The binding energy per nucleon for deuteron $(_1H^2)$ and helium $(_2He^4)$ are $1.1 \, MeV$ and $7 \, MeV$ respectively. When two deuterons fuse to form a helium nucleus,the energy released is ........... $MeV$.

Fission of nuclei is possible because the binding energy per nucleon in them

$U^{235}$ nuclear reactor generates energy at a rate of $3.70 \times 10^7 \text{ J/s}$. Each fission liberates $185 \text{ MeV}$ of useful energy. If the reactor has to operate for $144 \times 10^4 \text{ s}$, then the mass of the fuel needed is (Assume Avogadro's number $= 6 \times 10^{23} \text{ mol}^{-1}$, $1 \text{ eV} = 1.6 \times 10^{-19} \text{ J}$) (in $\text{ kg}$)

The electrostatic energy of a nucleus of charge $Ze$ is equal to $\frac{k Z^2 e^2}{R}$,where $k$ is a constant and $R$ is the nuclear radius. The nucleus divides into two daughter nuclei of charges $\frac{Ze}{2}$ and equal radii. The change in electrostatic energy in the process when they are far apart is

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.

If the energy released per fission of a ${ }_{92}^{235} U$ nucleus is $200 \text{ MeV}$, the energy released in the fission of $0.1 \text{ kg}$ of ${ }_{92}^{235} U$ in kilowatt-hour is: