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Binding Energy

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Question

Write the relation for binding energy (B.E) (in MeV) of a nucleus of mass $_{Z}^{A} M$ , atomic number (Z) and mass number (A) in terms of the masses of its constituents - neutrons and protons.

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Solution

The binding energy in (MeV) is $E_{B} = (Z m_{p} + N m_{n} - M_{A}^{Z}) c^{2}$
Where $m_{p} =$ mass of proton , $m_{n} =$ mass of neutron, $c =$ velocity of light.
Now $N = A - Z$ thus, $E_{B} = [Z m_{p} + (A - Z) m_{n} - M_{A}^{Z}] c^{2} = [Z (m_{p} - m_{n}) + A m_{n} - M_{A}^{Z}) c^{2}$

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