Question

If a nuclear fission reactor produces an average power of 1.0 GW over the course of a year, what mass of U-235 has undergone fission in a 365-day year? Assume on average 200 MeV energy is released per fission reaction. Hint: One mole of uranium (containing 6.023 x 1023 nuclei) has a mass of 235.043930 g.
please include units and where they cancel out. please explain. I do not understand where each number fits in. thank you

Answer 1

3.2 x 10-11 7 7 fo Power - IGN=109w. time = year= 365x24x60x60 = 3.15x10 see 1 year= Powerf time = 10 x 3.15x10 =3.15x10 I = E fission oncleus) = - 200 MeV=200 x 106 x 16 760-19 J23.2410"} Energy per Lex N= total number of nachei undergone fissiba in Energy released 1 year i E=Nx3.2x10-11 3.15x1016 = N*3.2x10-11 . N= 3.15x1016 9,8x1026 6.023X1023 3 = 1.627 x 10 nosan I mol contains nuculu i. Number of mals (o) in N nuclei - 9.8*1026 mass of imol = 235 6.023x1023 3 Hog = 235.043930g of mol = 1.627x103x235.043930 = 382-439x10 M = 382.439kg = mass of warum indergone fission in I year. max