Explain what is gong on with the solution and show all the work that matches the solution of the question since the solution work provided is confusing.

1. Consider a sphere of uranium with the following composition: "U 97.6 at% and U 2.4 at% (density 19.1 g/cm'); use the diffusion theory applying fast systems conditions to determine: a) critical radius of the sphere with vacuum boundary conditions; b) reflector saving when the sphere is surrounded by water (assume infinite reflector). Compare the results with those obtained using MCNP (turn in the code). Use the following data: Element Oc Of Str V 235 TJ 0.15 b 1.25 b 5.03 b 2.60 238 7 0.10 b 0.21 b 5.73 b 2.80 HO 0.13 b 16.68 b a) B2 = B. VEf - Za R = = 12.26 cm D V( vE f - E2 ) /D D = 1.35 cm R = R-2D =9.56cm Uranium Sphere 1 1 -19.1 -1 imp : n=1 3 0 1 imp : n=0 1 so 8 . 5 m1 92235 0 . 976 92238 0. 024 ksrc 0. 0. 0. kcode 1000 1 100 300 print mode n Keff = 1.00480 + 0.00130 R = 8.5 cm b) BRctg(BR)-1 = R D L De = 1.35 cm D, = 0.597 cm Bm = 0.256 cm- Ly = 11.72 cm R = 5.06 cm reflector saving 4.5 cmUranium Sphere with Water Reflector 0.5 1 -19.1 -1 imp : n=1 LHS 0 RHS WNA 2 -1 . 1 -2 imp : n=1 -0.56 O 2 imp : n=0 -1/ SO 6. 4 NH SO 50 . -1.5/ -2 m1 92235 0. 976 92238 0 . 024 m2 1001 2. 8016 1. -2.5/ ksrc 0. 0. 0. 0.5 1 3 kcode 1000 1 100 300 1.5 2 2.5 BR print mode n Keff = 1.00635 + 0.00174 R=6.4 cm refector saving 2.1 cm In MCNP an infinite volume is not allowed but to simulate an infinite reflector we can just make the reflector thick enough to be "effectively" infinite