A heavy nucleus X of mass number 240 undergoes alpha decay to form a daughter nucleus Y of mass number 236 . The binding energy per nucleon for nucleus X is 7.60 MeV , for nucleus Y is 7.70 MeV , and for the alpha particle is 7.10 MeV . The total energy released in this decay process is:

Step-by-step solution

The energy released ( Q -value) in a nuclear reaction is equal to the difference between the total binding energy of the products and the total binding energy of the reactants. Total binding energy of parent nucleus X = 240 7.60 = 1824.0 MeV Total binding energy of daughter nucleus Y = 236 7.70 = 1817.2 MeV Total binding energy of alpha particle = 4 7.10 = 28.4 MeV Total binding energy of products = 1817.2 + 28.4 = 1845.6 MeV Q = 1845.6 - 1824.0 = 21.6 MeV Answer: 21.6 MeV