Consider the nuclear reaction X200 → A110 + B90, If the binding energy per nucleon for X, A and B is 7.4 MeV, 8.2 MeV and 8.2 MeV respectively, what is the energy released-200 MeV160 MeV110 MeV90 MeV

To solve this problem, we need to calculate the total binding energy before and after the reaction and then find the difference.

1. Calculate the total binding energy before the reaction: The total binding energy for X is given by the product of the number of nucleons and the binding energy per nucleon. For X, this is 200 nucleons * 7.4 MeV/nucleon = 1480 MeV.

2. Calculate the total binding energy after the reaction: The total binding energy for A is 110 nucleons * 8.2 MeV/nucleon = 902 MeV. The total binding energy for B is 90 nucleons * 8.2 MeV/nucleon = 738 MeV. Adding these together gives a total of 902 MeV + 738 MeV = 1640 MeV.

3. Find the difference: The energy released is the difference in total binding energy before and after the reaction. This is 1640 MeV - 1480 MeV = 160 MeV.

So, the energy released is 160 MeV.