Calculate the minimum energy needed to separate a neutron from a nucleus with Z protons and N neutrons it terms of the masses M_Z.N' M_Z_,N−1 and the mass of the neutron.

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Solution

Before the separation of neutron, let the mass of the nucleus be M_Z_,N.
Then, after the separation of neutron, the mass of the nucleus will be M_Z,_N-1.
The reaction is given by
$E_{Z, N} = E_{Z, N - 1} + {}_{0}^{1}n$
If $M_{N}$ is the mass of the neutron, then the energy needed to separate the neutron b $(∆ E)$ will be
$∆ E$ = (Final mass of nucleus + Mass of neutron − Initial mass of the nucleus)c²
$∆ E = (M_{Z, N - 1} + M_{N} - M_{Z, N}) c^{2}$

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