The liquid-drop model of the atomic nucleus suggests high-energy oscillations of

Question

The liquid-drop model of the atomic nucleus suggests high-energy oscillations of certain nuclei can split the nucleus into two unequal fragments plus a few neutrons. The fission products acquire kinetic energy from their mutual Coulomb repulsion. Assume the charge is distributed uniformly throughout the volume of each spherical fragment and, immediately before separating, each fragment is at rest and their surfaces are in contact. The electrons surrounding the nucleus can be ignored. Calculate the electric potential energy (in electron volts) of two spherical fragments from a uranium nucleus having the following charges and radii: 32e and 5.42 times 10^-15 m, and 60e and 6.69 times 10^-15 m.

Explanation / Answer

distance between the two charges=sum of their radii

=(5.42+6.69)*10^(-15) m

=12.11*10^(-15) m

then potential energy of the system=k*q1*q2/d

where k=coloumb's constant=9*10^9

q1=32e=32*1.6*10^(-19) C

q2=60e=60*1.6*10^(-19) C

d=12.11*10^(-15) m

then potential energy

=9*10^9*32*1.6*10^(-19)*60*1.6*10^(-19)/(12.11*10^(-15))

=3.6529*10^(-11) J

=(3.6529*10^(-11)/(1.6*10^(-13)) MeV

=228.31 MeV

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