# Calculate attractive force between Cu2+ and O2- ions.

robertjordan

## Homework Statement

Calculate the attractive force between a pair of Cu2+ and O2- ions in the ceramic CuO that has an interatomic separation of 200pm.

## Homework Equations

$E_A= -\frac{(z_1\cdot e)(z_2\cdot e)}{4\pi\cdot\epsilon_o\cdot r}$
Where z_1 and z_2 are the valences of the two ion types, e is the charge of an electron (1.602 * 10^-19 C), epsilon_o is the permittivity of a vacuum (8.85*10^-12 F/m), and r is the distance between the two ions.

$E_n=\frac{m\cdot e^4 \cdot z^2}{2n^2 \cdot \hbar^2}$
Where m= mass of electron, z= atomic number, e= charge of an electron, n is the energy level.

## The Attempt at a Solution

The problem is that I don't know how to find z_1 and z_2. Do I use $E_n=\frac{m\cdot e^4 \cdot z^2}{2n^2 \cdot \hbar^2}$ to find the energy in the valence electrons? The problem is that I don't know how to use that equation because when I plug in what I think I should for the variables it gives me an answer with units all wrong... Here's an example from another problem where I tried to use that equation...

plugging in 1 for n, 3 for z, 9.11*10^-31 kg for m, -1.602*10^-19 Coulombs for e, and 1.054572×10^-34 J*s for h, we get
E_1= ((9.11*10^-31 kg))*((-1.602*10^-19 C)^4)*(3^2)/(2(1.054572×10^-34 J s)^2) = 2.428×10^-37 s^6A^4/(kg m^4) (second to the 6 amperes to the fourth per kilogram meter to the fourth).

So what to do?

nasu
Why are you writing these formulas for energies?
The problem asks to calculate the attractive force.
The charges of each ion are given in the problem.

robertjordan
Why are you writing these formulas for energies?
The problem asks to calculate the attractive force.
The charges of each ion are given in the problem.

Well I don't know the force equation, my teacher only gave us the equation for bonding energy...
Perhaps since energy=force*distance we can find force by dividing our energy equation by some distance?

I'm still stuck but I see now that z_1= 2 and z_2=-2.

Any more help?

robertjordan
See Coulomb's law. For example, here:
http://en.wikipedia.org/wiki/Coulomb's_law

What class is this? Chemistry?

The equation F= ke(|q1q2|)/r2 looks good.

So if I plug in 3.204 × 10^-19 coulombs for q1 and -3.204 × 10^-19 coulombs for q2 (because O2- has a net charge equal to -2 times the charge of an electron and Cu2+ has a net charge equal to twice the charge of an electron), then I get

2.307*10-8 N of force. Does that seem right?

nasu
Yes, it looks OK.