Question: Q. 4. Define the terms (i) mass defect (ii) binding energy for a nucleus and state the relation between the two for a given nuclear reaction for which the B.E. / nucleon of the product nucleus / nuclei is more than that for the original nucleus / nuclei. Is this nuclear reaction exothermic or endothermic in nature? Justify your choice.
U[SQP 2013]
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Solution:
Ans. (i) Mass defect $(\Delta M)$, of any nucleus ${ }_{Z}^{A} X$ is the difference in the mass of the nucleus $(=M)$ and the sum of masses of its constituent nucleons $\left(=M^{\prime}\right)$.
$$ \begin{aligned} \Delta M & =M^{\prime}-M \ & =\left[Z m_{p}+(A-Z) m_{n}\right]-M \end{aligned} $$
where, $m_{p}$ and $m_{n}$ denote the mass of the proton and the neutron respectively.
(ii) Binding energy is the energy required to separate a nucleus into its constituent nucleons. The relation between the two is
$$ \begin{equation*} E_{b}=\Delta M c^{2} \tag{1} \end{equation*} $$
(iii) There is a release of energy, i.e., the reaction is exothermic.
Reason : Increase in B.E/nucleon implies that mass has been converted into energy. This would result in release of energy.
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