Question

If one pound (453.6 g) of bituminous coal produces 13,000 BTU when fully combusted, determine the mass (in grams) of U-235 that would be consumed via fission to produce the same amount of energy, assuming 200 MeV per fission is released.

Answer 1

we have 13000 Btu energy released by coal,

we need same energy from U-235

1 fission gives 200 MeV

1 MeV = 1.5186 x 10^-16 Btu

200 MeV/atom = 200 x1.5186 x 10^-16 Btu = 3.0371 x 10^-14 Btu/atom

200 MeV = 1 atom fission

no of fissions for 13000 Btu = 13000 Btu / 3.0371 x 10^-14 Btu/atom = 4.2804 x 10¹⁷ atoms

mass of one uranium atom = 235 amu = 235 g / avogadro no. = 235 g / 6.022 x 10²³ atoms

mass of 4.2804 x 10¹⁷ atoms = 4.2804 x 10¹⁷ atoms x 235 g / 6.022 x 10²³ atoms = 0.00016703649 g

= 1.67 x 10^-4 g

Ans = 1.67 x 10^-4 g