An electron-positron pair (rest mass of each particle$=0.51 \mathrm{MeV}$) is produced by a $\gamma$-ray photon of energy $2.42 \mathrm{MeV}$. The K.E. imparted to each of the charged particles shall be

Given below are three schematic graphs of potential energy $V\left(r\right)$ versus distance $r$ for three atomic particles electron $\left(e\right)$, proton $\left(p^{+}\right)$ and neutron $\left(n\right)$ in the presence of a nucleus at the origin $O$. The radius of the nucleus is $r_0$. The scale on the $V$-axis may not be the same for all figures. The correct pairing of each with the corresponding atomic particle is,

A nuclear decay is possible if the mass of the parent nucleus exceeds the total mass of the decay particles. If $M (A\text{,} Z)$ denotes the mass of a single neutral atom of an element with mass number $A$ and atomic number $Z$, then the minimal condition that the $\beta$ decay,

$X_Z^A\to Y_{Z+1}^A+{\beta }^{-}+{\overline{v}}_e$

will occur is ($m_{\mathrm{e}}$ denotes the mass of the $\beta$ particle and the neutrino mass $m_v$ can be neglected),