A nucleus with mass number 242 and binding energy per nucleon as 7.6 MeV breaks into two fragment each with mass number 121. If each fragment nucleus has binding energy per nucleon as 8.1 MeV, the total gain in binding energy is ______ MeV.

A nucleus with mass number 242 and binding energy per nucleon 7.6 MeV breaks into two fragments, each with mass number 121 and binding energy per nucleon 8.1 MeV.

The total binding energy of the parent nucleus is calculated as $$BE_{\text{parent}} = 242 \times 7.6 = 1839.2$$ MeV.

Similarly, the total binding energy of the two daughter nuclei becomes $$BE_{\text{daughters}} = 2 \times 121 \times 8.1 = 1960.2$$ MeV.

The gain in binding energy is therefore $$\Delta BE = 1960.2 - 1839.2 = 121.0 \text{ MeV}$$ so that the total gain in binding energy is 121 MeV.