Radiation and Radioactivity 1
Radiation and Radioactivity This experiment has four parts: 1. Counting Statistics 2. Gamma (g) Ray Absorption Half-length and shielding 3. 137 Ba Decay Half-life 4. Dosimetry In the Optical Spectroscopy lab we learned that an atom consists of light electrons orbiting a dense, heavy nucleus made of protons and neutrons. In this lab we will concentrate on the nucleus itself. N P P N N N P 2
P Proton positive charge, mass = 938.3 MeV/c 2 N Neutron no charge, mass = 939.6 MeV/c 2 e Electron negative charge, mass =.511 MeV/c 2 E mc E 2 MeV m c 2 c 2 A Z X X Chemical symbol Z Atomic number protons A Mass number protons neutrons Number of neutrons AZ Example: Cobalt 6 27 protons 27Co 33 neutrons Isotope Nuclei with the same number of protons (Z) but different numbers of neutrons (A). 58 27 Co 59 27 Co 6 27 Co 61 27 Co 62 27 Co 3
Three Basic Types of Nuclear Decay Alpha (a) decay Nucleus emits alpha particle (Helium-4), maximally ionizing, light shielding. Pu U He 87.7 years 238 234 4 94 92 2 Beta (b ± ) decay Nucleus emits beta particle (electron or positron), medium shielding. 214 214 Pb Bi e 26.8 minutes 82 83 e Gamma (g) decay Nucleon within the nucleus drops to a lower energy level and emits a gamma particle (electron or positron), heavy shielding. Ba Ba g 2.55 minutes 137 * 137 56 56 Gamma decay often occurs after alpha or beta decay because the daughter nucleus is left in an excited state. 3.7 years 5.271 years Cs Ba e 137 137 * - 6 6 * - 55 56 e 27 28 e 137 6 56 Ba g 2.55 minutes Co Ni e Ni g 28 1.467 minutes 4
Counting Statistics Many radiation experiments are counting experiments in which a detector simply counts the number of particles that pass through it during a fixed interval of time. Detector N = 25 67 89 1 3 4 t 1. 3. 4. 4.5 5..5 2.5 3.5 1.5 2.. s Rate: N 1 R 2. Hz t 5. s Because the particles are emitted at random, the number of particles that pass through the detector in a time interval t will vary from one interval to the next. t 5. s Trial 1: N = 14 Trial 2: N = 11 Trial 3: N = 9 Trial 4: N = 9 Trial 5: N = 7 Trial 6: N = 12 Trial 7: N = 8 Trial 8: N = 1 Trial 9: N = 9 Trial 1: N = 6 Trial 11: N = 1 Trial 12: N = 11 Trial 13: N = 15 Trial 14: N = 12 Trial 15: N = 5 Trial 16: N = 16 Trial 17: N = 13 Trial 18: N = 8 Trial 19: N = 1 Trial 2: N = 11 Trial 21: N = 4 Navg 1 N 1 3.2 5
A radioactive source produces particles at random so if a detector is functioning correctly the distribution of counts will be Gaussian (Bell curve) with a standard deviation of N Mean = 316 = 17.9 N 316 17.78 If the standard deviation is not N then the detector is not functioning correctly. N N 1 N Fractional Uncertainty: N N N N Note that the fractional uncertainty gets smaller as N gets larger. 6
Background Radiation Background radiation is low level radiation that comes mostly from natural sources: Cosmic Rays Radon Gas Radioactive Isotopes (in building materials) Man made sources R R R RT Total rate R Rate from radioactive source R Rate of background radiation The total rate measured by a detector will be: T B B So to get the rate from a radioactive source it is necessary to also measure the background rate and subtract it from the total rate. R R R Note: The background rate is typically low so you will have to take data for a long period of time. That way N will be large and the fractional uncertainty will be small. T B 7
Gamma-Ray Absorption (Shielding and Half-Length) Slab of material with thickness x R Gamma-Ray Beam dr dx R x dr dx RR Linear Differential Equation = Linear Absorption Coefficient material dependent Solution: R R e x 8
Example: A gamma-ray beam with an initial rate of R = 1 Hz passes through x = 2. mm slab of copper. What is the rate on the other side of the copper? Copper: =.455/mm R R e x x 12 R R ln 2 1 Hz e 46.455 2. mm mm 1 Hz. 46 Hz The thickness of a material that reduces the rate by one-half is called the halflength. 1 R R Re x 2 12 2 e x ln 2 x 12 12 ln 2 x 12 9
What happens if: 12 R R nx x nx n 1,2,3, ln 2 exp 1 2 x12 R R exp n ln ln2n 2 R R 2 n ln 2 R R exp n How many half lengths of lead are required to decrease the rate of a radioactive source by a factor of 16? a) 16 b) 4 c) 3 d) 8 R R R It is relatively easy to use half-lengths to n 4 2 16 4 2 16 calculate the amount of shielding required to reduce the rate from a radioactive source by a given amount. 1
R R e x Take the natural logarithm of both sides: ln R ln R x Slope:.2849 ln 2 x12 ln 2 x12 24.3 mm.2849 Intercept: ln R b R e R 5.334 e 27 Hz Make a plot of ln R versus x: 11
Metal Tube Axial Wire The Geiger Mueller Tube Charged Particle Gas Charge Avalanche HV An axial wire passes through a gas filled metal tube. There is a high voltage between the wire and the tube. When a charged particle passes through the tube it knocks electrons from the gas molecules and these are accelerated in the electric field between the tube and the wire. The accelerated electrons knock out even more electrons and so produce an avalanche of charge on the wire. 12
Basic Procedure 1) Measure the background with the Geiger Mueller detector. 2) Measure rate versus material thickness. 3) Fit ln R versus x to a straight line and use the slope to find. 4) Repeat with a second metal. 13
137 Ba (Barium) Decay (Half-Life) 3.7 years Cs e e Ba g 56 137 137 * - 55 56Ba 137 153 seconds The 137 Cs (Cesium) is stored in a device called an isogenerator. An eluting solution is used to chemically extract the 137 Ba decay products (daughters) from the 137 Cs. 14
Nuclear Decay is a random process. The more particles there are in a sample, the more likely you are to see a decay take place in some given time interval dt. dn dt NN = Disintegration constant Solution: N N e t Write this in terms of the rate: R R e t dn R N e R e dt t t The half-life () is the time it takes for the rate to decrease by one half. ln 2 1 R R Re 2 2 e ln 2 ln 2 15
n n 1,2,3, R R exp ln 2 n ln 2 R R exp n What happens if: t R R exp n ln ln2n 2 R The 137 Ba sample has a half-life of 153 s. How radioactive is it after 2 hours? Number of half-lives: 2 hours 72 s n 47 153 s 153 s R 2 n R R R n 47 2 2 1 15 71 47 2 So the 137 Ba rate is down by 15 orders of magnitude, which means it is completely gone by the end of the lab. 16
R R e t Take the natural logarithm of both sides: ln R ln R t Slope:.4545 ln 2 ln 2 152.5 s.4545 Intercept: ln R b R e R 6.72 e 829 Hz Make a plot of ln R versus t: Note that the scatter in the data increases at low rates. 17
Basic Procedure 1) Measure the background with the Geiger-Mueller detector. 2) Measure rate versus time. 3) Fit ln R versus t to a straight line and use the slope to find. Dosimetry Measurement of Dose Not all radiation is created equal. Some forms of radiation are more harmful than others. Usually radiation damages the DNA of a cell causing apoptosis (cell death) or mutations that can lead to cancer. The extent of damage caused by radiation depends on the type and energy of the radiation and on the total absorbed dose. Alpha Rays (a) Maximally ionizing, deposit all of their energy over a very short range in biological tissue causing much damage. Neutrinos () Generally do not stop in biological tissue and so do not cause any damage. 18
Curie (Ci) = 1 1 3.71 Disintegrations per second 3.71 Hz This is the amount of gamma radiation produced by 1 gram of radium. A Curie is just a rate, it only tells us how much radiation there is. It doesn t tell us anything about the potential for that radiation to do harm to biological tissue. Therefore the Curie is not a good unit for dosimetry. 1 Ci of Alpha-rays Deadly 1 Ci of Neutrinos Harmless A good unit for dosimetry should include not only the amount of radiation but its potential for harm. 4 Roentgen (R) = The amount of ionizing radiation that produces 2.581 C kg of ions in 1 cubic centimeter of dry air. Roughly equivalent to the amount of ionization produced by one gram of radium at one yard. The Roentgen is useful for dosimetry, but only for low energy gamma-rays or X- rays. 19
Radiation Absorbed Dose (rad) = The amount of radiation that deposits 1 ergs per gram of tissue. This unit is good for all types of radiation and is approximately equal to the Roentgen for low energy gamma-rays and X-rays. A more common unit used today: Roentgen Equivalent Man (rem) = rad times quality factor (Q) The quality factor depends on the specific type and energy of radiation that is absorbed. rem rad Q Average yearly dose: 2 mrem =.2 rem Recommended maximum yearly dose: 5 mrem = 5 rem Type of Radiation Q Neutrino Gamma-ray 1 X-ray 1 Beta particle 1 Neutron 1 Alpha particle 2 Fatal dose: 25 rem 2
You will estimate your total dose during the course of the lab and then determine if the experiments will kill you or not. You will determine how the dose rate (mr/hr) varies with distance using a Geiger- Mueller detector and a 6 Co gamma-ray source. Since Q 1 for gamma-rays mr hr S D C 2 x x Distance in meters S Activity in Hertz DC D DB DB Background Dose Rate D Dose Rate from Source mrem hr Also for gamma-rays, 1 Curie produces 1 Roentgen = 1 rem, so we can write the combined dose rate D C as: Choosing a constant of proportionality of 1 D S x D 2 B 21
1 Sievert (Sv) 1 Roentgen (R) 5 1 mr 1 Sv mr 1 1 hr 5 Sv hr Basic Procedure 1) Measure the background dose rate with the Geiger-Mueller detector. 2) Measure the dose rate (D) versus distance (x). 3) Fit D versus 1/x 2 to a straight line and use the slope to find S. Compare the intercept to the background dose rate 4) Estimate your total dose over the three hours you worked in the lab. 22
23
D S Average Distance from Source 2 D B Total Dose Total Time in Lab D S Se t S Current source strength S Source strength when it was created t Years since the source was created ln 2 5.271 yr 24