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3. A new drug, PSMA-617, can be used to deliver a radionuclide to a tumor and kill it using dose. The drug is currently used with 17,Lu (A=-52.384 MeV), which decays into 173H f(A=-52.881 MeV), but plans are underway to replace it with 2254 (A=21.637 MeV) which decays into 87/ 224Fr (A=13.277 MeV) plus an a-particle (4=2.425 MeV). a. What is the approximate maximum range of the charged particle emitted in the decay of 7, Lu in tissue in cm. You can treat tissue as being H20 (p=1.0 g/cm'; Mole Weight=18 g) (2 pts.)? b. The a-particle emitted in the decay of 225 89Ac has a range of 5 um in tissue. 225 What is the ratio of the dose delivered by the decays 894c 177 Lu (2 pts.) c. What would the range of the a-particle be in 13 Al (p=2.7 g/cm2). Hint: Remember the Bragg-Kleeman Rule and that tissue can be approximated as H20 (A=18; p=1.0 g/cm2 ). (1 pts.)?CONSTANTS CO. Speed of light 2.99792458 x 108 m/s Charge of electron 1.602189 x 10-19 C Boltzmann constant 1.38066 X 10-23 J/K 8.6174 X 10 -5 eV/K Planck's constant h 6.62618 X 10-34 J . S 4.13570 x 10 -15 e eVS . h= h/2n 1.054589.X 10 34.J 34 . J. 6.58217 x 10-16 eV . s Gravitational constant G 6.6726 X 10-11 N . m2 /kg2 Avogadro's number NA 6.022045 x 1023 mole -1 Universal gas constant K 8.3144 J/mole . K Stefan-Boltzmann constant 5.6703 X 10-8 W/m2 . K4 Rydberg constant 1.0973732 x 10' m-1 Hydrogen ionization energy 13.60580 eV Bohr radius do 5.291771 x 10-11 m Bohr magneton P B 9.27408 X 10-24 J/T 5.78838 X 10-eV/T Nuclear magneton 5.05084 X 10-27 J/T 3.15245 x 10-8 eV/T Fine structure constant 1/137.0360 hc 1239.853 MeV . fm hc 197.329 MeV . fm e 2/4 TIED 1.439976 MeV . fm PARTICLE REST MASSES MeV/c2 Electron 5.485803 X 10-4 0.511003 Proton 1.00727647 938.280 Neutron 1.00866501 939.573 Deuteron 2.01355321 1875.628 Alpha 4.00150618 3727.409 0.1498300 139.5669 0.1448999 134.9745 0.1134292 105.6595 CONVERSION FACTORS 1 e.V = 1.602189 X 10-19 J 1 b = 10-28 m2 1 u = 931.502 MeV/c2 1 Ci = 3.7 x 1010 decays/s = 1.660566 X 10-27 kgShow your work and explain your reasoning clearly. You are allowed one page of notes (both sides). PLEASE WRITE YOUR STUDENT ID ON ALL PAGES! PLEASE PUT THE PROBLEM # ON TOP OF ANY ADDITIONAL SHEETS YOU USE! Group - 1 2 7 9 10 11 12 13 15 16 17 18 Period 2 I He 4 10 Be N O Ne 11 12 14 15 16 18 Na Ma Al 5 Ar 19 20 21 23 24 25 26 27 28 29 30 31 32 33 34 35 36 ca Sc V Cr Mn Fe Co Ni Cu Zn Ga Ge AS Se Kr 38 39 40 43 45 46 48 49 50 TC 52 53 54 Rb Sr Zr Nb Mo To Ru 3h Pd Ag Cd In Sn sb Te Xe 56 12 76 78 79 80 81 32 84 86 CS Ba Hf Ta W Re Os pt Au Ha TI Ri Po At Rn 87 88 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 Ra Rf Db Sq HS Mt DS Rg En Mh Mc LV TS Og Lanthanides 57 58 59 60 62 63 64 65 66 67 68 69 70 71 La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Actinides 89 90 91 93 94 95 96 9 98 99 100 101 102 103 Ac Th Pa Np Pu Am Cm BK Cf ES Fm Md No Lr (E1) = 1.0 x 1014 A2/3 E3 MIC 1(E2) = 7.3 x 107 A4/3E5 Atotal = Ay (1 + a); a = (E3) = 34 A2 EZ Feather's Rule: (E4) = 1.1 x 10-5 A8/3 E9 Energy (MeV) Range (cmz) = 2 1(E5) = 2.4 x 10-12 A10/3 E11 A(M1) = 5.6 X 1013 E3 Bragg-Kleeman Rule: 2(M2) = 3.5 x 107 A2/3 E5 R1 _ P2 VA1 2(M3) = 16 A4/3 EZ R2 P1 VA 2 2(M4) = 4.5 x 10-6 ARE9 2(M5) = 7.4 x 10-13 A8/3611 At = 8 sing