Th following qustions ar to b answrd individually. Usful information such as tabls with dtctor charactristics and graphs with th proprtis of matrials ar availabl in th cours wb sit: http://www.lip.pt/~patricia/fisicadaradiacao. If ncssary, us th cours slids too. Exrcis 1 Intraction of photons Th mass absorption cofficints of photons of diffrnt nrgis in watr ar displayd in tabl 1 (in units of [g/cm] -1 ). Tabl 1 a) What is th fraction of nrgy lost by th X-rays of 10 kv in 5 cm of soft tissu? b) Rpat a) for 100 MV gammas. c) Compar th valus of nrgy lost in soft tissu by bams of 10 kv x-rays and 100 MV gammas with th sam intnsity. d) What is th dominant procss of photon intraction in ach cas? (s figur ) Plas commnt what on th main diffrncs in th procsss by which 10 kv and 100 MV photons dposit nrgy in 5 cm of soft tissu. 1
Figur 1 Mass absorption coficint of photons in watr. Exrcis Dtction of photons a) In a gamma spctroscopy systm, two narby paks can only b distinguishd (rsolvd) if thir man valus ar sparatd by mor than th man valu of thir full widths at half maximum (FWHM). Considring th dtction of th photons mittd by th 60 Co, and assuming that th two paks hav qual FWHM, comput th maximum valu of th nrgy rsolution for th pak with th highst nrgy, in ordr that th two can b rsolvd. b) Knowing that th NaI scintillator mits on photon pr 6 V of nrgy dpositd, and considring that in a NaI+PMT systm th avrag global fficincy for th dtction of th scintillation photons is ~5%, show that such systm fulfills th limit computd in point a). (considr that th fluctuations in th numbr of dtctd scintillation photons ar poissonian) Exrcis 3 - Intraction of chargd particls with mattr Th nrgy loss of chargd particls in mattr, xcluding radiativ losss, can b dscribd by th Bth-Bloch quation. In Figur 1 th nrgy loss of chargd particls,
dscribd by that quation, whil crossing diffrnt matrials, is displayd as a function of βγ, whr β=v/c (v is th vlocity of th particls ) and γ is th Lorntz factor. Figur a) Knowing that th minimum nrgy loss of havy chargd particls in mattr trough xcitation and ionization corrsponds to βγ ~3, comput th corrsponding kintic nrgy for: i. Muons (M=105.7 MV) ii. Protons (M = 938.3 MV) iii. α particls (M=377.3 MV) b) Show that in th low vlocity approximation of th Bth-Bloch quation de dx ~, (for βγ < 3) k th avrag rang for chargd particls can b approximatd by : R= 1 k T E 3
whr T and E ar th initial kintic nrgy and th initial total nrgy of th particls, rspctivly. c) Knowing that soft tissu has a composition that can b approximatd by that of watr and noting that: Z m c k 0.1535 MV/(gcm ) z ln, A I whr z is th lctric charg of th particl, is th matrial dnsity, I is th man xcitation nrgy of th matrial and that IHO= 75 V and mc = 511 kv, dtrmin: i.) th avrag rang of 3 MV α particls in soft tissu; ii.) th avrag rang of th most nrgtic lctrons mittd by a 90 Sr sourc (nglcting radiativ nrgy losss). Exrcis 4 Intraction of lctrons Estimat th shilding fficincy of 1.5 mm of a plastic matrial (corrsponding to th thicknss of th lid of th box whr th Gigr-Mullr countr is placd in th lab stup) for th β mittd in th dcay of 04 Tl. Tak into account that th rang of ths particls in polythyln and considr th β mission spctrum givn by: N( T ) const * T T m c ( Q T ) ( T m c ) whr m c 511kV and Q is th nd point of th spctrum. Exrcis 5 Dtction of lctrons Considr th stup in th figur, in which a 04 Tl sourc (S in th figur) is alignd with a Gigr-Müllr dtctor placd at a distanc of d=15.00±0.05 cm. 4
Assuming that th mission of particls by th sourc is isotropic and that th dtctor is a cylindr with a window of radius a=1.5 cm and its axis alignd with th sourc: a) Comput th fraction of particls raching th dtctor with rspct to th total numbr of mittd particls, using both th xact dfinition of and th approximation for a<<d. Commnt th rsults. b) In th cas of a Mont-Carlo simulation of an isotropic sourc and of a Gigr- Müllr (GM) dtctor (as for xampl th Thallium sourc and th GM dtctor in th lab) how many lctrons hav to b gnratd isotropically for th statistical uncrtainty associatd to th sampl of dtctd lctrons to b blow 1%? Assum that th lctrons do not intract in th air bfor thy rach th dtctor and that th fficincy for lctrons dtction is 100%. c) In th dtction systm with th configuration shown in th figur, data wr acquird during 100 s and a count rat of 400 cnts/s was obtaind : i. assuming that th background rat is 1.0±0.1 cnts/s what is th counting rat of th particls mittd by th sourc and its statistical rror? ii. what is th acquisition tim of th background that is rquird for th background rat to b stimatd with a rlativ rror similar to that of th counting rat obtaind in c)? d) Considring a 04 Tl sourc with an initial activity of 1.0 Ci and an ag of 10 yars, stimat th count rat obtaind with th dtction systm of th figur abov, assuming that th fficincy of th dtctor for lctrons is 100%. (th half-lif of 04 Tl is T1/ = 3.78 yars) 5