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Question
Calculate the minimum energy needed to separate a neutron from a nucleus with Zprotons and N neutrons it terms of the masses MZ.N' MZ,N−1 and the mass of the neutron.
Solution
Before the separation of neutron, let the mass of the nucleus be MZ,N.
Then, after the separation of neutron, the mass of the nucleus will be MZ,N-1.
The reaction is given by
`E_(Z,N) = E_(Z,N-1) + _0^1n`
If `(M_N)` is the mass of the neutron, then the energy needed to separate the neutron b (ΔE) will be
ΔE = (Final mass of nucleus + Mass of neutron − Initial mass of the nucleus)c2
`ΔE = (M_(Z,N-1) + M_N - M_(Z,N))c^2`
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