A nuclear power plant delivers a continuous electrical power of 1.0 MW with an overall efficiency of 25%. Each U-235 fission releases 200 MeV. Take Avogadro constant Nₐ = 6.0×10²³ mol⁻¹ and 1 eV = 1.6×10⁻¹⁹ J. If the mass of U-235 actually fissioned in one day is N g, find N rounded to the nearest integer.
Physics · Nuclear physics · nuclear fission and fusion ,nuclear reactor
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Question

A nuclear power plant delivers a continuous electrical power of 1.0 MW with an overall efficiency of 25%. Each U-235 fission releases 200 MeV. Take Avogadro constant Nₐ = 6.0×10²³ mol⁻¹ and 1 eV = 1.6×10⁻¹⁹ J. If the mass of U-235 actually fissioned in one day is N g, find N rounded to the nearest integer.

Physics · Nuclear physics · nuclear fission and fusion ,nuclear reactor

G1 Physics · Accepted Answer

Electrical energy delivered in one day: E(electrical) = 1.0×10⁶×86400 = 8.64×10¹⁰ J. Efficiency is η = E(electrical) ÷ E(nuclear) = 0.25. Therefore, E(nuclear) = 8.64×10¹⁰ ÷ 0.25 = 3.456×10¹¹ J. Energy per fission: E(fission) = 200×10⁶×1.6×10⁻¹⁹ = 3.2×10⁻¹¹ J. Number of fissions: N(fissions) = 3.456×10¹¹ ÷ 3.2×10⁻¹¹ = 1.08×10²². Number of moles fissioned: n = 1.08×10²² ÷ 6.0×10²³ = 0.018 mol. Mass fissioned: m = 0.018×235 = 4.23 g. Rounded to the nearest integer, N = 4.