When a $_4Be^9$ atom is bombarded with $\alpha$-particles,one of the products of nuclear transmutation is $_6C^{12}$. The other product is:

In the given nuclear reaction
${ }_{4}^{9} Be+{ }_{2}^{4} He \rightarrow{ }_{6}^{12} C+X$
$X$ represents $\qquad$

Statement $1$: Energy is released when a heavy nucleus undergoes fission and when light nuclei undergo fusion.
Statement $2$: For heavy nuclei,the binding energy per nucleon decreases as $Z$ increases. For light nuclei,the binding energy per nucleon increases as $Z$ increases.

In a fission reaction ${}_{92}^{236}U \to {}^{117}X + {}^{117}Y + n + n$,the binding energy per nucleon of $X$ and $Y$ is $8.5\,MeV$,whereas that of ${}^{236}U$ is $7.6\,MeV$. The total energy liberated will be about:

$A$ nuclear reactor generates power by fission of ${}_{92}U^{235}$ into two equal fragments of ${}_{46}Pd^{116}$ with the emission of two $\gamma$-rays of $5.2 \text{ MeV}$ each and three neutrons. The average binding energies per nucleon of ${}_{92}U^{235}$ and ${}_{46}Pd^{116}$ are $7.2 \text{ MeV}$ and $8.2 \text{ MeV}$ respectively. The usable energy released per fission event is ......... $\text{MeV}$.

Which of the following statement$(s)$ is/are correct?