The energy released per fission of uranium-$235$ is about $200 \, MeV$. $A$ reactor using $U-235$ as fuel is producing $1000 \, kW$ power. The number of $U-235$ nuclei undergoing fission per second is approximately:

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).

Which reaction is not part of the proton-proton cycle?

Control rods used in nuclear reactors are made of:

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

For the nuclear fusion reaction ${ }_1^2 H +{ }_1^3 H \rightarrow{ }_2^4 He +{ }_0^1 n$,the temperature to which the gases must be heated is $3.7 \times 10^9 \, K$. The potential energy between two nuclei is closest to ........ $J$ (Boltzmann's constant $k = 1.38 \times 10^{-23} \, J/K$).