In fission, a nucleus of uranium–238, which contains 92 protons, divides into two smaller spheres, each having 46 protons and a radius of 5.9×10^-15 m5.9×1015m. What is the magnitude of the repulsive electric force pushing the two spheres apart?

1 Answer
Feb 20, 2016

The force's magnitude is approximately 3.5 kN.

Explanation:

|F|=k(|q_1q_2|)/r^2|F|=k|q1q2|r2

k is Coulomb's constant, which is roughly 8.99times10^9 N C^-2 m^28.99×109NC2m2
q_1=q_2=46(e)q1=q2=46(e) where e is the charge on an electron, which is approximately =1.602times10^-19C=1.602×1019C.
r_1=r_2=5.9times10^-15mr1=r2=5.9×1015m
The separation between the centres of the nuclei =r=r_1+r_2=2r_1r=r1+r2=2r1

Assuming the nuclei are just touching when fission occurs:

|F|=k(q_1^2)/r^2=k(46^2e^2)/(2times5.9times10^-15m)^2=(2116ke^2)/(34.81times10^-30 m^2)|F|=kq21r2=k462e2(2×5.9×1015m)2=2116ke234.81×1030m2

|F| ~= (2116(8.99times10^9 N C^-2 m^2)(1.602times10^-19C)^2)/(34.81times10^-30 m^2)|F|2116(8.99×109NC2m2)(1.602×1019C)234.81×1030m2

|F| ~= 3506 N|F|3506N

The force's magnitude is approximately 3.5 kN.