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Chapter 3 the Fundamentals of Nuclear Physics Outline Natural Outline Chapter 3 The Fundamentals of Nuclear • Terms: activity, half life, average life • Nuclear disintegration schemes Physics • Parent-daughter relationships Radiation Dosimetry I • Activation of isotopes Text: H.E Johns and J.R. Cunningham, The physics of radiology, 4th ed. http://www.utoledo.edu/med/depts/radther Natural radioactivity Activity • Activity – number of disintegrations per unit time; • Particles inside a nucleus are in constant motion; directly proportional to the number of atoms can escape if acquire enough energy present • Most lighter atoms with Z<82 (lead) have at least N Average one stable isotope t / ta A N N0e lifetime • All atoms with Z > 82 are radioactive and t disintegrate until a stable isotope is formed ta= 1.44 th • Artificial radioactivity: nucleus can be made A N e0.693t / th A 2t / th unstable upon bombardment with neutrons, high 0 0 Half-life energy protons, etc. • Units: Bq = 1/s, Ci=3.7x 1010 Bq Activity Activity Emitted radiation 1 Example 1 Example 1A • A prostate implant has a half-life of 17 days. • A prostate implant has a half-life of 17 days. If the What percent of the dose is delivered in the first initial dose rate is 10cGy/h, what is the total dose day? N N delivered? t /th t 2 or e Dtotal D0tavg N0 N0 A. 0.5 A. 9 0.693t 0.693t B. 2 t /th 1/17 t 2 2 0.96 B. 29 D D e th dt D h e th C. 4 total 0 0 0.693 0.693t /th 0.6931/17 C. 59 0 D. 15 e e 0.96 0 D. 75 E. 30 D t 0 1 D t Delivered : 4% E. 300 0 avg 0 avg Gy 17d h 10102 24 59Gy h 0.693 d Decay schemes Example 2 123 • Initial activity of an I sample (th = 13 h) injected • A decay (disintegration) in the blood is 480 MBq. After 12 h measured scheme depicts possible activity is 20 MBq / l. Assuming the volume of the routes of radioactive blood is 6 l find biological half-life, h. decay for a nuclide: A. 4 A0 480 / 6 80 MBq/l 1) a decay B. 6 t /teff 2 2) b+ (positron) decay or C. 9 A1 A0 2 ; A1 / A0 1/ 4 2 D. 11 electron capture teff 6 h E. 13 3) b- (negatron) decay 1/ teff 1/ tI 1/ tb 4) isomeric transition 1 1 Hendee, Ritenour, Medical imaging physics, 4th edition, fig. 3-1, p.29 tb 11 h 1/ teff 1/ tI 1/ 6 1/13 Alpha disintegrations Beta disintegrations • Emission of helium nucleus, mainly from • Ejection of positive or negative electron heavy nuclei • Positron (b+) or negatron (b-) emitters • Proton-rich nucleus – emits positron, neutron-rich emits electron ~ b emission : n p b Z increases by 1 b emission : p n b Z decreases by 1 In beta-minus emission an antineutrino is emitted instead of neutrino. They have opposite helicity (projection of spin on direction of momentum) 2 Beta disintegrations Beta disintegrations • The ejected beta particle shares its energy with Co-60 decay scheme: neutrino (anti-neutrino), and therefore may have energy in a continuous spectrum up to E Energy is released in max transitions from excited levels of Ni-60 to the ground state via emission of gamma rays (average g-ray energy 1.25MeV) Image from https://www.boundless.com Beta disintegrations Electron capture • In the production of isotopes in a nuclear reactor a A A neutron is usually added to a stable nucleus, Z X Z 1Q resulting in b- emitters • Orbital electron can be captured by nucleus • Example: to produce 60Co a neutron is added to 59Co • Particle accelerators (more expensive) produce p + e (usually K electron) n + b+ emitters 2 • Since 2m0c =1.022 MeV energy is required to • This process is competing with positron emission produce electron-positron pair – this is the minimum in proton-rich nuclei difference between the initial and final energy • The only process when the energy difference + (parent-daughter) for b emitters between the initial and final state <1.022 MeV Isomeric transitions: Isomeric transitions Photon emission • Isomeric transitions: • Technetium is predominantly an artificially produced metastable to stable state, no 99 change in A or Z radioactive metal. Example: 42Mo (th=66.7 hours) - 99m • Always preceded by another produced in nuclear reactors by b decay to 43Tc 99 transition, leaving nucleus in • All isotopes are radioactive, most common: 43Tc (th= excited state 99m 210,000 years) and 43Tc (th= 6 hours) • Energy is released by • 99mTc is widely used – Emission of a photon – as a tracer for medical diagnosis (g of 140 keV is detected – Internal conversion with gamma-camera) • Metastable state: an excited -6 – functional scans of brain, bone, liver, spleen, kidney, thyroid Simplified radioactive decay scheme for 99Mo state with the lifetime >10 s Hendee, Ritenour, Medical imaging physics, 4th edition, fig. 3-7 – for blood flow studies 3 Isomeric transitions: Internal conversion Auger electron production • A hole in K, L, or M shell has to be filled • Nucleus relaxes to the ground state • The relative probability of the emission of characteristic • Alternatively to a g-ray emission an orbital radiation to the emission of the Auger electron is called electron may be ejected with the energy E= g -E fluorescence yield b • Fluorescence yield is higher for larger Z Before Charts of isotopes Decay series • Almost all the radioactive isotopes of the lighter elements achieve stability by keeping their mass number constant, through beta decay or K capture • Decay is usually along an isobaric line (constant mass number) and often involves a number of successive transitions before stability is reached Isobaric line for mass number 90 Nuclear transformations Particle tracks A Z Energy deposition a disintegration -4 -2 Total energy of a particle - b decay 0 +1 Emean~1/3 Emax + b decay 0 -1 Emean~1/3 Emax and Eg=1.02 MeV Electron capture 0 -1 Most energy carried away by ; EFluorescence and/or EAuger Isomeric transitions 0 0 • Ionizations can be made visible in a cloud (bubble) g ray 0 0 Eg available chamber: the air is expanded just after the particle passage, making vapor condensate in the places of ionization Internal conversion 0 0 Eelectron=Eg-Eb EFluorescence and/or EAuger • Photons transfer energy to the secondary electrons, which then ionize the vapor 4 Example 3 Example 4 99 99m 99 42Mo -> 43Tc -> 43Tc • The mass number (A) changes only for I II ____ decay: • In the above decay of molybdenum, the modes of decay labeled (I) and (II) are, respectively: A. alpha B. beta minus A. beta minus, isomeric transition C. beta plus B. isomeric transition, beta minus C. beta plus, isomeric transition D. electron capture D. beta minus, beta minus E. isomeric E. electron capture, beta minus Growth of radioactive daughter Growth of radioactive daughter • Radioactive daughter is formed at the rate at • Express the same solution for activity which the parent decays (1), and itself decays 2 (2 1 )t with a different rate (2) A2 A1 1 e 2 1 dN2 N N • For a special case of >> can simplify to dt 1 1 2 2 2 1 2t 1 1t 2t A A 1 e Solution: N N ) e e 2 1 2 1 0 2 1 • After some time – reach a state of parent-daughter equilibrium, where A1=A2 Growth of radioactive daughter Example 5 2 A2 A1 99m 2 1 • After ____ hours, Tc will be approximately in radioactive equilibrium with its parent element 99Mo. (Half-lives are: 67 hours for 99Mo and 6 99m hours for Tc.) A A 2 1 e(2 1 )t A. 6 2 1 2 1 B. 24 (2 1 )t 1 A2 A1 1 e 1 C. 48 2 D. 54 1 1 0.693 0.693 t ln ; 1 ; 2 E. 268 1 2 2 th1 th2 1 67 t ln 10x2.4 24 h 0.7 / 6 0.7 / 70 6 5 Activation of isotopes Activation of isotopes • Atomic nuclei can be activated by neutron bombardment with the probability dependent on • More practically relevant quantity is the activity of the irradiated sample the interaction cross section s A N Nts t • Number of activated atoms: • If the bombardment N N st t time t >> th, activity reaches its maximum -24 2 s ~ 10 cm As Nts • Accounting for decay during irradiation: 0.693t /th A As 1e ) Example 6 Nuclear fission and fusion What is the activity of a 20 g sample of 59Co irradiated in a neutron flux of 1014 neutrons/(cm2s) • Nuclear fission – a nucleus is split into lighter fragments with release of very large energy. for 6 years? Cross section s=36 barns, th=5.3 years. Example: First find the number of atoms in the target m 20 23 Nt 23 2.0410 M / N A 59 /(6.0210 ) • Nuclear fusion – two lighter atoms are fused into a The activity at a time t: heavier one also with release of energy. Example: A N s 1 e0.693t /th ) t ~3.3 MeV 1014 2.041023 3610241 e0.6936/5.3 ) 4.01014Bq Summary • Terms: activity, half life, average life • Nuclear disintegration schemes • Parent-daughter relationships • Activation of isotopes 6.
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