Materials Science/Attraction Forces Between Ions

[mstevens199]

Homework Statement

Calculate the force of attraction between a Ca2+ and an O2- ion, the centers of which are separated by a distance of 1.25 nm.

Homework Equations

Attractive energy (E) = -(A/r)
*The constant A is equal to (1/(4∏ε0))(Z1e)(Z2e)
where ε0 is the permittivity of a vacuum (8.85 x 10^-12 F/m), Z1 and Z2 are the valences of the two ion types, and e is the electronic charge (1.602 x 10^-19 C).

Force-potential energy relationship for two atoms E = ∫ F dr
E=Energy F=Force d=diameter? r=spacing between atoms? (not sure about d and r)

The Attempt at a Solution

I am a high school senior taking an independent study Materials Science and Engineering course supervised by my chemistry teacher. I have taken and excelled in AP-level courses before and am currently taking AP Calculus, but the book I am using as a resource for this course is proving to be at a much higher level than I either expected or am used to. I've figured out so far that I probably need to find the attractive energy between the two ions, then use the second equation to find the corresponding attractive force, but my book (alarmingly devoid of any sort of example problems!) doesn't explain every variable. I think "d" is "diameter," and I have found a chart of atomic diameters, but I don't know which ion's diameter to use, or if I should combine them somehow. On top of that, I haven't yet learned how to integrate in Calculus...I have a TI-89 Titanium calculator, though, if that helps. Any assistance or advice is greatly appreciated...I'm just feeling very lost. Thank you!

 

[Borek]

I wonder if you are not making it more difficult than it is. I would start simply calculating Coulomb force between two point charges. You know the charges, you are given the distance, it is a simple plug and chug.

dr is a differential (it tells you what is the variable of integration), not a product of d and r.