If $200 \, MeV$ of energy is released per fission of a $_{92}U^{235}$ nucleus, how many nuclei must undergo fission per second to produce a power of $1 \, kW$?

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 an $\alpha -$ decay,the kinetic energy of the $\alpha -$ particle is $48 \ MeV$ and the $Q$ value of the reaction is $50 \ MeV$. The mass number of the mother nucleus is (assume that the daughter nucleus is in the ground state).

The energy released in the explosion of an atom bomb is mainly due to $\qquad$ .

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

In the proton-proton cycle in the Sun,the energy released when an electron and its antiparticle combine is $\qquad$ .