The source of the Sun's energy is

$A$ nucleus of mass $M + \Delta m$ at rest decays into two daughter nuclei of equal mass $M/2$. If the speed of light is $c$,the speed of each daughter nucleus is:

In the nuclear fusion reaction $_1^2H + _1^3H \to _2^4He + n$,the repulsive potential energy between the two nuclei is $7.7 \times 10^{-14} \, J$. To what temperature must the gas be heated to initiate the reaction? $[k = 1.38 \times 10^{-23} \, J/K]$

$A$ nucleus ${}^{220}X$ at rest decays by emitting an $\alpha$-particle. If the kinetic energy of the daughter nucleus is $0.2 \, MeV$,the $Q$-value of the reaction is ........ $MeV$.

Calculate and compare the energy released by
$(a)$ fusion of $1.0 \; kg$ of hydrogen deep within the Sun and
$(b)$ the fission of $1.0 \; kg$ of $^{235} U$ in a fission reactor.

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.