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$(i)$ and $(iii)$

$(ii)$ and $(iv)$

$(ii)$ and $(iii)$

$(i)$ and $(iv)$

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Step-by-Step Explanation Step 1: Understanding Binding Energy The binding energy $E_b$ of a nucleus is the amount of energy required to disassemble the nucleus completely into its constituent protons and neutrons. A higher binding energy means the nucleus is more stable and tightly bound. Step 2: Reason for Positive Energy Release in A + B → C + ϵ • In this reaction, two nuclei (A and B) combine to form a more stable nucleus (C). • The total binding energy of the product nucleus (C) is higher than the sum of the binding energies of nuclei A and B. Symbolically: $E_b(\text{C}) > E_b(\text{A}) + E_b(\text{B}).$ • Because the product is more tightly bound, the difference in binding energies is released as energy ϵ. Hence, ϵ is positive. Step 3: Reason for Positive Energy Release in F → D + E + ϵ • Here, the nucleus F breaks into two smaller nuclei D and E. • The total binding energy of D and E together is higher than that of F, i.e., $E_b(\text{D}) + E_b(\text{E}) > E_b(\text{F}).$ • The increased total binding energy again results in the release of the difference as ϵ. Hence, ϵ is positive. Conclusion In both reactions, the key factor is that a more stable nuclear configuration is reached in the products. Since the total binding energy increases, the difference appears as released energy.

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