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 :

First, calculate the total binding energy of the original nucleus.

$BE\_\{initial\}=A\; \backslash times\; BE\_\{per\backslash ;nucleon\}=240\; \backslash times\; 7.6\backslash \; \backslash text\{MeV\}=1824\backslash \; \backslash text\{MeV\}$

Next, calculate the binding energy of one fragment.

$BE\_\{fragment\}=120\; \backslash times\; 8.5\backslash \; \backslash text\{MeV\}=1020\backslash \; \backslash text\{MeV\}$

Since there are two identical fragments, the total binding energy after fission is

$BE\_\{final\}=2\; \backslash times\; 1020\backslash \; \backslash text\{MeV\}=2040\backslash \; \backslash text\{MeV\}$

The gain in binding energy is the difference between final and initial values:

$\backslash Delta\; BE\; =\; BE\_\{final\}\; -\; BE\_\{initial\}=2040\backslash \; \backslash text\{MeV\}\; -\; 1824\backslash \; \backslash text\{MeV\}=216\backslash \; \backslash text\{MeV\}$

Therefore, the process releases 216 MeV of energy, which matches the given correct option.