Assume every uranium-235 nucleus in a 1.00 g sample undergoes fission and each fission releases 200 MeV. Take Avogadro constant Nₐ = 6.0×10²³ mol⁻¹ and 1 eV = 1.6×10⁻¹⁹ J. If the total released energy is approximately N×10¹⁰ J, find N rounded to the nearest integer.
Physics · Nuclear physics · nuclear fission and fusion ,nuclear reactor
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Question

Assume every uranium-235 nucleus in a 1.00 g sample undergoes fission and each fission releases 200 MeV. Take Avogadro constant Nₐ = 6.0×10²³ mol⁻¹ and 1 eV = 1.6×10⁻¹⁹ J. If the total released energy is approximately N×10¹⁰ J, find N rounded to the nearest integer.

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

G1 Physics · Accepted Answer

Number of moles of U-235: n = 1.00 ÷ 235 mol. Number of U-235 nuclei: number of nuclei = (1.00 ÷ 235)×6.0×10²³ ≈ 2.553×10²¹. Energy per fission: 200 MeV = 200×10⁶×1.6×10⁻¹⁹ J = 3.2×10⁻¹¹ J. Total energy: E = 2.553×10²¹×3.2×10⁻¹¹ ≈ 8.17×10¹⁰ J. Therefore, E ≈ 8×10¹⁰ J. Hence N = 8.