A heavy nucleus X of mass number A = 240 , initially at rest, undergoes fission into two unequal fragments Y and Z of mass numbers 160 and 80 , respectively. The binding energy per nucleon of the parent nucleus X is 7.5 MeV , while the binding energy per nucleon of both the fragments Y and Z is 8.0 MeV . Assuming that the entire energy released in the fission process appears as the kinetic energy of the fragments, th

Step-by-step solution

First, we calculate the total energy released ( Q -value) in the fission process. The Q -value is the difference between the total binding energy of the products and the reactant. Total binding energy of reactant X : BE_ X = 240 7.5 = 1800 MeV Total binding energy of products Y and Z : BE_ products = 160 8.0 + 80 8.0 = 240 8.0 = 1920 MeV Energy released: Q = 1920 - 1800 = 120 MeV By the conservation of linear momentum, since the parent nucleus was at rest, the two fragments must have equal and opposite momenta. Let