$A$ certain stable nuclide,after absorbing a neutron,emits a $\beta$-particle and the new nuclide splits spontaneously into two $\alpha$-particles. The nuclide is

Let $E_1$ and $E_2$ be the binding energies of two nuclei $A$ and $B.$ It is observed that two nuclei of $A$ combine together to form a $B$ nucleus. This observation is correct only if

If the binding energy per nucleon for a deuteron is $1.112 \, MeV$ and for an $\alpha$-particle is $7.07 \, MeV$,then for the reaction $2 \, (_1H^2) \rightarrow _2He^4 + Q$,the value of $Q$ is .......... $MeV$.

During the nuclear fusion reaction,

$A$ star has $100 \%$ helium composition. It starts to convert three ${ }^4 He$ into one ${ }^{12} C$ via the triple alpha process as ${ }^4 He + { }^4 He + { }^4 He \rightarrow { }^{12} C + Q$. The mass of the star is $2.0 \times 10^{32} \ kg$ and it generates energy at the rate of $5.808 \times 10^{30} \ W$. The rate of converting these ${ }^4 He$ nuclei to ${ }^{12} C$ is $n \times 10^{42} \ s^{-1}$,where $n$ is. . . . . . . [Take,mass of ${ }^4 He = 4.0026 \ u$,mass of ${ }^{12} C = 12 \ u$,$1 \ u = 1.66 \times 10^{-27} \ kg$,$c = 3 \times 10^8 \ m/s$]

How much energy is produced from the combustion of $1\, kg$ of coal?