Answer
Initial mass = 462 kg
Work Step by Step
In this fission, after 3 years of consuming half of the radioactive substance, the power produced is 200 MW.
To find mass, first we need to calculate the energy from power-time equation.
3 years = $9.46 \times 10^{7}$ * Assuming a year is 365 days.
$ E = p \Delta t $
$ E = (200 MW) (9.46 \times 10^{7} s) $
$E = 1.89 \times 10^{16} J$
Change J to MeV
$E= (1.89 \times 10^{16} J ) (1.60 \times 10^{-19}J/eV)$
$E = 1.18 \times 10^{29} MeV$
Calculate how much fission has occured
$ \frac{1.18 \times 10^{29} MeV}{200 MeV} = 5.6 \times 10^{26} $
When this amount of fission occured, it's just half of the total substance.
thus, multiply with 2
$(2)(5.6 \times 10^{26}) = 1.18 \times 10^{27} nuclei$
The mass of $^{235}U$ nucleus is
$ (235u) (1.18 \times 10^{27}) = 3.90 \times 10^{-25} kg$
To know the total mass, multiply the total nuclei with the nuclei mass
$ (3.90 \times 10^{-25} kg) (1.18 \times 10^{27}) = 462 kg$
