Consider a plane source located at x = 0 of a finite slab (infinite in the y and equation for this problem was solved in class. 4. direction). the diffusion a) consider a slab of width 20 cm, with d 1 cm. plot the scalar flux in the slab for several different values of and so, the values i want are 1) ea-0.1 cm1 and so 1000 n/cm2-s, 2) a-0.01 cm1 and so- 100 n/cm2-s, .001 cm" and so-10 ncm. s. 3) 4) ? ? = 0.0001 cm" and so= 1 n/cm2-s. plot all of these solutions on the same plot. what is happening to the shape of the scalar flux as l gets small? b) solve the same problem . (go back to the original diffusion equation, write it for . get the general solution, and apply the boundary condition and source condition.) comment on the shape of the solution compared to what you observed in part (a). [not credit without some comments and discussion.] c) go back to the solution obtained in class. show by taking the appropriate mathematical lmits(s) that is the same as when + 0 this solution agrees with your answer to part (b) [hint, the limit as ? - the limit as l ? 00,] consider a slice of the slab, say from x1 to x2, in which both xi and x2 are in the left half of the slab. assuming e0, compute the following rates, per unit y-z area, for neutrons the slice: d) * absorption [note: integrate absorption rate density over the slice], net outleakage across face at x2 [note: which way is "out" of the slice? ]. net outleakage across face at xi [note: which way is "out" of the slice? ], show that things add up the way they should, that is, the neutrons are conserved. e) what happens to the solution of part (a), with e-0, if the slab width goes to infinity? does this make physical sense to you? explain.