KVPY SX SB Exam 2013 Question Paper

A nuclear decay is possible if the mass of the parent nucleus exceeds the total mass of the decay particles. If M(A,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 β decay
$\mathit{X}\stackrel{\mathit{A}}{{}_{\mathit{Z}}}\to \mathit{Y}\stackrel{\mathit{A}}{{}_{\mathit{Z}+1}}+{\mathit{\beta }}^{-}+{\overline{\mathit{v}}}_{\mathit{e}}$
w ill occur is (${\mathit{m}}_{\mathit{e}}$ denotes the mass of the β particle and the neutrino mass ${\mathit{m}}_{\mathit{v}}$ can be neglected):