Use Coulomb\'s Law to calculate the energy of a copper ion and an oxide ion at their equilibrium ion-pair separation distance?

The required to separate the ion pair = ##4.297xx10^(-19)"J"##

I have assumed a copper(II) ion and an electrostatic model.

For 2 charges ##q_1## and ##q_2## separated by a distance ##r## the force of attraction is given by :

##F=(1)/(4piepsilon_0).(q_1q_2)/(r^2)##

The constant ##(1)/(4piepsilon_0)## can be written as ##k## and has the value ##9xx10^(9)"m/F"##

The done in separating the 2 charges from ##r## to infinity is given by:

##W=-k.(q_1q_2)/(r) " "color(red)((1))##

I will assume a wholly electrostatic model where we have discrete ions in contact.

The ionic radii are:

##r^+=87"pm"## for ##Cu^(2+)##

##r^(-)=126"pm"## for ##O^(2-)##

This means the total distance between the centre of the 2 ions is:

##126+87=213"pm"=r##

The electronic charge = ##-1.602xx10^(-19)"C"##

So the charge on the ##Cu^(2+)## ion =

##+2(1.602xx10^(-19))=+3.204xx10^(-19)"C"##

The charge on the ##O^(2-)## must therefore be:

##-3.204xx10^(-19)"C"##

Putting these values into ##color(red)((1))rArr##

##W=-(9xx10^(9)xx(3.204xx10^(-19))xx(-3.204xx10^(-19)))/(215xx10^(-12))color(white)(x)J##

##W=4.297xx10^(-19)"J"##