The above is a plot of binding energy per nucleon Eb, against the nuclear mass M; A, B, C, D, E, F correspond to different nuclei. Consider four reactions: (i) A + B → C + ε (ii) C → A + B + ε (iii) D + E → F + ε (iv) F → D + E + ε, where ε is the energy released? In which reactions is ε positive? (a) (i) and (iii) (b) (ii) and (iv) (c) (ii) and (iii) (d) (i) and (iv)

Answer: (d). Energy is released ( ε > 0) when the products have a higher binding energy per nucleon than the reactants. (i) Light nuclei A + B → C: from the graph Eb(C) > Eb(A), Eb(B), so fusion releases energy. (ii) is the reverse of (i), so it needs energy. (iv) Heavy F → D + E: Eb(D), Eb(E) > Eb(F), so fission releases energy; (iii) is its reverse and needs energy. So the answer is (d) (i) and (iv).

The above is a plot of binding energy per nucleon Eb, against the… | JEE Main 2009 (AIEEE)

Q22JEE Main 2009 · AIEEEDifficult

Mass Defect & Binding Energy

The above is a plot of binding energy per nucleon $E_b,$ against the nuclear mass $M; A, B, C, D, E, F$ correspond to different nuclei. Consider four reactions:

$(i)\ \ A + B \rightarrow C + \varepsilon \quad (ii)\ \ C \rightarrow A + B + \varepsilon$

$(iii)\ \ D + E \rightarrow F + \varepsilon \quad (iv)\ \ F \rightarrow D + E + \varepsilon,$

where $\varepsilon$ is the energy released? In which reactions is $\varepsilon$ positive?

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Answer: (d)

Energy is released ( $\varepsilon > 0$ ) when the products have a higher binding energy per nucleon than the reactants.
(i) Light nuclei $A + B \to C$ : from the graph $E_b(C) > E_b(A), E_b(B)$ , so fusion releases energy.
(ii) is the reverse of (i), so it needs energy.
(iv) Heavy $F \to D + E$ : $E_b(D), E_b(E) > E_b(F)$ , so fission releases energy; (iii) is its reverse and needs energy.
So the answer is (d) (i) and (iv).

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Mass Defect & Binding Energy question from JEE Main 2009 (AIEEE)

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