The minimum frequency of a photon required to break a particle of mass $15.348 \ amu$ into $4 \ \alpha$ particles is . . . . . . $kHz$.
[Mass of $He$ nucleus = $4.002 \ amu$,$1 \ amu = 1.66 \times 10^{-27} \ kg$,$h = 6.6 \times 10^{-34} \ J \cdot s$ and $c = 3 \times 10^8 \ m/s$]

Consider the following statements $A$ and $B$. Identify the correct choice in the given answer.
$A$. $p-n, p-p$ and $n-n$ forces between nucleons are not equal and charge dependent.
$B$. In a nuclear reactor,the fission reaction will be in an accelerating state if the value of the neutron reproduction factor $k > 1$.

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 ........... $MeV$.

The source of the Sun's energy is

In the nuclear fusion reaction $_1^2H + _1^3H \to _2^4He + n$,the repulsive potential energy between the two nuclei is $7.7 \times 10^{-14} \, J$. To what temperature must the gas be heated to initiate the reaction? $[k = 1.38 \times 10^{-23} \, J/K]$

The energy released if hydrogen atoms are combined to form $^{4}_{2}He$ is . . . . . . MeV. (Take binding energies per nucleon of $^{2}H$ and $^{4}_{2}He$ as $1.1$ MeV and $7.2$ MeV,respectively)