Determine the energy released by 1 g of natural uranium, given that each fission event releases 200 MeV and the fissionable isotope ²³⁵ U constitutes 0.7 % by weight in natural uranium.

Step-by-step solution

Mass of ²³⁵ U in 1 g of natural uranium is m = 0.7 100 1 g = 0.007 g . Number of atoms of ²³⁵ U in 0.007 g is N = 0.007 235 6.022 10²³ 1.794 10¹⁹ . Energy released per fission is E₁ = 200 MeV = 200 10^6 1.6 10⁻¹⁹ J = 3.2 10⁻¹¹ J . Total energy released is E = N E₁ = 1.794 10¹⁹ 3.2 10⁻¹¹ J 5.7 10^8 J .