How much energy is produced by the fission of $1\, kg$ of uranium?

$A$ $1000 \; MW$ fission reactor consumes half of its fuel in $5.00 \; y$. How much $_{92}^{235} U$ (in $kg$) did it contain initially? Assume that the reactor operates $80 \%$ of the time, that all the energy generated arises from the fission of $_{92}^{235} U$, and that this nuclide is consumed only by the fission process.

If each fission in a $U^{235}$ nucleus releases $200 \, MeV$, how many fissions must occur per second to produce a power of $1 \, kW$?

The isotope ${}_{5}^{12}B$ having a mass $12.014 \text{ u}$ undergoes $\beta$-decay to ${}_{6}^{12}C$. ${}_{6}^{12}C$ has an excited state of the nucleus $({}_{6}^{12}C^*)$ at $4.041 \text{ MeV}$ above its ground state. If ${}_{5}^{12}B$ decays to ${}_{6}^{12}C^*$, the maximum kinetic energy of the $\beta$-particle in units of $\text{MeV}$ is ($1 \text{ u} = 931.5 \text{ MeV}/c^2$, where $c$ is the speed of light in vacuum).

Energy generation in stars is mainly due to

In the nuclear fusion reaction ${ }_1 H^2+{ }_1 H^3 \rightarrow{ }_2 He^4+n$, if the repulsive potential energy between the two nuclei is $2.07 \times 10^{-14} \,J$, then the temperature at which the gases must be heated to initiate the reaction is (Boltzmann constant $k = 1.38 \times 10^{-23} \,JK^{-1}$).