Determine the minimum energy required to separate a neutron from a...

The process of separating a neutron from a nucleus containing $Z$ protons and $N$ neutrons can be represented by the nuclear reaction:

_Z^{Z+N}X $\rightarrow _Z^{Z+N-1}Y + _{0}^{1}n$

The mass of the initial nucleus is $M_{Z, N}$.

The mass of the products is the sum of the mass of the residual nucleus and the mass of the neutron, which is $M_{Z, N-1} + m_n$.

The minimum energy required to separate the neutron is equal to the mass difference between the products and the initial nucleus, multiplied by $c^2$.

\Delta$m =$\text{Mass of products} - \text{Mass of reactant}

\Delta$m = M_{Z, N-1} + m_n - M_{Z, N}$

\text{Energy required} = \Delta$m$\cdotc^2 = (M_{Z, N-1} + m_n - M_{Z, N}) c²