The energy released in nuclear reactions is produced by a ch

The energy released in nuclear reactions is produced by a change in mass between the initial and final particles. In one of the possible alpha decays an isotope of uranium with m = 232.03714 u (atomic mass unit u = 1.6605 middot I0^-27 kg) decays to an isotope of thorium with m = 228.02873 u plus an alpha particle with m = 4.00260 u. Find out the energy released in this fission reaction in Joules____________ and in McV___________. Assume that all participating particle are practically at rest. In your calculations use many significant figures.

Solution

mass of uranium m = 232.03714 u

mass of thorium m \' = 228.02873 u

mass of alpha particle m \" = 4.00260 u

mass defect dm = m - m\' -m \"

                        = 232.03714 u - 228.02873 u-4.00260 u

                        = 5.81 x10 ^-3 u

                        = 5.81x10 ^-3 x1.6605 x10 ^-27 kg

Energy released E = dm c ²

                           = (5.81 x10 ^-3 )(1.6605 x10 ^-27 )(3 x10 ⁸ ) ²

                          = 8.682 x10 ^-13 J

                         =[(8.682 x10 ^-13 )/(1.6 x10 ^-13)] MeV

                         = 5.426 MeV