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

1. Sep 12, 2013

### robertjordan

1. The problem statement, all variables and given/known data
Calculate the attractive force between a pair of Cu2+ and O2- ions in the ceramic CuO that has an interatomic separation of 200pm.

2. Relevant 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.

3. 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...

So what to do?

2. Sep 12, 2013

### 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.

3. Sep 12, 2013

### robertjordan

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?

4. Sep 12, 2013

### nasu

5. Sep 12, 2013

### robertjordan

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?

6. Sep 13, 2013

### nasu

Yes, it looks OK.