College Physcs Student s Manual Chapter 3 CHPTER 3: MEDICL PPLICTIONS OF NUCLER PHYSICS 3.1 MEDICL IMGING ND DIGNOSTICS 1. neutron generator uses an α source, such as radum, to bombard beryllum, 4 9 1 nducng the reacton He + Be C + n. Such neutron sources are called RaBe sources, or PuBe sources f they use plutonum to get the α s. Calculate the energy output of the reacton n MeV.c Usng E Δmc, we can determne the energy output of the reacton by calculatng the change n mass of the consttuents n the reacton, where the masses are found ether n ppendx or Table 31.: ( m m ) E c f (4.00603 + 9.018 1.000000 1.0086)(931.5 MeV) 5.701MeV 6. 131 The actvtes of I and µc 13 I and used n thyrod scans are gven n Table 3.1 to be 50 131 13 70, respectvely. Fnd and compare the masses of I and I n such scans, gven ther respectve half- lves are 8.04 d and 13. h. The masses are so small that the radoodne s usually mxed wth stable odne as a carrer to ensure normal chemstry and dstrbuton n the body. Begnnng wth the equaton R t ( 0.693)( m M ) we can solve for the 1 mass of the odne sotopes, where the atomc masses and the half lves are gven n the appendces: t 1 N 7
College Physcs Student s Manual Chapter 3 m m 131 13 RMt1/ 4.0 RMt1/ 3.6 11 (5.0 g (7.0 g C)(3.70 Bq/C)(130.91 g/mol)(8.040 d) (0.693) 3 ( 6.0 ) C)(3.70 Bq/C)(1.91 g/mol)(13. h) (0.693) 3 ( 6.0 ) ( 86400s d) ( 3600s h) 3. BIOLOGICL EFFECTS OF IONIZING RDITION. How many Gy of exposure s needed to gve a cancerous tumor a dose of 40 Sv f t s exposed to α actvty? Usng the equaton Sv Gy RBE and Table 3., we know that RBE 0 for Sv 40 Sv whole body exposure, so Gy Gy RBE 0 3.3 THERPEUTIC USES OF IONIZING RDITION 1. Large amounts of Zn are produced n copper exposed to accelerator beams. Whle machnng contamnated copper, a physcst ngests 50.0 µc of Zn. Each Zn decay emts an average γ - ray energy of 0.550 MeV, 40.0% of whch s absorbed n the scentst s 75.0- kg body. What dose n msv s caused by ths n one day? Frst, we need to determne the number of decays per day: 4 11 decays/day ( 5.00 C)( 3.70 Bq/C)( 8.64 s/d) 1.598 /d Next, we can calculate the energy because each decay emts an average of 0.550 MeV of energy: 1.598 E / day d 5.633 11 decays J/d ( 0.400) 0.550 MeV 1.60 decay MeV Then, dvdng by the mass of tssue gves the dose: 13 J 8
College Physcs Student s Manual Chapter 3 Dose n rad/d.633 J/d 1rad 7.51 75.0 kg 0.00 J/kg 5 rad/d 3.5 FUSION Fnally, from Table 3., we see that the RBE s 1 for γ radaton, so: msv rem/d rad RBE ( 7.51 rad/d) ( 1) 7.51 rem/d 0.1rem 7.51 4 msv/d Ths dose s approxmately 700 mrem/y, whch s larger than background radaton sources, but smaller than doses gven for cancer treatments. 30. The energy produced by the fuson of a 1.00- kg mxture of deuterum and trtum was found n Example Calculatng Energy and Power from Fuson. pproxmately how many klograms would be requred to supply the annual energy use n the Unted States? 0 From Table 7.6, we know E 1.05 J and from Example 3., we know that a 1.00 kg mxture of deuterum and trtum releases 3.37 J of energy, so: 0 1.00 kg 5 M ( 1.05 J) 3.1 kg 3.37 J 6 35. The power output of the Sun s 4 W. (a) If 90% of ths s suppled by the proton- proton cycle, how many protons are consumed per second? (b) How many neutrnos per second should there be per square meter at the Earth from ths process? Ths huge number s ndcatve of how rarely a neutrno nteracts, snce large detectors observe very few per day. (a) Four protons are needed for each cycle to occur. The energy released by a proton- proton cycle s 6.7 MeV, so that 6 4 protons 1MeV # protons/s ( 0.90)( 4 J/s) 13 6.7 MeV 1.60 J 3 38 protons/s (b) For each cycle, two neutrnos are created and four protons are destroyed. To determne the number of neutrnos at Earth, we need to determne the number 9
College Physcs Student s Manual Chapter 3 3.6 FISSION of neutrnos leavng the Sun and dvde that by the surface area of a sphere wth radus from the Sun to Earth: 38 ( v e 4protons)( 3.37 protons/s) 11 4π ( 1.50 m) # # 6 neutrnos/m s area 4πR 45. (a) Calculate the energy released n the neutron- nduced fsson reacton 39 0 n + Pu Sr + Ba + 4n, gven m ( Sr) 95.91750 u and m ( 0 Ba) 139.9581 u. (b) Confrm that the total number of nucleons and total charge are conserved n ths reacton. (a) To calculate the energy released, we use energy before and after the reacton: E 39 0 ( mn + m( Pu) m( Sr) m( Ba) 4mn ) 39 0 ( m( Pu) m( Sr) m( Ba) 3m ) c E Δmc to calculate the dfference n [ 39.05157 95.91750 139.9581 ( 3)( 1.0086) ]( 931.5 MeV) 180.6 MeV n c 1 39 1 (b) Wrtng the equaton n full form gves 0 n 1+ 94Pu5 38Sr84 + 40n1 so we can determne the total number of nucleons before and after the reacton and the total charge before and after the reacton: Z 1+ 39 40 + 0 + 4 f ;. 0 + 94 94 56 + 38 + 4(0) Z f Therefore, both the total number of nucleons and the total charge are conserved. 3.7 NUCLER WEPONS 51. Fnd the mass converted nto energy by a 1.0- kt bomb. Usng E mc, we can calculate the mass converted nto energy for a 1.0 kt bomb: 1 E ( 1.0 kt)( 4. J/kT) 4 m 5.60 kg 0.56 g 8 c 3.00 m/s ( ) 30
College Physcs Student s Manual Chapter 3 57. ssume one- fourth of the yeld of a typcal 30- kt strategc bomb comes from fsson reactons averagng 00 MeV and the remander from fuson reactons averagng 0 MeV. (a) Calculate the number of fssons and the approxmate mass of uranum and plutonum fssoned, takng the average atomc mass to be 38. (b) Fnd the number of fusons and calculate the approxmate mass of fuson fuel, assumng an average total atomc mass of the two nucle n each reacton to be 5. (c) Consderng the masses found, does t seem reasonable that some mssles could carry warheads? Dscuss, notng that the nuclear fuel s only a part of the mass of a warhead. (a) Gven that for fsson reactons, the energy produced s 00 MeV per fsson, we can convert the 1 4 of 30 kt yeld nto the number of fssons: # of fssons ( 1 4)( 30 kt) (4. J/kT) 13 ( 00 MeV/fsson )( 1.60 J/MeV) 1 1.1 5 fssons 1mol 3 6.0 nucle 5 3 Then, m ( 1.1 nucle) ( 38 g/mol) 4.35 g 4.3 kg (b) Smlarly, gven that for fuson reactons, the energy produced s 0 MeV per fuson, we convert the 3 4 of 30 kt yeld nto the number of fusons: # of fusons Then: m ( 3 4)( 30 kt) (4. J/kT) 13 ( 00 MeV/fsson )( 1.60 J/MeV) 1 3. 6 fusons 6 1mol 3 ( 3. fusons) ( 5 g LD fuel/mol).66 g.7 kg 6.0 3 nucle (c) The nuclear fuel totals only 6 kg, so t s qute reasonable that some mssles carry overheads. The mass of the fuel would only be 60 kg and therefore the mass of the warheads, weghng about tmes the nuclear fuel, would be only 1500 lbs. If the fuel for the mssles weghs 5 tmes the total weght of the warheads, the mssle would wegh about 9000 lbs or 4.5 tons. Ths s not an unreasonable weght for a mssle. 31