What is the binding energy in NaCl?

[pearapple]

Homework Statement

Each Na atom transfers 1/6 of an electron, on average, to each Cl atom. Estimate the binidng energy of the ionic bonds in NaCl.

Homework Equations

The Attempt at a Solution

The answer says to use k*q1*q2 / r, where k is the electric constant, q1 and q2 are the charges, and r is the separation between the charges.

So it gives k*(1/6)e*e / r.

I'm wondering what would happen if it were a different atom. In NaCl, Na has a charge of +1 and Cl has a charge of -1. If I wanted to calculate the binding energy of something with charges that weren't necessarily 1, how would this change?

 

[Borek]

This is based on a simple coulomb interactions between point charges.

 

[pearapple]

I know. It's the charges of the ions I'm unclear on. I just wanted to know what the answer would look like if the question was about, say MgO instead of NaCl.

 

[Borek]

MgO would mean charges +2 and -2. 1/6th is just effect of the geometry, so in the case of MgO I would expect 2/6th.

 

[DeeNos]

I would first clarify what is meant by "binding energy" in this context. Is it the energy required to break the ionic bond between Na and Cl, or is it the energy released when the bond is formed?

Assuming it is the energy required to break the bond, the formula given is a simplified version of the electrostatic potential energy equation, which takes into account the charges and separation distance of two point charges. In the case of NaCl, the charges are +1 for Na and -1 for Cl, and the separation distance is the distance between the nuclei of the two atoms.

If you were to calculate the binding energy for a different atom, you would need to determine the charges and separation distance for that specific case. This could be done by looking at the atomic structure and determining the number of valence electrons and the atomic radius.

It's important to note that this formula is a simplified version and does not take into account the full complexity of the ionic bond. Other factors, such as the polarizability of the ions and the lattice energy of the crystal structure, also contribute to the overall binding energy. Therefore, the calculated value may not be entirely accurate, but it can provide a rough estimate.