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 $= 4.000 \text{ u}$,$1 \text{ u} = 931 \text{ MeV}/c^2$]

The energy released by the fission of a single uranium nucleus is $200 \,MeV$. The number of fissions of uranium nucleus per second required to produce $16 \,MW$ of power is (Assume efficiency of the reactor is $50\%$).

For nuclei with mass number close to $119$ and $238$, the binding energies per nucleon are approximately $7.6 \text{ MeV}$ and $8.6 \text{ MeV}$ respectively. If a nucleus of mass number $238$ breaks into two nuclei of nearly equal masses, what will be the approximate amount of energy released in the process of fission (in $\text{ MeV}$)?

Assertion : It is not possible to use ${}^{35}Cl$ as the fuel for fusion energy.
Reason : The binding energy of ${}^{35}Cl$ is too small.

The $Q$ value of a nuclear reaction $A+b \rightarrow C+d$ is defined by $Q=\left[m_{A}+m_{b}-m_{C}-m_{d}\right] c^{2}$ where the masses refer to the respective nuclei. Determine from the given data the $Q$ value of the following reactions and state whether the reactions are exothermic or endothermic.
$(i) \;_{1}^{1} H+_{1}^{3} H \rightarrow_{1}^{2} H+_{1}^{2} H$
$(ii)\;_{6}^{12} C+_{6}^{12} C \rightarrow_{10}^{20} N e+_{2}^{4} H e$
Atomic masses are given to be:
$m(_{1}^{1}H) = 1.007825 \; u$
$m(_{1}^{2}H) = 2.014102 \; u$
$m(_{1}^{3}H) = 3.016049 \; u$
$m(_{6}^{12}C) = 12.000000 \; u$
$m(_{10}^{20}Ne) = 19.992439 \; u$
$m(_{2}^{4}He) = 4.002603 \; u$

The energy of the fast neutrons emitted in a nuclear fission reactor is approximately $\qquad$ .