To solve this problem, we need to calculate the total gain in binding energy when a nucleus with mass number 240 splits into two fragments each with mass number 120.$\\$Given:$\\$• Mass number of the original nucleus $A_1 = 240 \\$• Mass number of each fragment $A_2 = 120 \\$• Binding energy per nucleon of the original nucleus $= 7.6$ MeV$\\$• Binding energy per nucleon of the fragments $= 8.5$ MeV$\\$Step 1: Calculate the total binding energy of the original nucleus.$\\$The total binding energy of the original nucleus $E_1$ is given by:$\\ E_1 = A_1 \times$Binding energy per nucleon of the original nucleus$\\ E_1 = 240 \times 7.6$ MeV$\\$Step 2: Calculate the total binding energy of the fragments.$\\$The total binding energy of both fragments $E_2$ is given by:$\\ E_2 = 2 \times (A_2 \times$Binding energy per nucleon of the fragments$) \\ E_2 = 2 \times (120 \times 8.5$ MeV$) \\$Step 3: Calculate the gain in binding energy.$\\$The gain in binding energy $\Delta E$ is the difference between the total binding energy of the fragments and the original nucleus:$\\ \Delta E = E_2 - E_1 \\$Substitute the values:$\\ E_1 = 240 \times 7.6 = 1824$ MeV$\\ E_2 = 2 \times (120 \times 8.5) = 2 \times 1020 = 2040$ MeV$\\ \Delta E = 2040 - 1824 = 216$ MeV$\\$Therefore, the total gain in the binding energy in the process is $216$ MeV.$\\$This corresponds to Option 4.