Auranium and iron atom reside a distance r = 44.10 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.

distance r from the uranium atom is 18.27 nm

Explanation:

given data

uranium and iron atom distance R = 44.10 nm

uranium atom = singly ionized

iron atom = doubly ionized

to find out

distance r from the uranium atom

solution

we consider here that uranium electron at distance = r

and electron between uranium and iron so here

so we can say electron and iron  distance = ( 44.10 - r ) nm

and we know single ionized uranium charge q2= 1.602 × C

and charge on iron will be q3 = 2 × 1.602 × C

so charge on electron is q1 =  - 1.602 × C

and we know F =  

so now by equilibrium

Fu = Fi

 =  

put here k = and find r

 =  

r = 18.27 nm

distance r from the uranium atom is 18.27 nm

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.