Jazan University College of Science Physics Department. Lab Manual. Nuclear Physics (2) 462 Phys. 8 th Level. Academic Year: 1439/1440

Transcription

1 Jazan University College of Science Physics Department جاهعة جازان كلية العل وم قسن الفيزياء Lab Manual Nuclear Physics (2) 462 Phys 8 th Level Academic Year: 1439/1440 1

2 Contents No. Name of the Experiment Page Plotting a GM Plateau Geiger Tube Efficiency Inverse Square Law Absorption of Gamma Rays Backscattering of Gamma Rays Determining the half-life of Ba-137 Recording and calibrating a γ spectrum Detection Efficiency of a NaI(Ti) Detector Calculation of β/ γ ratio 2

3 Experiment 1 Plotting a GM Plateau Objective: In this experiment, you will determine the plateau and optimal operating voltage of a Geiger-Muller counter. Theory: The ionizing effect of radiation is used in the Geiger-Muller (GM) tube as a means of detecting the radiation. The GM tube is a hollow cylinder filled with helium, argon or neon gases at low pressure. The tube has a thin window made of mica at one end. There is a central electrode inside the GM tube. A voltage supply is connected across the casing of the tube and the central electrode as shown in the following diagram. The plateau is a relation between the count rate and applied voltage. The optimal applied voltage is the applied voltage corresponding to the most stable count rate. 3

4 Equipment 1- ST-360 Counter/timer and power supply 2- GM Tube 3- stand 4- Radioactive Source (e.g., Cs-137, Sr-90, Co-60, Na-22) Procedures 1- Record the source information (name, activity(a o ),half life time t ½, product date) 2- Place the radioactive source in the second shelf from the top and count the gamma photons. 3- Set the high voltage to be 600 V 4- Set the time to be 60 s 5- Press count to Record the count of photons 6- Calculate the count rate = count / time 7- Increase the high voltage by 40 V to be 640 V 8- Repeat steps 3,4 and 5 until the high voltage become 1080 V 9- Represent the relation between high voltage (x-axis) and count rate (y-axis) 10- Determine the stable region of the count rate on the curve, Determine the start point (V 1,R 1 ) of this region and the end point (V 2,R 2 ) 11- Determine the optimal operating voltage V = (V 1 +V 2 )/2 12- Determine the error ΔV =( V - V 1 + V - V 2 ) / Write the optimal operating voltage in the form of V ± ΔV 14- Determine the quality of the plateau Results quality of the plateau= 100 R 2 R 1 R 1 V 2 V Isotope Half life time (t ½ ) Activity Product date =.. =... years =... μci = 4

5 Measuring time = High voltage Count Count / time

6 Experiment 2 Geiger Tube Efficiency Objective The student will determine the efficiency of a Geiger-Muller counter for various types of radiation. Theory A GM tube doesn t count every disintegration produced by the source of the radiation. There are a number of reasons for this, including the following: 1. Many particles do not strike the tube at all, since they are emitted uniformly from the radiation source in all directions and the G-M tube window only covers a small fraction of the space surrounding the source. 2. Even when a particle enters the GM tube it doesn t necessarily interact with the gas that fills the tube or with its walls, it might just pass right through the GM tube. 3. There is a time interval that follows the production of a count in a GM tube during which no other counts can be detected, even though radiation may have entered the tube. This time interval is known as the resolving time. The solid angle covered by the GMT (dω) should also be considered, the following figure will help in understanding the 6

7 geometric relationship between the radiation source and the end window of the GM tube. As an approximation assume the source to be a point source. The distance from the radioactive source to the center of the GM end window is d. The radius of the end window is r. We can then imagine a sphere of radius R surrounding the radioactive source. The top cap of this sphere cuts the GM end window. Assuming that the source radiates uniformly in all directions, it is only the portion of the emitted radiation that goes through the sphere s top cap that will also be incident upon the GM tube window. The area of the top cap (covered by the GM tube window) of the sphere is 2πr 2. The area of the sphere is 4πR 2. Therefore, the fraction (dω) of the emitted radiation that hits the GM end window is given by dω = πr 2 / 4πR 2. = r 2 / 4R 2 In this experiment, you will calculate the efficiency of a GM tube counting system for different isotopes by comparing the measured count rate to the disintegration rate (activity) of the source. Expected Activity A (-λ t) A = A o e λ is decay constant = ln 2 / t ½ = 0.693/ t ½ A o is the activity at the production time (written on the isotope) t ½ is the half life time (written on the isotope) t is the time between the product date and now. note that A in Bq (disintegration per second) 1 Ci = 3.7 x Bq 1 μci = 10-6 Ci 1 μci = 10-6 x 3.7 x = 3.7 x 10 4 Bq t and t ½ in second Measured activity = Count / Time Efficiency = Measured activity / ( Expected activity x dω) 7

8 Equipments 1- ST-360 Counter/timer and power supply 2- GM Tube 3- stand 4- Radioactive Source (e.g., Cs-137, Sr-90, Co-60, Na-22) Procedures 1. Record the source information (name, activity (A o ),half life time t ½, product date) 2. Set the operating voltage to be 900 Volts. 3. Set the time to be 60 s. 4. Record the background without a radioactive source. 5. Place the radioactive source in the second shelf from the top and count the gamma photons. 6. Calculated the measured activity 7. Calculated the expected activity 8

9 8. Calculate the efficiency Results Isotope Half life time (t ½ ) Decay constant ( ) Activity (A o ) Activity (A o ) Product date Day date Time (t) =.. =... years = second = 0.693/ t ½ = S -1 =... μci =.. Bq =. =.. = day date product date..... second Expected activity (A) = A o e (- t) =.. F (Solid angle correction) = r 2 / 4R 2 Background Count (BG) =.. =. Count Net Count = count BG Count rate = net count / time Efficiency = count rate / ( Expected activity x F ) Average E = (E 1 + E 2 + E 3 ) / 3 9

10 ΔE =( E - E 1 + E - E 2 + E - E 3 ) / 3 Efficiency = E ± ΔE 10

11 Experiment 3 Inverse Square Law Objective The student will verify the inverse square relationship between the distance and intensity of radiation. Theory In this experiment, you will verify the inverse square law of the intensity of radiation Where I α 1/ d 2 I = k / d 2 I d k is the intensity of radiation (count/sec) is the distance between the source of radiation and the radiation detector (cm) is called a constant of proportionality This relation means that, if you move to a distance d away from the window of the GM counter, then the intensity of radiation decreases by a factor 1/d 2. 11

12 Equipments 1. ST-360 Counter/timer and power supply 2. GM Tube 3. stand 4. Radioactive Source (e.g., Cs-137, Sr-90, or Co-60, Na-22) 12

13 Procedures 1. Set the operating voltage to be 900 Volts. 2. Set the time to be 60 s. 3. Record the background without a radioactive source. 4. Place the radioactive source in the first shelf and count the gamma photons. In this position, the source is 2 cm from the GM tube s actual. 5. Move the source down one shelf each time and take another run. You should notice that the distance between shelves is 1 cm. 6. Repeat step 5 up to 10 cm. 7. Fill the table date. 8. Represent the relation between the 1/d 2 (x-axis) and the net count rate (y-axis). 9. Calculate the proportional constant (k = slope) 13

14 Results Isotope =.. Half life time = year Activity =... Ci Product date =.. Measuring time (t)=. s Background (bk) =... Distance d (cm) D 2 (cm 2 ) 1/d 2 (cm -2 ) on X axis Count Net count = count - bk Net count rate = net count /t on Y axis k = slope = x / y 14

15 Experiment 4 Absorption of Gamma Rays Objective The student will investigate the attenuation of radiation via the absorption of gamma rays. Theory The attenuation (or absorption and scattering) of gamma rays is exponential in nature which is shown by the equation: I = I o e μ x (1) I=I ο e μ ρ ρx (2) where I is the intensity of the beam after passing through x thickness of absorbing material, I o is the intensity of the beam without any absorbing material, is the linear attenuation coefficient (cm -1 ), is the mass attenuation coefficient (cm 2 /g), x is the thickness (cm), x is the mass thickness (g/cm 2 ). we can rewrite equation 2 as ln I o I = ( μ ρ) ρ x (3) During your data analysis, the value ln I o I will be measured for each x, and thus the mass attenuation coefficient / can be found. 15

16 Equipments 1. ST-360 Counter and power supply 2. GM Tube 3. stand 4. Radioactive Source (e.g., Cs-137, Sr-90, or Co-60, Na-22) 5. Absorber materials set 16

17 Procedures 1. Set the operating voltage to be 900 Volts. 2. Set the time to be 60 s. 3. Record the background without a radioactive source. 4. Place the radioactive source in the second shelf from the top and count the gamma photons without any materials I o. 5. Place an absorber in the top shelf and record its mass thickness then count the gamma photons I. 6- Calculate ln I o /I 7. Repeat step 5 and 6 with different mass thickness of the absorber 8. Represent the relation between mass thickness x (x-axis) and ln I o /I (y-axis). 9. Determine the mass attenuation coefficients, Slope = / 17

18 Results Isotope =. Half life time =.. s Activity =. Ci Product date =.. Measuring time (t)=. s Background (bg) =.. Count without absorber =.. I o = count without absorber bg =.. Mass thickness Count Count-bg (I) I o /I Ln I o /I 18

19 Mass attenuation coefficient ( / ) = slope = 19

20 Experiment 5 Backscattering of Gamma Rays Objective The student will investigate the relation between absorber thickness and backscattering. Equipments 1- ST-360 Counter/timer and power supply 2- GM Tube 3- stand 4- Radioactive Source (e.g., Cs-137, Sr-90, or Co-60, Na-22) 5- Absorber kit 20

21 Procedures 1. Set the operating voltage to be 900 Volts. 2. Set the time to be 60 s. 3. Record the background without a radioactive source. 4. Place the radioactive source in the first shelf from the top and count the gamma photons without any materials I o. 5. Place an absorber in the first shelf and place the source directly on top of it. 6. Record the gamma photons I 7. Calculate the percent of counts from backscattering by using the formula %back = [(I- I o ) / I o ] * Repeat steps 5, 6 and 7 for the same absorber with different thickness. 9. Represent the relation between the thickness (x-axis) and the %backscattering (y-axis) for each absorber. 21

22 Results Radioactive source = Measuring time = Background (bk) = Count without absorber = I o = count without absorber bk = Thickness Count Count-bk (I) % backscattering G =141 I=216 K=328 M=522 O=655 P=840 22

23 Experiment 6 Determining the half-life of Ba-137 Objects of the experiment Elution of the metastable Ba-137 isotopes from a Cs-137 preparation. Measuring the activity of the eluate as a function of time and Determining the half-life of Ba-137. Theory During the decay, the change in the number of atoms dn after interval time dt is where is decay constant N is the num,ber of atoms dn N dt. N t N 0 e - t N t N 0 e - t A t A 0 e - t N0: number of radioactive nuclei at the time t = 0 Where T ½ is the half life T ½ = ln 2 / Apparatus 1- Cs/Ba-137m isotope generator 2- Giger Muller detector 3-1 Sensor CASSY 4-2 CASSY Lab 5- PC 23

24 Procedures 1- Call the CASSY Lab software. 2- Click the display of the GM box, and select the following settings: Measurement quantity: events, Measuring range: 1000, Gate time: 20 s 3- Select in the register Display of the dialog window Settings : x-axis: t, y-axis: events 4- Select the measuring parameters: Automatic Recording, Interval: 100 ms 5- Prepare the Ba-137 sample using the eluting solution 6- Notes that F9 button to start stop counting, F2 to save data, F4 for new measurement and F5 for setting parameters of the measurement. Measuring example and evaluation The following Figure shows the decay curve of Ba-137m. Further evaluation and determination of the half-life t 1/2 : 1. Click the diagram with the right mouse button, select the menu item Fit Function Exponential function e^x, and mark the beginning and the end of the range to be fitted with the mouse. 2. Activate the horizontal line (Alt+H) and place it at a well-defined value of the counting rate with the mouse. 3. Place further horizontal lines at the half, quarter and eighth of the selected value. 4. Activate vertical lines (Alt+V) and place them with the mouse at the intercepts of the fitted curve with the horizontal lines. 5. Activate the difference measurement (Alt+D), and determine the half-life t 1/2 as the difference between two neighbouring vertical lines. 24

25 Results Time Count Time Count Time Count

26 (T 1/2 ) 1 (T 1/2 ) 2 (T 1/2 ) 3 Sum Average 26

27 Experiment 7 Recording and calibrating a spectrum Experiment description The γ spectra of some standard preparations (Cs-137, Co-60, Na-22) are measured. After an energy calibration of the scintillation counter, the γ transitions are identified. Equipment list 1 Sensor CASSY 2 CASSY Lab 3 MCA Box (Multi-Channel Analyzer) 4 Radioactive sources set 5 Scintillation counter (NaI crystal, photomultiplier tube and the base) 6 High-voltage power supply 1.5 kv 7 PC with Windows 27

28 Procedures 1- Connect the power supply to the base of the photomultiplier tube 2- Connect the output signal to the preamplifier and signal in of the MCA box 3- Connect the CASSY Lab to the computer through USB cable, 4- click on the VKA-Box and MCA-Box icons in the LD in the screen. 5- Adjust the high voltage to be 600 volt (0.6 kv) 6- Adjust the measuring time to be 60 s 7- Adjust the number of channels for MCA to be 2048 channel 8- Notes that F9 button to start stop counting, F2 to save data, F4 for new measurement and F5 for setting parameters of the measurement. 9- Record the spectrum for Cs-137 by press F9 10- Calibrate the MCA by assigned the peak of the spectrum to be 661 kev energy. 11- Recording the spectrum of the isotope Na Record the corresponding energy for the peaks of the spectrum 13- Repeat steps 9 and 10 for radioactive isotope Co Write down the peaks energy for each source. Results Co-60 1 st line =.. kev 2 nd line =. kev Na-22 1 st line =.. kev 2 nd line =. kev Unknown 1 st line =.. kev 2 nd line =. kev 28

29 Experiment 8 Detection Efficiency of a NaI(Ti) Detector Objective: In this experiment, students will learn how a NaI(Ti) detector responses to the radiation source (e.g.: Cs-137). Theory: Thallium-doped sodium iodide, NaI(Ti) detector is widely used to study the radiation matter interaction in a few thousand electron volts to several millions electron volts (kev to MeV) energy range. Electromagnetic radiation can interact with matter via photoelectric, Compton and pair production effects. All effects, in principle have a chance to occur based on the incident energy of the radiation. Pair production can occur only if the radiation energy greater than 1.02MeV. In the photoelectric effect all energy of the radiation is converted into light. A typical photopeak for Cs-137 output from the NaI(Ti) detector (SCIONIX HOLLAND) is shown in the figure 1. Figure 1: A typical photopeak distribution for Cs-137 The absolute efficiency (εabs ) of the detector must be known for any radiation detection and measurement. It is defined as the ratio of the number of counts recorded by the detector (Nc) to the number of radiation (Ns) emitted by the source (in all directions). εabs = Nc / Ns.. (1) 29

30 Equipment list 1. Sensor CASSY 2. CASSY Lab 3. MCA (Multi Channel Analyzer) box 4. Radioactive sources 5. NaI(Ti) detector (SCIONIX HOLLAND) 6. High-voltage power supply 1.5 kv 7. PC with CASSY Lab software installed Procedures 1. Repeat the procedure (step1 to step10) of experiment 7 to calibrate the detector. 2. For better output put the high voltage at 630V and amplifier gain at Record the counts for 5 minutes without source for the background count. 30

31 4. Now put the Cs-137 source on the plastic tray and put the tray on the surface of the NaI(Ti) detector directly and record the photopeak count at 662keV for 5 minutes (300s) in order to get the enough statistics. 5. Take the maximum count in the photopeak. Calculations: Ns = N0 exp( λt).. (2) Where, Ns = number of radiation by the source in all direction in Bq (Becquerel = disintegration per second) N0 = source activity at the production time (written on the isotope) λ = decay constant = ln2/t1/2 = 0.693/t1/2 t1/2 = half-life time of the source in seconds (written on the isotope) t = time between the product date and the experiment date in seconds Note: 1 Ci = 3.7 x 1010 Bq [Students can recall the experiment 2 for calculating Ns] Results Phtopeak count (maximum count) Nc = photopeak count background count Ns εabs = Nc / Ns εabs = Nc / Ns (%) 31

32 Experiment 9 Calculation β/ϒ ratio Objective: Determination of β/ϒ ratio Theory: Radioactivity refers to the particles which are emitted from nuclei as a result of nuclear instability. The most common types of radiation are called alpha (α),beta (β), and gamma (γ) radiation, but there are several other varieties of radioactive decay. the alpha particle is the shortest in range because of its strong interaction with matter. The electromagnetic gamma ray is extremely penetrating, even penetrating considerable thicknesses of concrete. The electron of beta radioactivity strongly interacts with matter and has a short range. To determine the β/ϒ ratio we use for example source as 60 Co which decay as follow: Co 60 28Ni* Ni* + β + ϒ 60 28Ni + ϒ Our aim in this experiment is to separate between numbers of counts due to ϒ rays and numbers due to β particles. To make this process we must depend 32

33 on the fact that ϒ rays has higher energy than β particles so that ϒ rays have more penetration than that of β particle in absorption medium such as aluminum. If β particle and ϒ rays are incident together on a foil of aluminum, it will screen β-particles more than ϒ-photons. By increasing the number of foils, then β particles will be completely screened, and the transmitted radiation is pure ϒ- photons. So the number of counts observed belonged to ϒ radiation only. Calculation of β/ϒ theoretically: Let the number of counts due to β and ϒ is R A and number of counts to ϒ only is R B as shown in figure: Then the number of counts due to β only is (R A - R B ) Note that: The source of Co 60 in which every β-particle emission there are 2 photons emission of ϒ. So the factor (2) must be involved Β/ϒ = 2 (R A - R B ) / R B Log of counts R A R B 33

34 Thickness Procedure: 1- Adjust the G.M. at 900 volt, and the time rate at 60 second. 2- Determine the background (without any source). 3- Place the source of radiation in the second shelf. 4- Record 3 counting without foil. 5- Insert one foil with known thickness above the source, and then take 3 counting. 6- Repeat step (5) for different thickness foils. 7- Take the average or suitable counting, and then get the log of it. 8- Draw the relation between the thickness (x) and log of the counting (y). 9- Determine from the figure R A and R B then determine β/ϒ from above equation. Results Radioactive source =. Cobalt-60 Time = 60 s. Background (bk) = Mass thickness x (mg/cm 2 ) Thickness x mm (X-axis) no 0 G (141) 0.52 H (170) 0.63 I (216) Count 1-bk Count 2-bk Count 3-bk average Log (aver) (Y-axis) 34

35 J (258) K (328) L (425) M (522) N (645) O (655) Note: To convert from mass thickness (mg/cm 2 ) to thickness (cm) Mass thickness x = 4.5 mg/cm 2 x = 4.5 x 10-3 g/cm 2 Thickness x = x/ = 4.5 x 10-3 / 2.7 = 4.5 / 2700 = 1.67 x 10-3 cm = 1.67 x 10-2 mm = mm x = x / 270 mm 35