A uranium and iron atom reside a distance R = 29.50 nm apart. The uranium atom i

Question

A uranium and iron atom reside a distance R = 29.50 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?

A uranium and iron atom reside a distance R 29.50 nm apart. The uranium atom is singly ionized; the iron atom is doubly ionized. Calculate the distance rfrom the uranium atom necessary for an electron to reside in equilibrium. Ignore the insignificant gravitational attraction between the particles. Number iron ion uranium ion electron nm K What is the magnitude of the force on the electron from the uranium ion? Number

Explanation / Answer

Given that distance between uranium and electron = r

So distance between electron and iron = R - r = 29.50 nm - r

Charge on single ionized uranium Q1 = 1.6*10^-19 C

Charge on Fe+2, Q2 = 3.2*10^-19 C

Charge on electron ., Q3 = -1.6*10^-19 C

Now using the Force balance

F13 = F23

k*Q1*Q3/r^2 = k*Q2*Q3/(29.5*10^-9 - r)^2

Q1/r^2 = Q2/(29.5*10^-9 - r)^2

Q2 = 2*Q1

1/r^2 = 2/(29.5*10^-9 - r)^2

2r^2 = (29.5*10^-9 - r)^2

Solving the equation

r = 12.22*10^-9 m = 12.22 nm

B.

F13 = k*Q1*Q3/r^2

|Q1| = |Q3|

F13 = 9*10^9*(1.6*10^-19)^2/(12.22*10^-9)^2

F13 = 1.54*10^-12 N

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