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Calculate attractive force between Cu2+ and O2- ions.

  1. Sep 12, 2013 #1
    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
    [itex]E_A= -\frac{(z_1\cdot e)(z_2\cdot e)}{4\pi\cdot\epsilon_o\cdot r}[/itex]
    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.

    [itex]E_n=\frac{m\cdot e^4 \cdot z^2}{2n^2 \cdot \hbar^2}[/itex]
    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 [itex]E_n=\frac{m\cdot e^4 \cdot z^2}{2n^2 \cdot \hbar^2}[/itex] 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. jcsd
  3. Sep 12, 2013 #2
    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.
     
  4. Sep 12, 2013 #3
    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?
     
  5. Sep 12, 2013 #4
  6. Sep 12, 2013 #5
    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?
     
  7. Sep 13, 2013 #6
    Yes, it looks OK.
     
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