rere of alpha particles It is smaller than the true range of alpha particles in air because alpha particles lose energy not only in air but in the mica window of the detector too In order to obtain the true average range of alpha particles in air calculate the distance in air that must be traveled by the particles in order to lose the same amount of energy as the energy lost in the mica window This is done using the formula 4 14 the density of dry air at normal atmospheric pressure is 0 001293 g cm Then add that distance to the mentioned effective range Ref The result is the true mean range R of alpha particles in air Its error AR is mainly determined by the uncertainty of the mass thickness of the detector window see the description of the experimental setup 6 Calculate the energy of
29. icles emitted by the Am source Compare the obtained results with the known values given in literature or calculated from empirical formulas Compare the observed regularities of alpha and beta particle absorption ee a 1 Tasks Measure the dependence of the counting rate of alpha particles on the distance between the Am americium 241 alpha source and the Geiger Muller counter Measure the dependence of the counting rate of beta particles on thickness of aluminum and organic glass absorbers placed between the Sr Y strontium 90 yttrium 90 source and the Geiger Miiller counter Plot the dependence of the angular density of a particle flux on the distance Plot the absorption curves of beta particles Determine the mean range in air of a particles emitted by Am taking into account the energy loss in the mica window of the counter Using the empirical range energy relation calculate the energy of the a particles Determine the absorption coefficients and ranges of B particles in aluminum and organic glass Compare the obtained values of the range with the value predicted by the empirical formula Discuss the observed peculiarities of absorption of a and B particles in matter 2 Control questions What are the types of ionizing radiation What it the origin of energy losses of charged particles in matter Explain the concept of the stopping power of the medium What are the main parameters determining the rate
30. ients Um u p and their errors Aum Au p aluminum density p 2 70 g cm organic glass density p 1 33 g cm Extend the absorption curve until the intersection with the background level see Fig 5 Calculate the extrapolated range Re _ In No InN a where M is the average background count rate and M is the approximate initial count rate of B particles the difference between the approximate initial count rate N p and the true initial count rate No is illustrated in Fig 5 R e 11 2 Calculate the mass range pR and its error Compare the obtained value with the value predicted by the empirical formula 4 24 In this formula Emax must be replaced by the maximum energy of beta particles emitted by Y 2 280 MeV 2J 12 Linear fitting The aim of linear fitting is determination of the least squares estimates of the coefficients A and B of the linear equation y At B x 12 1 The essence of the method of least squares is the following Let us assume that a data set consists of the argument values x1 X2 X 1 Xn and corresponding values of the function y x A typical example is a set of measurement data In such a case n is the number of measurements The measured function values will be denoted y1 y2 Yn The theoretical value of y at a given argument value x is a function of the unknown coefficients A and B see 12 1 hence we can write y x y x A B k 1 2
31. ion of the last measurement E amp Eu Average count rate 0 28 is Masimum relatie error Absorber thickness Number of detected particles Standard deviation OO 1s Relative standard deviation n standard deviation average e4 4 b Fig 18 The main window of Beta EN exe a when measuring background b before starting measurement of the aluminium absorption curve 23 Fig 19 Position of the beta radioactive source during the measurements here the source container is photographed from the side that is directed towards the GM tube Continue measuring absorption curve of beta particles in aluminium by placing aluminium foils and plates between the source and the detector entrance window Each measurement is started by clicking the button Start the measurement entering absorber thickness and then clicking the button OK The aluminum foils or plates must be put into the slide holder see Fig 19 as close as possible to the source i e as far as possible from the detector entrance window When replacing the absorbers the source container must not be touched so that its position does not change It is also not recommended to keep one s fingers in the path of beta particles which exit the small hole in the container of the radioactive source At this stage the total thickness of the aluminum layer between the source and the detector must be increased from 0 to 2 mm in 0 1 mm increm
32. lpha radiation Am emits gamma radiation and internal conversion electrons beta particles Therefore this background depends on the distance between the source and the detector In addition there is a small constant term caused by natural radioactivity of the environment The measurement results must be written down in the form of a table with three columns the distance the particle count with uncovered entrance window and the particle count when the entrance window is covered with paper After finishing all measurements that table must be shown to the laboratory supervisor for signing 13 7 Ratemeter for investigation of alpha particle absorption User s manual Below are four pages scanned from an Isotrak booklet that is included with the measurement equipment used for investigation of alpha particle absorption The Geiger Muller counter consists of a detector the Geiger Miller tube and a ratemeter The ratemeter has a built in adjustable power supply for the detector an LCD display for showing the counts and buttons for selection of various counting modes Note This is supplementary information The description of experimental setup for measuring absorption of alpha particles is in Sections 5 6 1 Front panel of G M counter Caution Before connecting the tube to the G M counter make sure that the tube voltage has been set correctly see also section 2 2 Input isotrak Ld E Ratemet
33. n thickness d of a material R and Rmax are the regardless of the particle s energy we can conclude average and maximum ranges respectively that presence of a material between the particle source and the detector has no effect on the detection probability of the particle the material only slows down the particles but does not affect their direction of motion This situation is changed when thickness of the material approaches the particle range Then some particles lose all their energy and do not reach the detector so the count rate drops abruptly The shape of electron absorption curve is quite different see Fig 5 The number of electrons that reach the detector starts to decrease immediately when the layer thickness d is increased This is because an increase of d causes an increase of probability that an electron will miss the detector due to its scattering in the layer The absorption curves of beta particles emitted during beta decay of radioactive nuclei are approximately exponential see Fig 5 B particles emitted during beta decay have a continuous distribution of energies all energies from zero to the maximum energy which is approximately equal to the total decay energy are possible The rapid initial decrease of the absorption curve see Fig 5 is caused by the fact that electrons and positrons with lower energies are less penetrating than the ones with higher energy hence they are completely absorbed at smaller InN
34. ng The instrument can now be either set to count for one time period or set to run automatically 16 a One time period Press SELECT and then START STOP to start data collection the instrument will count the number of pulses registered in the chosen count time Press RESET to store the result in the memory b Automatic counting Operating mode CONTINUOUS In this mode the instrument will store the results from repeated consecutive measurements Press the ENTER button to activate this mode The control lamp CONTINUOUS will stop blinking Press the START STOP button to commence counting The instrument will make repeated measurements each for the selected time period To stop the sequence press the START STOP button again At the end of each count period the display pauses for about 5 seconds to show the number of pulses received so that the result can be written down if needed There is no delay between the counting periods but pulses registered during the first 5 seconds of a count period are not shown the display is instead used to show the result from the previous period There is an easier method to record the results rather than writing them down between measurements the results are also automatically stored in the memory Up to 50 points can be stored if the memory has been cleared by pressing START STOP and RESET simultaneously before starting the measurements The results cari then be retrieved following the method gi
35. nnected from the counter Install the battery in the battery compartment or connect the adapter to the 9V DC terminal Switch the instrument on by pressing ON OFF 2 2 Setting the working voltage for the G M tube Operating mode G M VOLTAGE It is essential that the correct voltage is applied to the G M tube If the voltage is too low the counter will not function correctly if the voltage is too high the tube could be destroyed The recommended working voltage for the tube delivered with the demonstration set is 500V For other tube types please refer to the relevant data sheet With the SELECT button you can choose between the different operating modes of the counter To set the operating mode G M VOLTAGE press the SELECT button until the corresponding control lamp starts to blink The MEMORY lamp may start to blink this can be ignored Now press ENTER to activate the currently selected operating mode When the G M VOLTAGE control lamp is lit the tube voltage is indicated in the display The only thing you have to do now is to set the voltage to the recommended voltage for your G M tube by turning the REG G M VOLTAGE control A small difference a few volts between the set voltage and the recommended voltage doesn t matter If you want to leave the operating mode press ENTER or simply switch off the instrument 2 3 Audible indication of pulses Operating mode SOUND Connect the lead from the G M tube to the INPUT terminal
36. on of Sr 90 because Y 90 emits electrons with higher energy than Sr 90 Fig 16 Aluminum container with the beta radioactive source Sr 90 inside Radiation is emitted through the small hole at the top that hole has no special cover and is uncovered at all times 21 9 Measurement procedure for investigation of absorption of beta particles Three datasets must be measured when investigating absorption of beta particles 1 background radiation 2 counting rate with aluminum absorber 3 counting rate with organic glass absorber Background is measured for approximately 5 min in total five 1 minute long measurements in absence of either the radioactive source or the absorbers When measuring absorption curves a needed thickness of the absorber aluminum or glass is obtained by placing absorber plates or foils in the case of aluminum next to each other the first measurement corresponds to zero thickness 1 e to absence of the absorber At each thickness of the absorber duration of the measurement is chosen so as to ensure that the relative standard deviation of the average counting rate does not exceed 7 Since the number of detected particles is distributed according to the Poisson distribution the mentioned relative standard deviation is equal to IIN where N is the total number of detected particles Thus in order to keep the relative standard deviation below 7 the number of particles N should be greater than
37. on of radiation with matter is the average decrease of particle kinetic energy per unit path length This quantity is called the stopping power of the medium and is denoted S An alternative notation is dE dx or dE dx such notation reflects the mathematical meaning of the stopping power it is opposite to the derivative of particle energy E relative to the traveled path x The main mechanism of the energy loss of heavy charged particles and electrons with energies of the order of a few MeV or less is ionization or excitation of the atoms of matter excitation is the process when internal energy of the atom increases but it does not lose any electrons All such energy losses are collectively called ionization energy losses this term is applied to energy losses due to excitation too Atoms that are excited or ionized due to interaction with a fast charged particle lie close to the trajectory of the incident particle at a distance of a few nanometers from it The nature of the interaction that causes ionization or excitation of atoms is the so called Coulomb force which acts between the incident particles and electrons of the matter When F an incident charged particle passes by an atom it continuously interacts with the electrons of the atom For example if the incident particle has a positive electric charge it continuously pulls the electrons whose charge is negative toward itself see Fig 1 If the pulling force is sufficiently
38. or 0 01 0 1 1 0 10 MeV example electron and proton are equal E However stopping powers of electrons and Fig 2 Dependences of electron mass stopping power in air protons with equal energies are very aluminum and lead on electron kinetic energy The solid lines different This is because velocity of a correspond to atomic ionization and excitation and dashed lines particle with a given energy is strongly are for radiation from 1 dependent on the particle mass For example velocity v and kinetic energy F of a non relativistic particle are related as follows 2E 2 V 4 7 M ee where M is the particle mass After replacing v in Eq 4 1 with the expression 4 7 and taking into account that for non relativistic particles lt lt 1 we obtain o l ze nM In Am E Sneg mE IM We see that ionization energy losses of non relativistic particles are directly proportional to the mass of the particle Therefore ionization stopping power of heavy charged particles e g protons is much larger than ionization stopping power of electrons with the same energy For example the stopping power for 0 5 MeV protons is about 2000 times larger than the stopping power for 0 5 MeV electrons Hence a heavy charged particle is able to travel a much smaller distance in a material than an electron with the same energy 4 8 4 4 Estimation of particle path in a material from initial and final energies Particle range If the
39. ower given by formulas 4 1 and 4 2 depends on two characteristics of the incident particle its velocity v and charge z and on two parameters of the material its density p and the average atomic excitation energy J all other quantities in those formulas are principal physical constants In addition the quantities z and p enter the expression of the stopping power as a multiplicative factor z p velocity v is uniquely determined by particle kinetic energy E and dependence on Z is logarithmic i e weak Thus Sxz p f E 4 6 where f depends only on particle energy dE dx p The quantity dE pdx S p is a i MeV g cm called mass stopping power From 4 6 it 10 follows that mass stopping power due to ionization energy losses is relatively weakly affected by chemical composition of the material e g see Fig 2 Therefore if energy is lost mainly due to atomic ionization and excitation then the total path 1 0 of a given particle with a given initial energy i e the length of the path where the particle loses all its kinetic energy range is mainly determined by density of the material and is inversely proportional to the latter 0 1 The expressions of stopping power 4 1 4 2 and 4 6 do not include the mass of the incident particle This means that ionization stopping powers of different particles with equal velocity and equal 4 9 absolute values of electric charge z f
40. pd No EXP Hmdm 4 18 where dm 1s the mass thickness the product of the material thickness d and density p The attenuation coefficient decreases with increasing energy of beta particles Due to statistical nature of the energy transfer to an atom ranges of identical particles with equal initial energies are slightly different Therefore when the layer thickness becomes equal to the range the count rate does not immediately drop to zero That drop is gradual see Fig 3 The distance where the count rate becomes equal to half of its maximum value is equal to the average range This is the quantity that is most frequently used in practice Further on we will refer only to the average range therefore the word average will be omitted If ionization energy losses dominate then the particle range can be expressed by formula 4 10 where E 0 E 1 dE l pE 4 19 Z Po f E z where Eo is a universal function of the particle s initial energy Thus if the range R of the particle in material 1 is known than its range R in material 2 can be calculated using a simple relation je 4 20 P2 where p and p are densities of the two materials For this reason the previously defined concept of range is frequently replaced by the concept of mass range Rm which is equal to the product of range and material density R pR 4 21 The mass range of charged particles is approximately the same in all ma
41. r thickness because particle s trajectory inside the layer may not be straight Since the path is the length of the trajectory regardless of its shape the path is in general longer than the thickness However since heavy charged particles travel in straight lines the path of those particles is equal to the layer thickness assuming that the particles fall normally to its surface Therefore in the case of heavy charged particles the path x in the relation 4 11 may be replaced with thickness of the layer of the material d E EN P2 P2 This formula allows calculating thickness d of a material 2 such that the particles passing through that layer lose the same amount of energy as they lose passing through a layer of material 1 with thickness d The particle range is the total path traveled by the particles in the material until the particle stops In other words the range is the total length of the particle s trajectory The range can be expressed via the stopping power of the material That expression is a separate case of a more general relation 4 9 with equal to 0 4 14 dE R E 4 15 where amp is the initial energy of the particle In general the particle s range is not the same as the particle s penetration depth The penetration depth is defined as the largest distance between the surface of the material and the particle as it travels inside the material The penetration depth depends on the shape of the parti
42. ring results The instrument can store the results from up to 50 measurements To do this Press the START STOP and RESET buttons simultaneously to erase any data already stored The MEMORY control lamp will go out Initiate the first counting process by pressing START STOP and stop it by pressing the START STOP button again To store the result press the RESET button Repeat the procedure to store results from further counting periods The MEMORY control lamp is lit if any results are stored The lamp will start to blink if the maximum number of results 50 is exceeded storage overflow 2 5 Reading stored results Operating mode MEMORY Press the SELECT button repeatedly until the MEMORY control lamp starts blinking even if storage overflow has already been indicated The display will show the last value stored Previous data points can be recalled by pressing ENTER The stored data points can therefore be retrieved in reverse order at the end of the list the display shows three dashes lf required the stored data can be called off a second time by repeating these steps 2 6 Counting pulses for predefined periods Operating mode GATE Press the SELECT button until the GATE control lamp starts blinking and press ENTER to confirm the selection Press SELECT again to step through the available count times and press ENTER when the required time is indicated by a control lamp The control lamp marked CONTINUOUS will start blinki
43. s not a network printer instead it is connected to a computer that is connected to LAN If the system can not establish connection with the printer this probably means that the mentioned computer 1s not switched on 11 Switch off the computer and pulse counter Close the detector shielding case After finishing all measurements the table with the measurement results must be presented to the laboratory supervisor for signing 25 10 Analysis of alpha particle absorption data 1 Adjust results of all measurements taking into account the so called dead time of the detector 1 e of the GM counter tube This is the time that must pass after each detected particle for the detector to be able to detect the next particle All particles that hit the detector during that interval of time are not detected hence the number of detected particles is always smaller than the actual number of particles that entered the active volume of the detector If the number of particles that were detected in 1 min is N then the corrected number is N l N T where 71s the dead time in minutes The dead time is given in Section 5 N 10 1 2 Subtract the corrected counts corresponding to the covered detector from the corrected counts corresponding to the uncovered detector In this way the counts N of alpha particles are obtained 3 Divide the obtained numbers N of alpha particles by the solid angle 2 subtended by the detector win
44. scattering by atomic electrons When energy of the incident electron becomes sufficiently high the energy loss due to electromagnetic radiation becomes prominent It is known from classical electrodynamics that accelerated charged particles emit electromagnetic radiation whose intensity is directly proportional to acceleration squared The force that slows down an incident particle in the material arises from internal electric fields of the material their sources are atomic nuclei and atomic electrons The electromagnetic radiation that arises due to the mentioned acceleration or slowing down is called bremsstrahlung German for braking radiation Since acceleration is inversely proportional to the mass of the particle bremsstrahlung is negligible in the case of heavy charged particles but it can become the dominant mechanism of energy loss of electrons when their kinetic energy becomes large enough The ratio of the stopping power due to radiation energy losses Siaa and due to the previously discussed ionization energy losses can be calculated using the following approximate formula aie ee 4 3 S 1600m c where F is the kinetic energy of the incident electron Z is the atomic number of the material and c is velocity of light Bearing in mind that mec 0 5 MeV it follows from 4 3 that radiation energy losses exceed ionization energy losses when electron energy exceeds 800 Z MeV Since the largest possible value of Z is approximat
45. ss 2 the graph with functions In N od for aluminum and organic glass The mass thickness pd must be expressed in units of g cm The background must not be subtracted from the counts because the extrapolated range will be determined by the method illustrated in Fig 5 When pd gt 0 1 g cm those curves should be approximately linear i e the decrease of counting rate with increasing thickness must be approximately exponential By the method of linear fitting determine the attenuation coefficients 4 and their random errors Aw The fitted function should be In Md Linear fitting can be done using various computer programs or it can be done by hand using a calculator see Section 12 Only the points corresponding to pd gt 0 1 g cm must be used for linear fitting in both cases This is because the investigated B source is composed of two radioactive nuclides the isotope of strontium Sr the maximum energy of B particles is 0 546 MeV and the isotope of yttrium Y the maximum energy is 2 280 MeV At small values of thickness both nuclides contribute to the measured counts but at larger values of thickness only the B particles emitted by Y are detected Since the number of points in the initial part of the absorption curve corresponding to pd lt 0 1 g cm is insufficient for quantitative analysis of radiation emitted by Sr those points must not be used Calculate the mass attenuation coeffic
46. strong and if its time variation is sufficiently fast 1 e if the incident particle s velocity is sufficiently large then some of the electrons may by liberated from the atom 1 e the atom may be ionized Alternatively the atom may be excited to higher energy levels without ionization Coulomb interaction of the incident particles with atomic nuclei is also possible but it has a much smaller effect on the x 0 motion of the incident charged particles because the nuclei of the material occupy only about 10 of the volume of their atoms Using the laws of conservation of energy and Fig 1 The classical model of ionization of an atom due to Coulomb interaction of its electrons with an incident heavy charged particle ze is the electric charge of the momentum it can be proved that the largest energy that a non relativistic particle with mass M can transfer to an electron with mass M is equal to 4m E M where E is kinetic energy of the particle Using the same laws it can be shown that the largest possible angle between the direction of particle motion after the interaction and its direction prior to the interaction is equal to Mme M Since M exceeds me by three orders of magnitude see above we can conclude that the decrease of energy of a heavy charged particle due to a single excitation or ionization event is much smaller than the total kinetic energy of the particle and the incident particle practically does not chang
47. ter Pan aae Entrance window Radioactive source Hole of the protective cap housing Protective cap Fig 8 Cross section of the Geiger Miuller counter tube and the alpha radioactive source the distances are given in millimeters The diameter of the entrance window is D 9 mm 6 Measurement procedure for investigation of absorption of alpha particles During the measurements the distance between the source package and the GM counter tube is varied from 0 to 16 mm in increments of 1 mm As we can from Fig 8 the actual distance between the entrance window and the radioactive material is larger by 13 mm 1 e it is varied from 13 mm to 29 mm At each distance two 1 min long counts of alpha particles are measured one with uncovered entrance window and one with the window covered by a paper sheet the instructions on how to use the ratemeter that is connected to the detector of alpha particles are in Section 7 All measurements are done without the plastic protective cap which is shown in Fig 8 The paper practically does not absorb gamma and beta radiation but it completely absorbs alpha particles Thus the measurement results obtained with the covered entrance window correspond to the so called background which will have to be eliminated so that only the investigated alpha radiation remains This is done by calculating the difference of the two counts The mentioned background is mainly caused by the fact that in addition to a
48. terials The fact that particle range in a given material is proportional to a universal function of particle initial energy see Eq 4 19 was important in early years of investigation of radioactivity Having measured the range of a particles in a given material and knowing the function and density p of the material it is possible to calculate approximate energy of the a particle Since now there are detectors whose signal height directly reflects particle energy such indirect methods of energy measurements are no longer applied in practice By comparing 4 1 and 4 6 we can see that in the case of heavy non relativistic particles flE 1 v 1 E Therefore from 4 19 the following proportionality relation follows R E Further on we will omit the subscript 0 in the notation of initial energy In a general case the exponent is different from 2 R E k 0 75 2 4 22 The exponent k depends on the particle nature energy range in question and weaker on the material For example the range of a particles with energy 4 5 lt E lt 8 MeV in air can be calculated from the empirical formula R 3 18 E 4 23 10 where the range R is expressed in mm and the energy E is expressed in MeV In order to determine the maximum energy Emax of beta particles emitted by radioactive nuclei the following empirical relationship between the mass range and the maximum energy Emax can be used RSs Ae 1 4 24 where
49. ven in section 2 5 17 8 Experimental setup for investigation of absorption of beta particles The experimental equipment that is used for investigation of absorption of beta particles consists of 1 Sr Y B radioactive source in an aluminum container 2 Geiger Muller GM tube dead time 0 001 s with a voltage source an amplifier and a lead shielding case 3 emitter follower seen in Fig 10 on the left 4 a pulse counting device with a microcontroller seen in Fig 10 on the right 5 a PC 6 a set of aluminum and organic glass absorbers Organic glass density p 1 33 g cm The general view of the mentioned equipment is shown in Fig 9 The simplified block diagram of this equipment is shown in Fig 11 The GM tube is inside the Russian device UMF Russian for YMQ Ycmpo cmeo manroeo bona meaning low background device Its photographs are shown in Fig 13 Fig 15 The positions of the detector 1 e GM tube radioactive source and absorbers relative to each other inside the UMF device are shown in Fig 12 The only discrepancy between Fig 12 and the recommended configuration is that the container with the source of beta particles 1 must touch the slide holder 3 unlike in Fig 12 The entire device is placed into a metal case which serves to decrease influence of the background radiation to measurement results The purpose of the emitter follower is to decrease the output resistance of the
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