If $M(A, Z), M_P$ and $M_n$ denote the masses of the nucleus ${ }_Z^A X$, proton and neutron respectively in…
If $M(A, Z), M_P$ and $M_n$ denote the masses of the nucleus ${ }_Z^A X$, proton and neutron respectively in units of $u\left(1 \mathrm{u}=931.5 \mathrm{MeV} / c^2\right)$ and $\mathrm{BE}$ represents its binding energy in $\mathrm{MeV}$, then
$M(A, Z)=Z M_p+(A-Z) M_n-\mathrm{BE} / c^2$
$M(A, Z)=Z M_p+(A-Z) M_n+\mathrm{BE}$
$M(A, Z)=Z M_p+(A-Z) M_n-B E$
$M(A, Z)=Z M_p^P+(A-Z) M_n^n+B E / c^2$
Solution
Binding energy of a nucleus containing $N$ neutrons and $Z$ protons is
$\begin{aligned}
& \mathrm{BE}=\left[N M_n+Z M_p-M(A, Z)\right] c^2 \\
\Rightarrow & \frac{\mathrm{BE}}{c^2}=N M_n+Z M_p-M(A, Z) \\
\Rightarrow & \frac{\mathrm{BE}}{c^2}=(A-Z) M_n+Z M_p-M(A, Z) \\
\Rightarrow & M(A, Z)=Z M_p+(A-Z) M_n-\mathrm{BE} / c^2
\end{aligned}$