When a neutron collides with a uranium-235 nucleus it can induce a variety of fission reactions.
One such reaction is
$${ } _ { 92 } ^ { 235 } \mathrm { U } + { } _ { 0 } ^ { 1 } \mathrm { n } \rightarrow { } _ { 54 } ^ { 140 } \mathrm { Xe } + { } _ { 38 } ^ { 94 } \mathrm { Sr } + 2 { } _ { 0 } ^ { 1 } \mathrm { n }$$
The following mass values are known:
$$\begin{array} { l l }
{ } _ { 54 } ^ { 140 } \text { Xe: } & 139.921620 \mathrm { u } \
{ } _ { 38 } ^ { 94 } \mathrm { Sr } : & 93.915367 \mathrm { u } \
{ } _ { 92 } ^ { 235 } \mathrm { U } : & 235.043924 \mathrm { u } \
{ } _ { 0 } ^ { 1 } \mathrm { n } : & 1.008665 \mathrm { u }
\end{array}$$
What mass of uranium is needed to produce a 10-kiloton yield? $\left( 1 \mathrm { u } = 931.5 \mathrm { MeV } / c ^ { 2 } = 1.66054 \times \right.$ $10 ^ { - 27 } \mathrm {~kg}$, 1-kiloton yield $= 5.0 \times 10 ^ { 12 } \mathrm {~J}$ )

Question

When a neutron collides with a uranium-235 nucleus it can induce a variety of fission reactions.
One such reaction is
$${ } _ { 92 } ^ { 235 } \mathrm { U } + { } _ { 0 } ^ { 1 } \mathrm { n } \rightarrow { } _ { 54 } ^ { 140 } \mathrm { Xe } + { } _ { 38 } ^ { 94 } \mathrm { Sr } + 2 { } _ { 0 } ^ { 1 } \mathrm { n }$$
The following mass values are known:
$$\begin{array} { l l } 
{ } _ { 54 } ^ { 140 } \text { Xe: } & 139.921620 \mathrm { u } \
{ } _ { 38 } ^ { 94 } \mathrm { Sr } : & 93.915367 \mathrm { u } \
{ } _ { 92 } ^ { 235 } \mathrm { U } : & 235.043924 \mathrm { u } \
{ } _ { 0 } ^ { 1 } \mathrm { n } : & 1.008665 \mathrm { u }
\end{array}$$
What mass of uranium is needed to produce a 10-kiloton yield? $\left( 1 \mathrm { u } = 931.5 \mathrm { MeV } / c ^ { 2 } = 1.66054 \times \right.$ $10 ^ { - 27 } \mathrm {~kg}$, 1-kiloton yield $= 5.0 \times 10 ^ { 12 } \mathrm {~J}$ )

Quizplus · Accepted Answer

The mass defect is calculated by subtracting the mass of the products from the mass of the reactants. This mass defect is converted to energy using $E=mc^2$. The energy per fission is then used to find the total mass of uranium needed to produce a 10-kiloton yield.

When a Neutron Collides with a Uranium-235 Nucleus It Can