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hmwk4 - Department of Chemical Engineering University of...

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Department of Chemical Engineering University of California, Santa Barbara Eng 5A Fall 2001 Instructor: David Pine Homework #4 Homework due: Wednesday, 24 October 2001 Note: Every student should work on the homework by himself or herself. It is ok to to get help from others, but the work should be your own. Reading: Chapter 8 in The Mathematica Primer discusses troubleshooting strategies. It’s useful reading. Demo 7 illustrates many of the concepts addressed in problems 2-5 on lists & matrices. 1. Consider the radioactive decay of 239 U 239 Np 239 Pu. We can model these three reactions by the ODEs d [U] dt = - k u [U] (1) d [Np] dt = k u [U] - k n [Np] (2) d [Pu] dt = k n [Np] (3) (a) Solve these ODEs using Mathematica by the following method. First solve Eq. (1) to obtain an expression for the time dependent concentration [U]( t ). Assume that 100% of the starting material is uranium (U). Then, substitute your solution for [U]( t ) into Eq. (2) and solve for [Np]( t ). Finally, use these results to obtain an expression for [Pu]( t ). Hint: [U]( t ) + [Np]( t ) + [Pu]( t ) = 1
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