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).

Suppose a ${ }_{88}^{226} Ra$ nucleus at rest and in the ground state undergoes $\alpha$-decay to a ${ }_{86}^{222} Rn$ nucleus in its excited state. The kinetic energy of the emitted $\alpha$ particle is found to be $4.44 \text{ MeV}$. The ${ }_{86}^{222} Rn$ nucleus then goes to its ground state by $\gamma$-decay. The energy of the emitted $\gamma$-photon is . . . . . . . $\text{keV}$.
[Given: atomic mass of ${ }_{88}^{226} Ra = 226.005 \text{ u}$,atomic mass of ${ }_{86}^{222} Rn = 222.000 \text{ u}$,atomic mass of $\alpha$ particle $= 4.000 \text{ u}$,$1 \text{ u} = 931 \text{ MeV}/c^2$]

When a slow neutron goes sufficiently close to a ${U^{235}}$ nucleus,then the process that takes place is

In a fission reaction $_{92}^{236}U \to ^{117}X + ^{117}Y + n + n$,the binding energy per nucleon of $X$ and $Y$ is $8.5\, MeV$,whereas that of $^{236}U$ is $7.6\, MeV$. The total energy liberated will be about . . . . . . $MeV$.

Mention the use of controlled nuclear fission. Mention the use of uncontrolled nuclear fission.

Which of the following is used as a moderator in nuclear reactors?