Units. Chapter 1 Basic Concepts. Units. Example 1. Atoms. Example 2. Radiation Dosimetry I

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1 Unis Chaper Basic Conceps Radiaion Dosimery I Tex: H.E Johns and J.R. Cunningham, The physics of radiology, 4 h ed. Special uni of energy: elecron vol ev ev=.60x0-9 C x vol=.60x0-9 J Unis Absorbed dose: describes energy deposiion in waer phanom, deecor, paien, ec. Exposure: describes he abiliy of radiaion o ionize air, used for energies < MeV (below ypical radioherapy range) Aciviy: describes radioacive isoopes; Ci is close o he aciviy of g of radium ( 6 Ra) Example A curren of ma mus flow ino 00 nf capacior for how many seconds o produce a 50 V poenial difference across he capacior? A. B. C..5 D. 5 E. 5 Q I C V V 9 CV 000 f 50V.5 s I 6 0 A Example -cc-volume ionizaion chamber is placed in a radiaion field of 00 R/s. Wha is he curren generaed in amperes (ρ air = 0.00 g/cm )? A. 5. x 0 - B. 6. x 0-0 C. 5. x R. 580 C/kg D. 6.7 x 0-8 E. 5. x R/s m air V ρ air air 4 C/(kg s). 580 C/(kg s) cm 0. 00g/cm g. 60 kg -6-8 I. 580 C/(kg s). 60 kg A -6 Aoms Aomic number Z: number of elecrons (proons) Mass number A: oal number of proons + neurons Aomic mass: Carbon has aomic mass.0000 amu (6 proons + 6 neurons) Typical noaion: A Z Elemen

2 Aoms Isoopes: have he same number of proons, bu differen number of neurons Same aomic number Z, and number of elecrons Same chemical properies Differen mass number A Isoones: have he same number of neurons (A-Z) Isobars: have he same aomic mass A (oal number of proons + neurons) There is redundancy in full noaion A Z X Aomic number Z deermines he elemen X Isomers: he same A and Z, differen nuclear energy sae (sable vs. measable, or excied); noaion: A Z m X Aomic energy levels Elecron orbis have defined energies (levels) The innermos is K (up o wo elecrons wih opposie spins), nex is L (up o eigh elecrons), ec. Filled ouer shell chemically iner aom Aomic energy levels Nucleus and is energy levels X-rays arise from ransiions o K, L, M levels (ev o kev energy range) Sysem of nuclear energy levels Nuclear ransiions produce phoons (g-rays) and paricles in MeV energy range Mass and energy Mass and energy Phoon energy: E = hv = hc/l Mass-o-energy conversion: E = mc Relaivisic mass: m0 m Res mass m 0 Kineic energy: K.E. = mc m 0 c v / c Mass-o-energy conversion facors: elecron mass = 0.5 MeV amu = 9.5 MeV

3 Example From he following able of paricle res masses, calculae he gamma energy emied when a proon capures a neuron o creae a deueron. amu corresponds o he res mass energy of 9.5 MeV paricle res mass. amu Proon.0077 Neuron Deueron.055 A..875 MeV B..0 MeV C.. MeV E g ErmP ErmN ErmD D..8 MeV ( ) 9.5 MeV E. 4.0 MeV MeV.697MeV.MeV Example 4 Find he velociy of an elecron acceleraed hrough he poenial difference of 5 MeV. KE=5MeV E m 0c v / c 5 MeV 0.5MeV v / c ~ v / c ~ v ~ m/c v / c Exponenial behavior Exponenial behavior dn d ln N N N e a N e N l / a / h The sign deermines he process: decay or growh l l - ransformaion consan a average life; h half-life; l = / a = ln/ h = 0.69/ h If more han one process akes place: dn d ( l ) l ln N Exponenial behavior N N / h 0 Example 5 In he case of simulaneous physical decay and biological clearance, when T p, is he physical half-life and T b is he biological half-life, he ecive half-life T is generally equal o: A. T p + T b B. l/t p + /T b C. T p x T b D. /(l/t p + /T b ) E. Tp Tb dn d N p b Since T T Tp Tb p / ln N N b

4 X-ray ube design Chaper The Producion and Properies of X Rays Radiaion Dosimery I Tex: H.E Johns and J.R. Cunningham, The physics of radiology, 4 h ed. hp:// Figure - (a). Schemaic diagram of x-ray ube and circui Filamen is heaed, releasing elecrons via hermionic emission (V f ~ 0V, I f ~ 4A, resuling in T>000 o C) X rays are produced by high-speed elecrons bombarding he arge Typically < % of energy is convered o x rays; he res is hea X-ray ube curren Figure - (b). Tube curren as funcion of ube volage. Curve : ube operaing a a lower curren Elecron cloud near he filamen creaes space charge region, opposing he release of addiional elecrons Increase in ube volage increases ube curren; limied by filamen emission High filamen currens and ube volage of 40 o 40kV mus be used X-ray ube: power source The source of elecrical power is usually ac (easier o ransmi hrough power lines) X-ray ubes are designed o operae a a single polariy: posiive anode, negaive cahode Need o manipulae available power source (suppress or recify wrong polariy) The highes x-ray producion iciency can be achieved a a consan poenial Alernaing currens and volages Alernaing currens and volages Curren flows in one direcion: series of pulses Phase changes from 0 o 60 o during he cycle ime of /60 s Negaive wave is suppressed or recified Averaging: Vav V0 or Vrms V0 Figure. 4

5 Recificaion Three phase unis Need o increase pulse repeiion rae o deliver high x ray flux in a shor period of ime Three phase unis: volage beween any pair of wires Tube poenial is almos consan, wih a ripple Example Which ype of x-ray generaor produces he highes ecive ube volage, assuming he peak volage is applied across he ube? A. One-phase B. Three-phase C. Consan poenial D. The ecive volage is he same for all ypes above In C - ecive volage = peak volage / V RMS V 0 Example Raio of he urns in a ransformer is N. Given an inpu RMS (primary) volage, wha is he peak oupu (secondary) volage? Faraday s law: d VS NS ; d VS NS N V N P S P V N V P RMS d VP N P d Diagnosic x ray ubes The objecive is o deliver x ray beam from a poin source in a very shor ime To overcome heaing need o spread elecrons over some area ha appears as a poin Example Wha energy (kj) is impared o a roaing anode (0.5 kg) during a s exposure ha produced a emperaure of 500 o C. Specific hea of ungsen is 0.05 kcal/kg o C, and cal = 4.86 J A. 7.9 B C D. 9.5 Duraion of exposure is irrelevan E. 8.9 E cmt kj 5

6 Diagnosic x ray ubes Raing of diagnosic ubes Image from hp:// X-rays ha are emied from he arge ravel hrough differen hickness of cahode maerial Heel ec: radiaion inensiy oward he cahode side of he x- ray ube is higher han on he anode side Cahode is ypically mouned over he hicker par of he paien o balance he amoun of ransmied phoons on he imager Focal spo loading deermines he maximum permissible exposure: here is a maximum power ha can be oleraed before arge sars meling (T meling =400 o C for ungsen) Anode cooling and housing cooling raes deermine he number of exposures ha may be given in a sequence Inensiy profile Raing of diagnosic ubes Raing of diagnosic ubes The combinaion of curren and volage mus lie o he lef of he appropriae curve The maximum duraion of a single exposure depends on spo size, anode roaion speed, curren, volage, power supply ype Hea sored in he anode and is cooling rae limis he number of exposures given in a sequence Hea uni HU characerizes he energy deposied wihin he anode in a single exposure X ray ubes for radioherapy X-ray specra Mosly for superficial reamens No need for a small spo source The insananeous energy inpu is small (abou /0) bu he average energy inpu is ~ 0 imes greaer compared wih a diagnosic ube Due o much higher energy (>00keV) of elecrons bombarding he arge, here is a problem of secondary elecrons emerging from he arge Soluion: he arge is placed in a hood - hollow ube wih copper shielding inerceping he secondary elecrons 6

7 Ineracions of elecrons wih he arge o give x rays Characerisic radiaion Mos probable; no x-rays produced Breaking radiaion Differen ransiions have differen probabiliies, according o quanum mechanics selecion rules (some ransiions are forbidden) Bremssrahlung ineracion Thick arge Example 4 Thin arge The energy levels of K, L, and M shells in ungsen are -69.5, -.0, and -.5 kev. Wha phoon energies will be presen in is characerisic X-ray specrum? Thin arge approximaion: one collision per elecron Thick arge approximaions: I(E) = C Z (E max - E) Phoon energies are equal o he differences A. 67.0, 58.5, 8.5 kev beween corresponding energy levels B. 80.5, 7.0,.5 kev C. 69.5,.O,.5 kev D. Coninuous specrum from.5 o 69.5 kev E. Coninuous specrum below.5 kev Example 5 A arge maerial has he following binding energies: K=0 kev, L=4 kev, M=0.7 kev. If 40.0 kev elecrons are fired a he arge, wha kind of x-rays can have he following energies? 6-: 4 kev 6-: 6 kev 6-: 40.7 kev A. Characerisic only B. Bremssrahlung only C. Boh A and B D. Neiher A nor B Answers: 6-: B 6-: C 6-: D Summary X-rays are produced via bremssrahlung ineracions of high-energy elecrons wihin a arge Efficiency is low, mos energy goes ino arge heaing Coninuous specrum includes characerisic x-rays due o arge maerial Required high volage (~50-00 kv) o accelerae elecrons Power source: ac o dc conversion 7