Answer :
Final answer:
To find the total gain in binding energy when a nucleus with mass number 240 breaks into two fragments, multiply the initial and final binding energies per nucleon by the number of nucleons. After calculation, the gain in binding energy is determined to be 216 MeV, which corresponds to answer (a).
Explanation:
The question asks about the gain in binding energy when a nucleus with a mass number of 240 breaks into two fragments, each with a mass number of 120. To find the total gain in binding energy, we calculate the initial and final binding energies of the system and compare them.
Initially, the unfragmented nucleus with mass number 240 has a binding energy per nucleon of 7.6 MeV. Therefore, the total initial binding energy is 240 nucleons × 7.6 MeV/nucleon = 1824 MeV.
After the nucleus breaks into two fragments, each with a mass number of 120 and a binding energy per nucleon of 8.5 MeV, the total binding energy for both fragments is 2 × (120 nucleons × 8.5 MeV/nucleon) = 2040 MeV.
The gain in binding energy is the final total minus the initial total, which is 2040 MeV - 1824 MeV = 216 MeV. Hence, the correct answer is (a) 216 MeV.