A nucleus with mass number 240 breaks into two fragments each of mass number 120, the binding energy per nucleon of unfragmented nuclei is 7.6 MeV while that of fragments is 8.5 MeV. The total gain in the Binding Energy in the process is:

To find the total gain in binding energy during the nuclear fission process, we calculate the binding energy before and after the fragmentation.

1. Initial State (Unfragmented Nucleus):
The parent nucleus has a mass number ($A$) of 240.
The binding energy per nucleon of the unfragmented nucleus is given as 7.6 MeV.
Therefore, the initial binding energy ($E_i$) is:
$E_i=240\times 7.6\text{ MeV}$
$E_i=1824\text{ MeV}$

2. Final State (Fragments):
The nucleus breaks into two fragments, each with a mass number of 120.
The binding energy per nucleon of each fragment is given as 8.5 MeV.
Therefore, the total final binding energy ($E_f$) of the two fragments is:
$E_f=2\times (120\times 8.5)\text{ MeV}$
$E_f=2\times 1020\text{ MeV}$
$E_f=2040\text{ MeV}$

3. Total Gain in Binding Energy:
The gain in binding energy is the difference between the final and initial binding energies:
$\mathrm{Gain}=E_f-E_i$
$\mathrm{Gain}=2040-1824$
$\mathrm{Gain}=216\text{ MeV}$

Thus, the total gain in the Binding Energy in the process is 216 MeV.