The radioactive decay of samarium-147 (\(^{147}_{62}\text{Sm}\)) by alpha emission can be represented by the following balanced nuclear equation:
\[ ^{147}{62}\text{Sm} \rightarrow ; ^{143}{58}\text{Ce} + ; ^4_{2}\text{He} \]
In this equation:
- \(^{147}_{62}\text{Sm}\) is samarium-147.
- \(^{143}_{58}\text{Ce}\) is cerium-143, the daughter nuclide produced from the decay.
- \(^{4}_{2}\text{He}\) represents the alpha particle emitted during the decay process.
The sum of the atomic numbers and the mass numbers on both sides of the equation remain balanced, which is consistent with the principles of nuclear reactions.
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