A heavy nucleus X of mass number A = 200 undergoes nuclear fission, splitting into two identical lighter nuclei Y . The binding energy per nucleon of the parent nucleus X is 7 MeV . If the total energy released in the fission process is 200 MeV , the binding energy per nucleon of the product nucleus Y is _______ MeV .

Step-by-step solution

Let the binding energy per nucleon of the product nucleus Y be E . The total binding energy of the reactant nucleus X is: BE_ X = 200 7 = 1400 MeV Since the nucleus splits into two identical nuclei Y , each has a mass number of 100 . The total binding energy of the products is: BE_ Y = 2 (100 E) = 200E The energy released ( Q -value) in the fission process is the difference between the total binding energy of the products and the reactants: Q = BE_ Y - BE_ X Given that Q = 200 MeV , we have: 200 = 200E - 1400 200E