Two nuclei of mass number 3 combine with another nucleus of mass number 4 to yield a nucleus of mass number 10 . If the binding energy per nucleon for the mass numbers 3 , 4 and 10 are 5.6 MeV, 7.4 MeV and 6.1 MeV, respectively, then in the process, Mc^2 = _____ MeV.

Step-by-step solution

The nuclear reaction is given by: 2 X³ + Y⁴ Z¹⁰ The total binding energy of the reactants is the sum of the binding energies of the two nuclei of mass number 3 and the nucleus of mass number 4 . Binding energy of reactants = 2 (3 5.6) + (4 7.4) = 33.6 + 29.6 = 63.2 MeV The total binding energy of the product nucleus of mass number 10 is: Binding energy of product = 10 6.1 = 61.0 MeV The change in mass energy M c^2 is equal to the difference in the total binding energies of the reactants and the product. M c^2 = |63