$A$ nucleus of mass $M + \Delta m$ is at rest and decays into two daughter nuclei of equal mass. If $C$ is the speed of light,and $E_1$ is the binding energy per nucleon for the parent nucleus and $E_2$ is that for the daughter nuclei,then:

Assertion : In a decay process of a nucleus, the mass of products is less than that of the parent.
Reason : The rest mass energy of the products must be less than that of the parent.

For a nucleus ${ }_Z^A X$ having mass number $A$ and atomic number $Z$:
$A.$ The surface energy per nucleon $(b_s) = a_1 A^{2/3}$
$B.$ The Coulomb contribution to the binding energy $b_c = -a_2 \frac{Z(Z-1)}{A^{4/3}}$
$C.$ The volume energy $b_v = a_3 A$
$D.$ Decrease in the binding energy is proportional to surface area.
$E.$ While estimating the surface energy,it is assumed that each nucleon interacts with $12$ nucleons,($a_1, a_2$ and $a_3$ are constants)
Choose the most appropriate answer from the options given below:

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?

$\gamma$-rays radiation can be used to create an electron-positron pair. In this process of pair production,$\gamma$-rays energy cannot be less than ....... $MeV$.

If $m$ is the mass of the $_Z{X^A}$ nucleus,and $m_n$ and $m_p$ are the masses of a neutron and a proton respectively,then which of the following is correct?