Practice 060519

Disclaimer: These are some random questions which does not have anything to do with the exam. I have no idea or any say about exam questions.

Question 1

The liquid-drop model of the nucleus suggests that high-energy oscillations of certain nuclei can split (“fission”) a large nucleus into two unequal fragments plus a few neutrons. Using this model, consider the case of a uranium nucleus fissioning into two spherical fragments, one with a charge $q_{1}=+38$ e and radius $r_{1}=5.5\times 10^{-15}$ m, the other with $q_{2}=+54$ e and $r_{2}=6.2\times 10^{-15}$ m. Calculate the electric potential energy (MeV) of these fragments, assuming that the charge is uniformly distributed throughout the volume of each spherical nucleus and that their surfaces are initially in contact at rest. The electrons surrounding the nuclei can be neglected. This electric potential energy will then be entirely converted to kinetic energy as the fragments repel each other. How does your predicted kinetic energy of the fragments agree with the observed value associated with uranium fission (approximately 200 MeV total)? [1 MeV = $10^{6}$ eV].