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

The binding energy per nucleon of ${}_3^7Li$ and ${}_2^4He$ nuclei are $5.60 \, MeV$ and $7.06 \, MeV$, respectively. In the nuclear reaction ${}_3^7Li + {}_1^1H \to 2 \, {}_2^4He + Q$, the value of energy $Q$ released is ............ $MeV$.

Which of the following statement$(s)$ is/are correct?
$(1)$ The rest mass of a stable nucleus is less than the sum of the rest masses of its constituent nucleons.
$(2)$ The rest mass of a stable nucleus is greater than the sum of the rest masses of its constituent nucleons.
$(3)$ Nuclear fusion involves the fusion of two light nuclei to form a heavier nucleus.
$(4)$ Nuclear fission involves the release of energy by the splitting of a heavy nucleus.

Fast neutrons can be easily slowed down by:

Heavy water is

For the nuclear fusion reaction ${ }_1^2 H +{ }_1^3 H \rightarrow{ }_2^4 He +{ }_0^1 n$,the temperature to which the gases must be heated is $3.7 \times 10^9 \, K$. The potential energy between two nuclei is closest to ........ $J$ (Boltzmann's constant $k = 1.38 \times 10^{-23} \, J/K$).