To complete the nuclear reaction equation where plutonium-239 (\(^{239}{94}\text{Pu}\)) transforms into curium-242 (\(^{242}{96}\text{Cm}\)) by absorbing an alpha particle (\(^{4}{2}\alpha\)) and emitting a neutron (\(^{1}{0}\text{n}\)), we can represent this process as follows:
- Start with the plutonium-239 nuclide.
- Add the alpha particle to it.
- Subtract the neutron produced in the reaction from the total mass and atomic numbers.
The reaction can be represented as:
\[ ^{239}{94}\text{Pu} + ^{4}{2}\alpha \rightarrow ^{242}{96}\text{Cm} + ^{1}{0}\text{n} \]
The complete nuclear reaction equation is:
\[ ^{239}{94}\text{Pu} + ^{4}{2}\text{He} \rightarrow ^{242}{96}\text{Cm} + ^{1}{0}\text{n} \]
In this equation, \(^{4}_{2}\text{He}\) is used to represent the alpha particle. This indicates that when plutonium-239 captures an alpha particle, it becomes curium-242 and emits a neutron.
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