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8-HW Solutions

8-HW Solutions - HW#8 Nuclear Homework 8 Solutions Phys320...

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HW #8: Nuclear Phys320 – Spring 2007 (Reshchikov) p. 1 Homework # 8 Solutions Problem 1 Compute the total binding energy B (in MeV) and the binding energy per nucleon B/A (in MeV/nucleon) for the stable isotope 66 Zn (65.926037). () 222 6 6 30 22 2 2 ( ) ( ) where 30 and 66 30 36 for Zn 30(1.007825 amu) 36(1.008665 amu) (65.926037 amu) (0.6207 amu) 0.6207 amu 931.5 MeV amu 578.2 MeV 578.2 MeV 66 nucle HnA BZ M cN M c M c Z N Bc cc c c B A =+− = = = = == = 8.76 MeV/nucleon ons = Problem 2 Compute the total binding energy B (in MeV) and the binding energy per nucleon B/A (in MeV/nucleon) for unstable isotope 74 Zn (73.929460). Its half-time is 95.6 s. 7 4 30 2 2 ( ) ( ) where 30 and 74 30 44 for Zn 30(1.007825 amu) 44(1.008665 amu) (73.929460 amu) (0.68655 amu) 0.6866 amu 931.5 MeV amu 639.5 MeV 639.5 MeV 74 nucl M M c M c Z N c c B A = = = = = 8.642 MeV/nucleon eons = Problem 3 The activity of a radioactive sample is initially 10 14 decays per second and it decreases to 10 10 decays per second after 30 days. Find τ and t 1/2 of this radioactive element in any appropriate time units (s, min, h, days,…, as you prefer). Also, find the initial number of radioactive nuclei in the sample. ( ) 0 55 1/2 1 0 10 1 14 Solving for in the decay equation R R exp gives: 30 days × 24 h/day 3.257 days = 78 h = 2.8 10 and ln2 2.257 days = 54 h 1.95 10 10 ln ln 10 Using the differential e τ t t τ st τ s R s R s τ =− = × = = = × ⎛⎞ ⎜⎟ ⎝⎠ 00 14 19 quation R dN/dt = N/ , the initial number of radioactive nuclei is given by: 3600 s 10 decays N

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8-HW Solutions - HW#8 Nuclear Homework 8 Solutions Phys320...

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