(II) The liquid-drop model of the nucleus suggests that

Chapter , Problem 63

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(II) The liquid-drop model of the nucleus suggests that highenergyoscillations of certain nuclei can split (fission) a largenucleus into two unequal fragments plus a few neutrons.Using this model, consider the case of a uranium nucleusfissioning into two spherical fragments, one with a chargeqi = +38e and radius r\ = 5.5 X 10-15m, the other withq2 = +54e and r2 = 6.2 X 10-15m. Calculate the electricpotential energy (MeV) of these fragments, assuming that thecharge is uniformly distributed throughout the volume of eachspherical nucleus and that their surfaces are initially in contactat rest. The electrons surrounding the nuclei can be neglected.This electric potential energy will then be entirely convertedto kinetic energy as the fragments repel each other. How doesyour predicted kinetic energy of the fragments agree with theobserved value associated with uranium fission (approximately200 MeV total)? [l MeV = 106eV.]