Calculating Energy Released in Uranium Fission: A Step-by-Step Guide

The total binding energy of a nucleus is equal to the sum of the binding energies of its individual nucleons. Therefore, the total binding energy of a 238U nucleus is:

Total binding energy = (number of nucleons) x (binding energy per nucleon) Total binding energy = (238) x (7.5 MeV) Total binding energy = 1785 MeV

When a 238U nucleus splits into two equal-sized nuclei, each nucleus will have half the mass of the original nucleus, or 119 nucleons. The binding energy per nucleon for nuclei of this mass is 8.3 MeV. Therefore, the total binding energy of the two new nuclei is:

Total binding energy = (2 x 119) x (8.3 MeV) Total binding energy = 1966.6 MeV

The difference in binding energy between the original nucleus and the two new nuclei is the energy released in the process:

Energy released = (total binding energy of original nucleus) - (total binding energy of new nuclei) Energy released = 1785 MeV - 1966.6 MeV Energy released = -181.6 MeV

Note that the negative sign indicates that energy is released in the process (i.e., it is exothermic). Therefore, the answer is 181.6 MeV (positive, without the negative sign), accurate to one decimal place.