A heavy nucleus of mass number 240 has binding energy per nucleon 7.6 MeV. It fissions into two fragments of mass numbers 100 and 140, whose binding energies per nucleon are 8.5 MeV and 8.3 MeV respectively. Neglect any emitted neutrons. If the energy released is N MeV, find N.
Physics · Nuclear physics · radioactivity and law of decay
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Question

A heavy nucleus of mass number 240 has binding energy per nucleon 7.6 MeV. It fissions into two fragments of mass numbers 100 and 140, whose binding energies per nucleon are 8.5 MeV and 8.3 MeV respectively. Neglect any emitted neutrons. If the energy released is N MeV, find N.

Physics · Nuclear physics · radioactivity and law of decay

G1 Physics · Accepted Answer

Initial total binding energy: BE(initial) = 240×7.6 = 1824 MeV. Final binding energy of the A=100 fragment: BE₁ = 100×8.5 = 850 MeV. Final binding energy of the A=140 fragment: BE₂ = 140×8.3 = 1162 MeV. Total final binding energy: BE(final) = 850+1162 = 2012 MeV. The energy released equals the increase in total binding energy: Q = BE(final)−BE(initial) = 2012−1824 = 188 MeV. Hence N = 188.