# Problem: Nuclear reactors generate power by harnessing the energy from nuclear fission. In a fission reaction, uranium-235 absorbs a neutron, bringing it into a highly unstable state as uranium-236. This state almost immediately breaks apart into two smaller fragments, releasing energy. One typical reaction is 235 92U+10n→ 140 54Xe+9438Sr+210n, where 10n indicates a neutron. In this problem, assume that all fission reactions are of this kind. In fact, many different fission reactions go on inside a reactor, but all have similar reaction energies, so it is reasonable to calculate with just one. The products of this reaction are unstable and decay shortly after fission, releasing more energy. In this problem, you will ignore the extra energy contributed by these secondary decays. You will need the following mass data: mass of 235 92U=235.04393u, mass of 140 54Xe=139.92144u, mass of 9438Sr=93.91523u, and mass of 10n=1.008665u.Using fission, what mass m of uranium-235 would be necessary to supply all of the energy that the United States uses in a year, roughly 1.0 x 1019J, given that reaction energy, Q = 185 MeV?Express your answer in kilograms to two significant figures.

###### FREE Expert Solution

Total required mass:

m' = Nm

The number of reactions:

$\begin{array}{rcl}\mathbf{N}& \mathbf{=}& \frac{\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{×}{\mathbf{10}}^{\mathbf{19}}}{\mathbf{\left(}\mathbf{185}\mathbf{\right)}\mathbf{\left(}\mathbf{1}\mathbf{.}\mathbf{6}\mathbf{×}{\mathbf{10}}^{\mathbf{-}\mathbf{13}}\mathbf{\right)}}\end{array}$

###### Problem Details

Nuclear reactors generate power by harnessing the energy from nuclear fission. In a fission reaction, uranium-235 absorbs a neutron, bringing it into a highly unstable state as uranium-236. This state almost immediately breaks apart into two smaller fragments, releasing energy. One typical reaction is 235 92U+10n→ 140 54Xe+9438Sr+210n, where 10n indicates a neutron. In this problem, assume that all fission reactions are of this kind. In fact, many different fission reactions go on inside a reactor, but all have similar reaction energies, so it is reasonable to calculate with just one. The products of this reaction are unstable and decay shortly after fission, releasing more energy. In this problem, you will ignore the extra energy contributed by these secondary decays. You will need the following mass data: mass of 235 92U=235.04393u, mass of 140 54Xe=139.92144u, mass of 9438Sr=93.91523u, and mass of 10n=1.008665u.

Using fission, what mass m of uranium-235 would be necessary to supply all of the energy that the United States uses in a year, roughly 1.0 x 1019J, given that reaction energy, Q = 185 MeV?

Express your answer in kilograms to two significant figures.