Consider the nuclear reaction $X^{200} \rightarrow A^{110} + B^{90}$. If the binding energy per nucleon for $X$,$A$,and $B$ is $7.4 \, MeV$,$8.2 \, MeV$,and $8.2 \, MeV$ respectively,then the amount of energy released is .......... $MeV$.

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

From the given data,the amount of energy required to break the nucleus of aluminium ${ }_{13}^{27} {Al}$ is $x \times 10^{-3} {J}$.
Mass of neutron $= 1.00866 \, {u}$
Mass of proton $= 1.00726 \, {u}$
Mass of aluminium nucleus $= 26.98154 \, {u}$
(Assume $1 \, {u}$ corresponds to $1 \, {J}$ of energy for the purpose of this calculation)
(Round off to the nearest integer)

An electron and a positron annihilate each other to produce two $\gamma$-ray photons of equal energy. The minimum energy of each photon is .....

Assertion : Binding energy (or mass defect) of hydrogen nucleus is zero.
Reason : Hydrogen nucleus contains only one nucleon.

Given the masses of various atomic particles $m_{p} = 1.0072 \ u$,$m_{n} = 1.0087 \ u$,$m_{e} = 0.000548 \ u$,$m_{\bar{v}} = 0$,and $m_{d} = 2.0141 \ u$,where $p \equiv$ proton,$n \equiv$ neutron,$e \equiv$ electron,$\bar{v} \equiv$ antineutrino,and $d \equiv$ deuteron. Which of the following processes is allowed by momentum and energy conservation?