To complete the nuclear chemical equation for the transformation of aluminum-27 into sodium-24 by absorbing a neutron and emitting an alpha particle, we can represent the process as follows:
The aluminum-27 nuclide (\(^{27}{13}\text{Al}\)) absorbs a neutron (\(^{1}{0}\text{n}\)), resulting in an excited state of aluminum-28, which then emits an alpha particle (\(^{4}{2}\text{He}\)) to form sodium-24 (\(^{24}{11}\text{Na}\)).
The full equation can be written as:
\[ ^{27}{13}\text{Al} + ^{1}{0}\text{n} \rightarrow ^{24}{11}\text{Na} + ^{4}{2}\text{He} \]
This equation summarizes the transformation of aluminum-27 into sodium-24 by absorbing a neutron and emitting an alpha particle.