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Homework answers / question archive / 9-13 When a spent fuel rod is removed from a reactor core, it is stored in an on-site storage pool of water so that the most intense, short-lived radioactive fission products decay, and the rod is safe for further handling and possible shipment to a reprocessing plant
9-13 When a spent fuel rod is removed from a reactor core, it is stored in an on-site storage pool of water so that the most intense, short-lived radioactive fission products decay, and the rod is safe for further handling and possible shipment to a reprocessing plant. Consider for simplicity only the radioisotope xenon- 133 which B decays into a stable isotope with a half-life of 5.27 days. If a 30-kg fuel rod contains 0.1 percent by mass of Xe's when removed from the core, what is the minimum time it should be stored in the pool so that the activity may not exceed 300 mci?
answer is below, please refer below
Rate of decay = d X N ( N = no . of atoms) where I = decay constant = on 2 ty ty = 5.27 days = 5.27 x 24 x 3600 sec ( given) Now, wer wish the rate of decay to be < 300 mle J Rate of decay < < 3x 3.7 x 10" decays/ sec On 2 AN *0 . 3 X 3 7 x 10 10 5-27 X24X3600 NS 7.29 x 10", atoms This should be the number of atoms of yo' in the sample after storage in the pool of water 7 No of males n = N = 7:29 *10's NA 6.022 X1023 n = 1.21 x 10-8 m = M (M= 133 (et Xe 123) M When fuel rod is placed in water, mass of Xe" was 0. 1% of 30 kg. ) my = 30 g Radioactive decay lane - N = No Q- At = On (m A In 2 t= 5.27 k In 30X106 1.61 In 2 ~ 127.28 days
