Nuclear Physics • The forces holding together the nucleus are large. And so are the energies involved. • Radioactivity is a natural process. Certain nuclei fall apart and emit ionizing radiation as they do. • Radiation and radioactivity are dangerous but useful. They can cause illness, but they can cure or diagnose as well. Where Are We Headed? • Lecture: Monday, April 6: ! ! Nuclear Physics Basics Wednesday, April 8: ! Nuclear Physics Applications • Friday, April 10: ! ! Duck and Cover: Tales of the Atomic Age • Monday, April 13: !! Applications to Bodies and the Biosphere • Wednesday, April 15: !Exam #2 Review • Friday, April 17: ! ! Exam #2 Exam: • Exam #2 is on Friday, April 17. • Practice Exam posted Monday, April 13. • Practice in recitation on Tuesday, April 14. • Practice in lecture on Wednesday, April 15. • • • This isn’t an x ray; it’s a bone scan. Radioactive nuclei were used to show the presence of arthritis in a woman’s hands. How was this image created? Remember: Particles have a wave nature. Only certain wavelengths meet the boundary conditions, so only certain energies are allowed. The Nucleus Confining neutrons and protons in the “box” of the nucleus means that their allowed energies are enormous. Changing Scale The diameter of a typical atomic nucleus is about 10 fm. (1 fm is 1x10-15 m.) What are the “particle in a box” energy states for a proton in a 1D box of this size? 2 1 ⎡ hn ⎤ h2 2 En = = n 8mL2 2m ⎢⎣ 2L ⎥⎦ n = 1, 2, 3, 4... The Nucleus Number of protons determines the element, number of neutrons the isotope. Most elements have more than one stable isotope. We will never use this number. Never. Notation Mass number: A=Z+N 238 92 U Atomic number: Z Z = # of protons N = # of neutrons 112 50 Sn 114 50 Sn 115 50 Sn 116 50 Sn 117 50 Sn 118 50 Sn 119 50 Sn 120 50 Sn 122 50 Sn 124 50 Sn Mass of an atom: e.g. chlorine 1) Never acceptable: Using atomic weights from the periodic table. 2) Quick and dirty: Use mass number: 35Cl: mass = 35 u 3) For energy calcs: Use data from Appendix D: 35Cl: mass = 34.968853 u 11 3 Li 11 4 Be Oxygen 18 variation from average (%) Notation How many neutrons are in each of the following nuclei? -3.0 11 5 B 11 6 C A. 8 B. 7 C. 6 D. 5 Isotopes More 18 8 O Warmer Less 18 8 O Cooler -3.5 -4.0 -4.5 -5.0 100000 50000 0 Years before present Boron, atomic number Z=5, has two stable isotopes, with atomic mass numbers A=10 and A=11. Boron’s chemical atomic mass is 10.81. What are the approximate fractions of the two stable boron isotopes found in nature? ! A.!! 92% 11B,! 8% 10B ! B.!! 80% 11B, ! 20% 10B ! C.!! 50% 11B, ! 50% 10B ! D.!! 20% 11B, ! 80% 10B ! E.! ! 8% 11B, !! 92% 10B Holding it All Together Helium nucleus neutron Strong force proton An especially stable combo n n n p p p Coulomb force Stability Too big; Coulomb repulsion too strongZ 5 83 Bismuth, Just right. 160 140 Stable isotope Unstable isotope Neutron number N 120 Too many neutrons 100 80 N 5 Z line 60 16 O 40 Line of stability 12 C Too few neutrons 4 He 20 0 0 10 20 30 40 50 60 70 80 Proton number Z Energy Levels in the Nucleus Energy (MeV) 0 Neutrons n53 n52 n51 Protons 2 4 2 4 2 2 n53 n52 n51 250 For light nuclei, neutron and proton energy levels are about the same. 90 100 Beta Decay 11 4 U (MeV) Energy (Mev) Be 0 2 4 2 4 2 2 250 Neutrons Protons Beta Decay 11 5 U (MeV) Energy (Mev) B 0 2 4 2 4 2 2 250 Neutrons Protons 11 4 Be ⇒ 115 B + −10 e- Alpha Decay Parent nucleus Nucleus too darn big. And it does. Wants to break apart. Before: A XZ After: A24 YZ22 Daughter nucleus 238 92 U⇒ 234 90 Alpha particle Th + 24α When atoms decay, they don’t disappear. 238 92 U⇒ 234 90 Th + 24α Gamma Decay Excited level Gamma-ray photon Lower level 99 Mo Beta decay e2 99 Tc * Excited state Ground state Gamma decay g 99 Tc Determining the Daughter Nucleus ! 90Sr → ?X + e- A. B. C. D. 90Y 89Y 90Rb 89Rb ! 222Rn A. B. C. D. → ?X + α 220Po 218Po 220Ra 218Ra Determining the Decay Mode What is the decay mode of the following decays? → 137Ba + ? A.!! alpha decay B.!! beta-minus decay C.!! beta-plus decay D.!! gamma decay 137Cs ! ! ! ! → 226Ra + ? A.!alpha decay B.!beta-minus decay C.!beta-plus decay D.!gamma decay 230Th ! ! ! ! 12B • • is an unstable isotope of boron (Z=5). Sketch the energy level structure for the neutrons and the protons in this nucleus. What decay mode would you expect for this nucleus? Energy (MeV) 0 Neutrons n53 n52 n51 Protons 2 4 2 4 2 2 n53 n52 n51 250 Properties of Radiation alpha least penetrating gamma most penetrating Nuclear Radiation is Ionizing Radiation Operation of Geiger counter Radiation burn from cancer treatment Radiation is Part of Your Life You Light Up My Half Life ⎡1⎤ N = N0 ⎢ ⎥ ⎣2⎦ t t1/2 Chernobyl Cheese The Chernobyl nuclear reactor accident in the Soviet Union in 1986 released a large plume of radioactive isotopes into the atmosphere. Of particular health concern was the short-lived (half life: 8.0 days) isotope 131I, which, when ingested, is concentrated in and damages the thyroid gland. This isotope was deposited on plants that were eaten by cows, which then gave milk with dangerous levels of 131I. This milk couldn’t be used for drinking, but it could be used to make cheese, which can be stored until radiation levels have decreased. How long would a sample of cheese need to be stored until the number of radioactive atoms decreased to 3% of the initial value? ⎡1⎤ N = N0 ⎢ ⎥ ⎣2⎦ t t1/2 Activity is the rate of decay. Decay: ⎡1⎤ N = N0 ⎢ ⎥ ⎣2⎦ t t1/2 Activity: 0.693 t1/2 tt ⎡1⎤ 12 R = R0 ⎢ ⎥ ⎣2⎦ R = rN = Short half life means high activity. activity = decay rate = R = 238Pu, half 0.693N t1/2 life 88 years ray photon with energy 140 keV. What is the mass loss of the nucleus, u, upon decay, emission of thisactivity gamma ray?decreases. As the in atoms the 27. || Cobalt has one stable isotope, 59Co. What are the likely decay modes and daughter nuclei for (a) 56Co and (b) 62Co? Decay: 28. || Manganese has one stable isotope, 55Mn. What are the likely t t1/2 decay modes nuclei for (a) 51 Mn and (b) 59Mn? ⎡ 1and ⎤ daughter N = N0 ⎢ ⎥ ⎣2⎦ Section 30.5 Nuclear Decay and Half-Lives Activity: 29. | The radioactive hydrogen isotope 3H is called tritium. It decays by beta-minus0.693 decay with a half-life of 12.3 years. = rNis=the daughter nucleus of tritium? a. RWhat t1/2 b. A watch uses the decay of tritium to energize its glowing t t1 2 ⎡ 1 ⎤ fraction dial. What of the tritium remains 20 years after the R = R0 ⎢ ⎥ watch was created? 2 ⎣ ⎦ 30. | The barium isotope 133Ba has a half-life of 10.5 years. A sample begins with 1.0 * 1010 133Ba atoms. How many are left after (a) 2 years, (b) 20 years, and (c) 200 years? 31. | The cadmium isotope 109Cd has a half-life of 462 days. A sample begins with 1.0 * 1012 109Cd atoms. How many are left after (a) 50 days, (b) 500 days, and (c) 5000 days? 32. || How many half-lives must elapse until (a) 90% and (b) 99% Half Life and Activity of a radioactive sample of atoms has decayed? 235U and 238U. two main isotopes 33.There || The are Chernobyl reactor accidentof in uranium, what is now Ukraine was the worst nuclear disaster of all time. Fission products from 235 Two billion years ago, U comprised 3% of the uranium the reactor core spread over a wide area. The primary radiation in the earth’s crust. Now, it’s prevalence has dropped to exposure to people in western Europe was due to the short-lived 0.7% of the uranium in the earth’s crust. (half-life 8.0 days) isotope 131I, which fell across the landscape of thebyisotopes has athat longer half life? was ingested grazing cows concentrated the isotope •andWhich in Iftheir milk. Farmers couldn’t sell the contaminated 238U, so have a sample of 235U and a sample of milk, each •manyyou opted to use the milk to make cheese, aging it until the with the same mass (and therefore approximately the radioactivity decayed to acceptable levels. How much time same number atoms) sample have a131I must elapse for the of activity of awhich block of cheese will containing activity? to higher drop to 1.0% of its initial value? 34. |||| What is the age in years of a bone in which the 14C/12C ratio t t* 10-13? is measured to be 0.693N ⎡ 11.65 ⎤ 1/2 85 R = used in bone N 0 ⎢ ⎥ (half-life 65 days) isotope 35. || Sr N is a=short-lived 2 ⎦ receives a dose of 85Sr witht1/2an activity scans. A typical ⎣patient of 0.10 mCi. If all of the 85Sr is retained by the body, what will be its activity in the patient’s body after one year has passed? 36. || What is the half-life in days of a radioactive sample with 5.0 * 1015 atoms and an activity of 5.0 * 108 Bq? 37. ||| What is the activity, in Bq and Ci, of 1.0 g of 226Ra? Marie Curie was the discoverer of radium; can you see where the unit of activity named after her came from? 38. || Many medical PET scans use the isotope 18F, which has a half-life of 1.8 h. A sample prepared at 10:00 a.m. has an0.693N activity of 20 mCi. activity = decay rate = R = What is the activity at 1:00 p.m., when the patientt is injected? 1/2 39. ||| An investigator collects a sample of a radioactive isotope Use the form mass: with an activity of “quick 370,000and Bq. dirty” 48 hours later,ofthe activity is 120,000 Bq. What is the half-life of the sample? m ( 226 Ra ) = 226 u = 3.75 × 10 −25 kg m= 0.001 kg sample = 2.67 × 10 21 atoms 3.75 × 10 −25 kg per atom t1 2 ( 226 Ra ) = 1600 yr = 5.05 × 1010 s R = 3.7 × 1010 Bq = 1.0 Ci 24/10/13 5:28 PM A small sample can give a big count rate. t tt t ⎡⎡11⎤⎤ 1/21/2 N R == RN0 0⎢⎢ ⎥⎥ ⎣⎣22⎦⎦ My watch has a tritium (t1/2 = 12 yr) dial. When I purchased it in 2004, it had an activity of about 100 MBq. What is the activity now? Radioactive Dating A scrap of parchment from the Dead Sea Scrolls was found to have a 14C/12C ratio that is 79.5% of the modern value. Determine the age of this parchment. ⎡1⎤ N = N0 ⎢ ⎥ ⎣2⎦ t t1/2 Relevant data from Appendix D: t1/2 = 5730 yr Special Relativity Mass-energy conversion The most famous equation in the world: E = mc 2 1u is equivalent to 931.49 MeV Antimatter A positron is an anti-electron: Same mass, but positive charge What, in MeV, is the minimum energy gamma ray that can give rise to an electron-positron pair? FIGURE 30.5 The binding energy of the woofhydrogen atoms (taking account thebinding atoms are only a few eV, ofthe energies of nuclei are tens or hundreds of wo free neutrons as shown in FIGURE 30.5 . helium nucleus. MeV, that mass equivalent is not negligible. eater thanenergies that of thelarge heliumenough atom. The dif-their Electron Separate atoms (taking account of the wewas break a helium atom into two hydrogen Binding Energy om theSuppose energy that put into the system into can useprotons the conversion of Equation 30.2 to and two freecomponents two and the two electrons) neutrons as shown in FIGURE 30.5 . erence; this energy the binding components energy B: The mass of theis separated is greater than that of the helium atom. The dif- Helium ∆m ference=in28.30 mass MeV/u) MeV = 0.03038 u arises from the energy that was put into the system Proton to separate the tightly bound We can use the conversion of Equation 30.2 to y is computed by energy: considering thenucleons. mass Neutron Binding Helium atom hydrogen is atoms, findcomponents, the energyZequivalent of this difference; this22 energy the binding energy B: ated hydrogen atoms andmass neutrons 28.30 MeV Mass: B = (0.03038 u)(931.49 MeV/u) =Mass: 28.30 MeV 4.00260 u 2 H atoms: 2.01566 u Binding * (931.49 MeV/u)energy Generally, the nuclear(30.4) binding + 2 neutrons: 2.01732 u energy is computed by considering the mass 4.03298 u Total mass: per nucleon: components, Z hydrogen atoms and ordifference an atom of between the atom and its separatedDifference in mass: From ∆m = 0.03038 u 7.075 MeV and neutrons N Nneutrons: Appendix D energy of iron B = (ZmH + Nmn - matom) * (931.49 MeV/u) (30.4) Nuclear binding energy for an atom of mass m atomic with Z protons and N neutrons ss of Fe as 55.934940 u. Iron hasatom o the nearest MeV? 56 FIGURE 30.5 The binding energy of the helium nucleus. Electron Separate into components Neutron Proton Helium atom Mass: 4.00260 u 2 hydrogen atoms, 2 neutrons Mass: 2 H atoms: 2.01566 u + 2 neutrons: 2.01732 u Total mass: 4.03298 u Difference in mass: ∆m = 0.03038 u arated into 26 hydrogen atoms and 30 neuts is more than that of the iron nucleus; the ng Equation 30.4. The of the hydroEXAMPLE 30.1masses Finding the e 30.2. We find is the nuclear binding Binding Energy 65 u) What - 55.934940 u)(931.49 MeV/u) binding energy of iron energy of 56Fe to the nearest MeV? D gives the atomic mass of 56Fe as 55.934940 u. Iron has atomic number 26,the so anbinding atom of 56 Fe couldper be separated atoms and 30 neuWhat nucleonintoof2656hydrogen Fe? he nucleus and is its components a energy small trons. The mass of the isseparated components is more than that of the iron nucleus; the must use several significant figures in our us thethe binding —aboutdifference half that of agives proton—but energy energy. PREPARE = 492.26 MeV ≃Appendix 492 MeV . A nuclear fusion weight-loss plan The ! 55.934 940 ! Mass of 56Fe:! We solve for the binding energy Thethatmasses of the hydrosun’susing energyEquation comes from30.4. reactions 1 ! Mass of theH:! ! 1.007 825 hydrogen atoms to create a gen atom and neutron are given incombine Tablefour 30.2. We find atom of helium—a process called ! Mass of n:! ! ! 1.008 665single nuclear fusion. Because energy is released, SOLVE B = (26(1.007825 u) + 30(1.008665 u) - 55.934940 u)(931.49 MeV/u) ke a comparison with another energy value the mass of the helium atom is less than that (0.52846tou)(931.49 = hydrogen 492.26 MeV ≃the 492 MeV of the four atoms. As fusion le iron nucleus is=equivalent the energyMeV/u) on molecules of ATP! The energy scale of reactions continue, the mass of the sun decreases—by 130 trillion tonsits percomponents year! The difference the nucleus and is a small fromASSESS that of chemical processes.in mass between That’s a lot of mass, but given the sun’s enorergy fraction increases,ofsimply because there are mous the mass of the nucleus, so we must use several significant figures in our size, this change will amount to only a ure for comparing to anotheris small—about mass values.one Thenucleus mass difference that of ofthe a proton—but the energy few hundredths ofhalf a percent sun’s mass over its 10-billion-year lifetime. rgy per nucleon. Iron, with B=energy, 492 MeV equivalent, the binding is enormous. 1u is equivalent to 931.49 MeV How much energy is 492 MeV? To make a comparison with another energy value we have seen, the binding energy of a single iron nucleus is equivalent to the energy 24/10/13 5:27 PM released in the metabolism of nearly 2 billion molecules of ATP! The energy scale of nuclear processes is clearly quite different from that of chemical processes. As A increases, the nuclear binding energy increases, simply because there are more nuclear bonds. A more useful measure for comparing one nucleus to another is the quantity B/A, called the binding energy per nucleon. Iron, with B= 492 MeV 30.indd 979 Can get energy by fusion Can get energy by fission A nuclear fusion weight-loss plan The sun’s energy comes from reactions that combine four hydrogen atoms to create a single atom of helium—a process called nuclear fusion. Because energy is released, the mass of the helium atom is less than that of the four hydrogen atoms. As the fusion reactions continue, the mass of the sun decreases—by 130 trillion tons per year! That’s a lot of mass, but given the sun’s enormous size, this change will amount to only a few hundredths of a percent of the sun’s mass over its 10-billion-year lifetime. 24/10/13 5:27 PM So where did the heavy elements come from... 65. ||| All the very heavy atoms found in the earth were created long ago by nuclear fusion reactions in a supernova, an exploding star. The debris spewed out by the supernova later coalesced to form the sun and the planets of our solar system. Nuclear physics suggests that the uranium isotopes 235U (t1/2 = 7.04 * 108 yr) and 238U (t1/2 = 4.47 * 109 yr) should have been created in roughly equal amounts. Today, 99.28% of uranium is 238U and 0.72% is 235U. How long ago did the supernova occur? 66. |||| About 12% of your body mass is carbon; some of this is radioactive 14C, a beta-emitter. If you absorb 100% of the 49 keV energy of each 14C decay, what dose equivalent in Sv do you receive each year from the 14C in your body? 67. ||||| Ground beef may be irradiated with high-energy electrons from a linear accelerator to kill pathogens. In a standard treatment, 1.0 kg of beef receives 4.5 kGy of radiation in 40 s. a. How much energy is deposited in the beef? b. What is the average rate (in W) of energy deposition? c. Estimate the temperature increase of the beef due to this proFission cedure. The specific heat of beef is approximately 3/4 of that of water. A nucleus of 240Pu can be induced to fission into smaller 68. ||| A 70 kgWhat humanare body 140per g ofnucleon potassium. fragments. thetypically bindingcontains energies of Potassium has a chemical atomic mass of 39.1 u and has three 240Pu and the possible fission product 133Xe? naturally occurring isotopes. One of those isotopes, 40K, is Data from Appendix C: of 1.3 billion years and a natural radioactive with a half-life abundance ofAtomic 0.012%.mass Each 40K decay deposits, on average, Nucleus!! 1.0 MeV of energy into the body. What yearly dose in Gy does 240Pu:!! ! 240.053 808 the typical person receive from the decay of 40K in the body? 133 69. || Xe:! A chest uses 10906 keV photons. A 60 kg person receives ! !x ray 132.905 a 30 mrem dose from 1H:!! ! ! 1.007 825 one x ray that exposes 25% of the patient’s body. How many x-ray photons are absorbed in the n:! ! ! body? ! 1.008 665 patient’s MCAT-Style Passage Problems 1u is equivalent to 931.49 MeV Plutonium-Powered Exploration The Curiosity rover sent to explore the surface of Mars has an electric generator powered by heat from the radioactive decay of Fusion 238 Pu, a plutonium isotope that decays by alpha emission with a 3 Rounding nucleus a binding energy of half-life of 88slightly, years. the At the start ofHe thehas mission, the generator 6 24 238 2.5 MeV nucleon; contained 9.6per * 10 nuclei ofLi has Pu. a binding energy of 5.0 MeV 70. What is the daughter nucleus of the decay? per| nucleon. 238 238 236 234 Amit beB.energetically Pu C. 238 Np D. Th 3HeE.nuclei U possible for two • A.Would 71. ||toWhat the approximate of theof plutonium source at 6Li? fusewas together to formactivity a nucleus the start of the mission? much energy would be released in the • A.If so, 2 * how 1021 Bq 19 reaction? B. 2 * 10 Bq C. 2 *the 1017exact Bq details of how the reaction would go.) (Ignore D. 2 * 1015 Bq E. 2 * 1013 Bq 72. || The generator initially provided 125 W of power. If you assume that the power of the generator is proportional to the activity of the plutonium, by approximately what percent did the power output decrease over the first two years of the rover’s mission? Carbon dating can be used to date skeletons, wood, paper, fur, food material, and Up matter. It is quite accurate for ages to about 15,000 thing Warming else made of organic rs, about three half-lives. dated about 50,000 992 Items C H Aare PTE R 30 toNuclear Physicsyears with a fair degree eliability. sotopes with longer half-lives are used to date geological samples. PotassiumCarbon dating can be used to date skeletons, wood, paper, fur, food mat useful for of organic matter. It is quite accurate for ages to abou on dating, using 40K with a half-life of 1.25 billion years, is especially anything else made ng rocks of volcanic origin. years, about three half-lives. Items are dated to about 50,000 years with a fa of reliability. A sample of 1000 radioactive atoms has a 10 minute half-life. Isotopes withand longer half-lives are used to date geological samples. Po rbon dating can be used to date skeletons, wood, paper, fur, food material, 40 wing oldelse is the sample when 750 atoms have decayed? argon dating, using made of organic matter. It is quite accurate for ages to about 15,000 K with a half-life of 1.25 billion years, is especially u OP TO THINK 30.6 dating rocks volcanic origin. , about three half-lives. Items are dated to 50,000 years a fair of degree A. 10 minutes B. 15 minutes C. about 20 minutes D.with 30 minutes iability. otopes with longer half-lives are used to date geological samples. STOP TOPotassiumTHINK 30.6 A sample of 1000 radioactive atoms has a 10 minute 40 How old isuseful the sample dating, using K with a half-life of 1.25 billion years, is especially for when 750 atoms have decayed? g rocks of volcanic origin. 0.6 Medical Applications A. 10 minutes B. 15 minutes C. 20 minutes D. 30 mi of Nuclear Physics A sample of 1000 radioactive atoms has a 10 minute half-life. learisphysics has brought both perilhave and decayed? promise to society. Radioactivity can old the sample when 750 atoms P TO THINK 30.6 se tumors. At the same time, radiation can be used to diagnose and cure some A. 10This minutes 15 minutes C. 20 minutes of nuclear D. 30physics. minutes cers. section is B. a brief survey of medical applications 30.6 Medical Applications of Nuclear Physics Radiation Dose Calculations diation Dose Nuclear physics has brought both peril and promise to society. Radioact lear radiation disrupts a cell’s machinery by altering and damaging biological molcause tumors. At the same time, radiation can be used to diagnose and cu es, as we saw in Section 30.4. The biological effects of radiation depend on two cancers. This section is a brief survey of medical applications of nuclear ph ors. The first is the physical factor of how much energy is absorbed by the body. The ond is the biological factor of how tissue reacts to different forms of radiation. Radiation Dose Suppose a beta travels tissue, losingtokinetic energy as it ionizes ear physics hasparticle brought both through peril and promise society. Radioactivity can mstumors. it passes. The energy lost by the beta particle is a good measure of the number Nuclear radiation disrupts a cell’s machinery by altering and damaging biolog At the same time, radiation can be used to diagnose and cure some ons produced and thus the amount of damage done. In a certain volume of tissue, we saw in Section 30.4. The biological effects of radiation depen rs. This section is a brief survey of medical applications of ecules, nuclearasphysics. dose e ionization means more damage. For this reason, we define the radiation factors. The first is the physical factor of how much energy is absorbed by the b he energy from ionizing radiation absorbed by 1 kg of tissue. second The SI unit for the is the biological factor of how tissue reacts to different forms of radiati Dose abbreviated Gy. The Gy is defined as eiation is the gray, Suppose a beta particle travels through tissue, losing kinetic energy as ar radiation disrupts1 aGy cell’s machinery alteringenergy and damaging atomsbiological it passes.molThe energy lost by the beta particle is a good measure of the = 1.00 J/kg of by absorbed of doses: s, as we Two saw in different Section 30.4.types The biological effects of radiation depend on two of ions produced and thus the amount of damage done. In a certain volume of depends only on the energy absorbed, not on the type of radiation External /factor exposure to radiation s.number The first the physical of how much energy is absorbed byionization the body. The •isGy more means more damage. For this reason, we define the radiat on the absorbing Another common unit for dose is the rad; d iswhat the biological factormaterial how is. tissue reacts to different forms /ofinhaled or ingested isotopes • Internal as of theradiation. energy from ionizing radiation absorbed by 1 kg of tissue. The SI un dppose = 0.01 Gy. a beta particle travels through tissue, losing kinetic dose energy as itgray, ionizes abbreviated Gy. The Gy is defined as is the A 1 Gy dose of gamma rays and a 1 Gy dose of alpha particles have different s it passes. The energy lost by the beta particle is a good measure of the number ogical consequences. To account for such differences, the relative biological Ionizing radiation the s produced and thus the amount ofdamages damage cells done.ofIn a certain volume of tissue, 1 Gy = 1.00 J/kg of absorbed energy ctiveness (RBE) body, is defined as the biological effect of a it also damages bacteria and given dose relative to ionization means morebut damage. For this reason, we defineThe the number radiationofdose Gy depends only on the energy absorbed, not on the type of biological effect of an equal dose of This x rays. Tablesource 30.3 lists biological other pathogens. gamma is the relative Dose & Dose Equivalent energy from ionizing radiation absorbed by 1 kg of tissue. The SI unit for the or ontowhat absorbing material is. Another common unit for dose is usedforms for sterilizing medical equipment. ctiveness of different of radiation. Larger values correspond largerthe bioDose: Unit is the gray: gray, abbreviated Gy. The Gy is defined as is the The blue glow is due to the ionization of 1 rad = 0.01 Gy. cal effects. air around the source. Gyand dose the of product of the energy doseAin1 Gy theof gamma rays and a 1 Gy dose of alpha particles have The radiation dosethe 1equivalent Gy = 1.00isJ/kg absorbed energy biological consequences. To account for such differences, the relative b tive biological effectiveness. Dose equivalent is measured in sieverts, abbreviumber of Gy depends only on the energy absorbed, not on the type of radiation effectiveness (RBE) is defined as the biological effect of a given dose re equivalent: Unit is the sievert: Sv. ToDose be precise, 30.3 what the absorbing TABLE material is.Relative Anotherbiological common unit for is theeffect rad; of an equal dose of x rays. Table 30.3 lists the relative b thedose biological dose equivalent in Sv = dose in Gy * RBE effectiveness of radiation effectiveness of different forms of radiation. Larger values correspond to la = 0.01 Gy. One Svdose of radiation produces thetype same biological regardless of the type logical effects. 1 Gy of gamma rays and a 1 Gy doseRBE ofdamage alpha particles have different Radiation adiation. Another common unit of dose equivalent (also called biologically dose equivalent is the product of the energy dose in Gy The radiation gical consequences. To account for such differences, the relative biological X rays 1 1 rem = 0.01 Sv. ivalent dose) is the rem; relative tiveness (RBE) is defined as the biological effect of a given dosebiological relative toeffectiveness. Dose equivalent is measured in sieverts, Gamma rays 1 ated Sv. To be precise, ological effect of an equal dose of x rays. Table 30.3 lists the relative NOTE ▶ In practice, the term “dose” is often used for both dose and dosebiological equiva- 6 Medical Applications of Nuclear Physics Beta particles 1 iveness values to larger bio- dose equivalent in Sv = dose in Gy * RBE ent. Use of thedifferent units as aforms guide.ofIf radiation. the unit is Larger Sv or rem, it is correspond a dose equivalent; if Gy Protons 5 al effects. or rad, a dose. ◀ One radiation produces the same biological damage regardless of Neutrons is the product 5–20 e radiation dose equivalent of the energy dose in Sv Gyofand the radiation. Another common unit of dose equivalent (also called bio Alpha particles 20 measured inofsieverts, abbrevive biological effectiveness. Dose equivalent is equivalent dose) is the rem; 1 rem = 0.01 Sv. Sv. To be precise, Typical Doses: External TABLE 30.4 Radiation exposure Typical exposure (mSv) Radiation source gible een. nize y. PET scan 7.0 Natural background (1 year) 3.0 Mammogram 0.70 Chest x ray 0.30 e is no Transatlantic airplane flight 0.050 cessary natural Dental x ray 0.030 d from ven the though FIGURE 30.18 The use of gamma rays to a tumor in the brain. n. Doses:treat Internal al x ray (a) t he or Food dose, per year 0.40 mSv ammo(typical) body. ), may Eating 40 tablespoons 0.10 mSv of peanut butter e. This re. Eating 1000 bananas 0.10 mSv rapidly a large minimal Smoking 1 pack per 30 (b) day Gamma from for rays a year Collimator external source mSv or that mator is Radiation, Part I Tumor on Internal the mor are Most of the internal radiation of the human body is due to a single isotope, the beta emitter 40K, with half urgical life of 1.28×109 years. The body contains about 0.35% f treat- potassium by mass; of this potassium, about 0.012% is 40K. What is the total activity, in Bq, of a 70 kg human? hin the decay n has a The paths of the allowed gamma rays 40K: 40 Atomic mass of intersect atuthe tumor. The collimator allows -27 kg 1 u = 1.66 x 10 gamma rays to penetrate only along certain lines. R= 0.693N t1/2 Internal Radiation, Part II In a previous example, we computed the activity of the 40K in a typical person. Each 40K decay produces a 1.3 MeV beta particle. If 40% of the energy of these decays is absorbed by the body, what dose, and what dose equivalent, will a typical person (70 kg) receive in one year? 1 MeV = 1.6 x 10-13 J Radiation From Above Radiation vs. Height 450 400 350 300 250 200 150 100 50 0 0 2000 4000 6000 8000 10000 12000 Radiation vs. Height on a Plane External Radiation A passenger on an airplane flying across the Atlantic will receive an extra radiation dose of about 5 µSv per hour from cosmic rays. How many hours of flying would it take in one year for a person to double his or her yearly radiation dose? Assume there are no other significant radiation sources besides natural background. 80 hours / month 960 hours / year Chain Reaction 1 0 n+ 235 92 U → 236 92 92 1 U → 141 56 Ba+ 36 Kr+3 0 n Difficult Daughters 141 56 0 Ba → 141 t1 2 = 18.27 minutes 57 La+ -1 e 141 57 0 La → 141 t1 2 = 3.92 hours 58 Ce+ -1 e 141 58 0 Ce → 141 t1 2 = 32.5 days 59 Pr+ -1 e 141 59 Pr : stable 131 53 0 I → 131 54 Xe + -1 e t1 2 = 8.0 days taken up by thyroid 137 55 0 Cs → 137 56 Ba* + -1 e t1 2 = 30.2 years chemically similar to potassium 90 38 Sr → 90 39 Y + -10 e- t1 2 = 28.1 years chemically similar to calcium Turning Lead into Gold Transuranic elements 238 92 U + 01 n → 239 93 Np → 239 94 239 92 U→ Pu + -10 e- 239 93 Np + -10 e- Fusion: More Energy Released. H + H → He + n 2 2 3 1 1 1 2 0 The problem? Coulomb repulsion. The solution?
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