If $1 \, g$ of hydrogen is converted into $0.993 \, g$ of helium in a thermonuclear reaction,the energy released in the reaction is ......... $J$.

$U^{235}$ 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 $\text{ kg}$)

Carbon-$11$ decays to boron-$11$ according to the following formula:
${ }_{6}^{11} C \rightarrow{ }_{5}^{11} B +e^{+}+ v _{e}+0.96 \,MeV$
Assume that,positrons $\left(e^{+}\right)$ produced in the decay combine with free electrons in the atmosphere and annihilate each other almost immediately. Also,assume that the neutrinos $\left(v _{e}\right)$ are massless and do not interact with the environment. At $t=0$,we have $1 \,\mu g$ of ${ }_{6}^{11} C$. If the half-life of the decay process is $t _{0}$,the net energy produced between time $t=0$ and $t=2 t _{0}$ will be nearly ........... $MeV$.

In a nuclear reactor,the fuel is consumed at the rate of $1 \times 10^{-3} \text{ g s}^{-1}$. The power generated in kW is

$113$. Energy released in the fission of a single uranium nucleus is $200 \text{ MeV}$. Then the number of fissions per second to produce $5 \text{ mW}$ power is

The binding energy per nucleon of deuteron $({ }_{1} H^{2})$ and the helium atom $({ }_{2} He^{4})$ are $1.1 \ MeV$ and $7 \ MeV$ respectively. If two deuteron nuclei fuse to form a single helium nucleus,then the energy released is: (in $MeV$)