Write the equation of mass-energy equivalence.

$A$ nucleus of mass $ 20 u $ emits a $ \gamma $ photon of energy $ 6 MeV $. If the emission is assumed to occur when the nucleus is free and at rest, then the nucleus will have a kinetic energy nearest to (take $ 1 u = 1.6 \times 10^{-27} kg $): (in $keV$)

The neutron separation energy is defined as the energy required to remove a neutron from the nucleus. Obtain the neutron separation energies of the nuclei $_{20}^{41} Ca$ and $_{13}^{27} Al$ from the following data:
$m(_{20}^{40} Ca) = 39.962591 \; u$
$m(_{20}^{41} Ca) = 40.962278 \; u$
$m(_{13}^{26} Al) = 25.986895 \; u$
$m(_{13}^{27} Al) = 26.981541 \; u$
(Given mass of neutron $m_n = 1.008665 \; u$)

The energy equivalent to a substance of mass $1 \,g$ is

Assertion : The binding energy per nucleon,for nuclei with atomic mass number $A > 100$,decreases with $A$.
Reason : The nuclear forces are weak for heavier nuclei.

Explain the following forms and principles of energy:
$(a)$ The Equivalence of Mass and Energy
$(b)$ Nuclear Energy
$(c)$ The Principle of Conservation of Energy