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(A) Statement $1$ is true because in nuclear fission of heavy nuclei,the binding energy per nucleon increases,resulting in a release of energy. Simila

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Statement $1$ is true and Statement $2$ is false.

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(A) Statement $1$ is true because in nuclear fission of heavy nuclei,the binding energy per nucleon increases,resulting in a release of energy. Similarly,in nuclear fusion of light nuclei,the binding energy per nucleon increases,also resulting in a release of energy.Statement $2$ is false. The binding energy per nucleon $(E_{bn})$ versus mass number $(A)$ graph shows that for light nuclei,$E_{bn}$ increases rapidly with $A$. For heavy nuclei,$E_{bn}$ decreases slowly as $A$ increases beyond $A = 56$. It does not depend solely on the atomic number $Z$ in the manner described,and the trend stated is incorrect.

Statement $1$: Energy is released during the fission of heavy nuclei or the fusion of light nuclei.
Statement $2$: Binding energy per nucleon increases with an increase in $Z$ for heavy nuclei,whereas it decreases with an increase in $Z$ for light nuclei.

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Statement $1$: Energy is released during the fission of heavy nuclei or the fusion of light nuclei.Statement $2$: Binding energy per nucleon increases with an increase in $Z$ for heavy nuclei,whereas it decreases with an increase in $Z$ for light nuclei.