Question

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 $\beta$ decay
$X_Z^A\to Y_{Z+1}^A+{\beta }^{-}+\overline{V_e}$
will occur is ( $m_e$ denotes the mass of the $\beta$ practicle and the neutrino mass $m_v$ can be neglected) :

• A. $M(A,Z)>M(A,Z+1)+m_e$
• B. $M(A,Z)>M(A,Z+1)$
• C. $M(A,Z)>M(A,Z+1)+Z{m}_e$
• D. $M(A,Z)>M(A,Z+1)-m_e$

Answer 1

The correct option is A $M(A,Z)>M(A,Z+1)+m_e$

Given reaction is

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

Mass of the reactants $M_R=M(A,Z)$

Mass of the products $M_P=M(A,Z+1)+M\left({\beta }^{-}\right)+M\left({\nu }_e\right)=M(A,Z+1)+m_e$

Thus, for the reaction to occur, we must have $M_R>M_P$

Therefore, $M(A,Z)>M(A,Z+1)+m_e$