What does mean by mass defect? Establish relation between mass defect and nuclear binding energy. And hence write the expression for binding energy per nucleon.

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Solution

Mass defect: It is found that the mass of a stable nucleus is always less than the sum of masses of its constituent protons and neutrons in their free state.
Consider the Nucleus $_{Z}^{A} X$ .
Expression for binding energy: The nucleus $_{Z}^{A} X$ contains Z protons and $(A - Z)$ neutrons.
Its mass defect is
$Δ m = Z_{m_{p}} + (A - Z) m_{n} - m_{N}$
Where $m_{N} \to$ mass of nucleus
The binding energy $E_{b}$ of the nucleus is given by,
$Δ E_{b} = Δ m \times c^{2} = [Z_{m_{p}} + (A - Z) m_{n} - m_{N}] c^{2}$
The binding between the constituents of the nucleus is the binding energy per nucleon, $E_{b n}$ , which is the ratio of the binding energy $E_{b}$ of a nucleus to the number of the nucleons, A, in that nucleus:
$E_{b n} = \frac{E_{b}}{A}$ .

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