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 $c = 3 \times 10^8 \ m/s$]

Assertion: Energy is released when heavy nuclei undergo fission or light nuclei undergo fusion.
Reason: For heavy nuclei,binding energy per nucleon increases with increasing $Z$,while for light nuclei,it decreases with increasing $Z$.

$A$ nuclear fission process is given by $A^{240} \rightarrow B^{100} + C^{140} + Q$ (energy). If the binding energy per nucleon for nuclei $A, B,$ and $C$ are $7.6 \, MeV, 8.1 \, MeV,$ and $8.1 \, MeV$ respectively,then the energy $Q$ released is approximately $...... \, MeV$.

Two lighter nuclei combine to form a comparatively heavier nucleus by the relation given below:
${ }_{1}^{2} X +{ }_{1}^{2} X ={ }_{2}^{4} Y$
The binding energies per nucleon of ${ }_{1}^{2} X$ and ${ }_{2}^{4} Y$ are $1.1 \, MeV$ and $7.6 \, MeV$ respectively. The energy released in this process is in $MeV$.

Slowing down of neutrons: In a nuclear reactor,a neutron of high speed (typically $10^{7} \; m s^{-1}$) must be slowed to $10^{3} \; m s^{-1}$ so that it can have a high probability of interacting with isotope $^{235}_{92}U$ and causing it to fission. Show that a neutron can lose most of its kinetic energy in an elastic collision with a light nucleus like deuterium or carbon,which has a mass of only a few times the neutron mass. The material making up the light nuclei,usually heavy water $(D_{2}O)$ or graphite,is called a moderator.

The nuclear fusion reaction is given as $_1H^2 + _1H^2 \to _2He^3 + n + 3.2 \, MeV$. How much energy is released when $2 \, kg$ of deuterium undergoes fusion?