Calculate attractive force between Cu2+ and O2- ions.

[robertjordan]

Homework Statement

Calculate the attractive force between a pair of Cu²⁺ and O^2- 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?

 

[nasu]

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

What class is this? Chemistry?

 

[robertjordan]

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

What class is this? Chemistry?

The equation F= k_e(|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.