3. (a) Consider a fast, spherical reactor. It is made of Pu-239 with properties given below. Outside of the reactor is vacuum. Find the critical radius for this reactor. What is the flux profile at steady-state? Plot the flux profile for a total power rating of 100 kW. (b) Now consider another reactor with a radius 1 cm less than the critical radius (made out of the same material). What is the neutron flux at steady-state in this reactor? (c) A point source is placed at the center of this reactor emitting 100 n/s. Find the flux distribution due to the point source. (d) Find the flux distribution due to the point source assuming the fission cross section of the material is zero while the absorption cross section is kept at the same value as in case b). (e) Plot and compare the flux profiles for cases c and d. v= 2.98;0 =1.85 b;0=0.26 b;0,=6.8b; p=15.4 g/cm. (These properties are given in Problem 5.32 in D & H.)