Question

A uranium and iron atom reside a distance R = 54.70 nm apart. The uranium atom is singly ionized; the iron atom is doubly ionized. Calculate the distance r from the uranium atom necessary for an electron to reside in equilibrium. Ignore the insignificant gravitational attraction between the particles.What is the magnitude of the force on the electron from the uranium ion?

Answer 1

F uranium = F iron
k e^2/r^2 = k 2 e^2/(54.7E-9-r)^2
so
(54.7E-9-r)^2 = 2 r^2
solve for r
r=2.266E-8 m = 22.66 nm

F uranium = k e^2/r^2 = 9E9*(1.6E-19)^2/(22.66E-8)^2=4.487E-11 N