## (Solved) NE124 Radioactive Waste Management, Spring 2017 Department of Nuclear Engineering, University of California, Berkeley Homework Set No. 2 Due 5 p....

Problem B with detailed solutions please, thank you

NE124 Radioactive Waste Management, Spring 2017
Department of Nuclear Engineering, University of California, Berkeley Homework Set No. 2
Due 5 p.m. February 10, 2017
(A) (4 points) Consider the radioactive decay chain, U-234 Th-230 Ra-226 .
Assume that there exists 1 gram of U-234, and no Th-230 or Ra-226 exists initially.
(1) Calculate the radioactivity for 1 gram of U-234.
(2) Plot the log10 of radioactivities of these three radionuclides as a function of log10 of
time for the range between 1 year and 100 million year. (This should show that these
three radionuclides eventually establish a secular equilibrium.)
(3) If there is also 1 gram of Th-230, will this decay chain reach a secular equilibrium
eventually? If so, is the equilibrium radioactivity different from that obtained in (2)?
(Hint: you can consider two decay chains: one starting with U-234 and the other
starting with Th-230. The radioactivity of Th-230 can be obtained by the sum of these
chains. Same for Ra-226. You can obtain the answer by showing mathematical
manipulation or results of numerical calculation.)
(B) (6 points) A uranium isotope separation plant has been operating as an ideal cascade
to produce 200kg of 235U/day in product containing 3.2 w/o 235U while stripping tails to
0.2 w/o, from natural uranium feed containing 0.711 w/o 235U. Assume that the plant can
be rearranged to operate as an ideal cascade at constant separative capacity when
operating conditions are changed individually as described in each of the following ways:
(1) If tails assay were raised to 0.3 w/o, what would be the feed and product rates?
(2) If product assay were raised to 4.0 w/o, what would be the feed and product rates?
(3) If the natural uranium feed rate were changed to 45,000 kg/day, at what rate could 3.2
w/o product be produced? What would be the tails assay?
(4) If 3000 kg/day of uranium containing 2.0 w/o 235U were also to be produced while
keeping the tails assay constant at 0.2 w/o, at what rate could 3.2 w/o product be
made? What would be the natural uranium feed rate? 1

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