Question

A uranium 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.

Answer 1

distance r from the uranium atom is 18.27 nm

Step-by-step 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 ×
`10^(-19)` C

and charge on iron will be q3 = 2 × 1.602 ×
`10^(-19)` C

so charge on electron is q1 = - 1.602 ×
`10^(-19)` C

and we know F =
`k(q*q)/(r^(2) )`

so now by equilibrium

Fu = Fi

`k(q*q)/(r^(2) )` =
`k(q*q)/(r^(2) )`

put here k =
`9*10^(9)` and find r

`9*10^(9)(1.602 *10^(-19)*1.602 *10^(-19))/(r^(2) )` =
`9*10^(9)(1.602 *10^(-19)*1.602 *10^(-19))/((44.10-r)^(2) )`

`(1)/(r^(2) ) = (2)/((44.10 -r)^2)`

r = 18.27 nm

distance r from the uranium atom is 18.27 nm