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

Answer:

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 × $10^{-19}$ 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 = $k\frac{q*q}{r^{2} }$  

so now by equilibrium

Fu = Fi

$k\frac{q*q}{r^{2} }$  =  $k\frac{q*q}{r^{2} }$

put here k = $9*10^{9}$ and find r

$9*10^{9}\frac{1.602 *10^{-19}*1.602 *10^{-19}}{r^{2} }$  =  $9*10^{9}\frac{1.602 *10^{-19}*1.602 *10^{-19}}{(44.10-r)^{2} }$

$\frac{1}{r^{2} } = \frac{2}{(44.10 -r)^2}$

r = 18.27 nm

distance r from the uranium atom is 18.27 nm