Isn't Born-Landé equation double the electrostatic energy?

In summary, the conversation discusses the application of the Born-Landé equation to find the electrostatic potential for an ionic lattice. The equation, as described on Wikipedia, involves summing the products of the charge of each ion in the lattice with the electric potential at its location, but does not include a factor of 1/2. The question is raised as to whether the electrostatic potential needs to be halved before using the equation, but the Wikipedia page does not mention this. The conversation ends with a request for clarification on how the Born-Landé equation can be applied without halving the electrostatic potential.
  • #1
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I'm confused as to how the Born-Landé equation can be extrapolated to find the electrostatic potential for an ionic lattice without halving it, as each interaction is otherwise counted twice.

As I understand it, and according to Wikipedia, the electric potential energy in a charge configuration can be found by this equation:
9464d36ae5844070bd99178f3858f25a.png

This is half the sum of the products of the charge of each ion in the lattice with the electric potential at its location provided by each other ion - the Born-Landé equation, however, does not include this factor of 1/2.
I accept that
gRi8SXa.png

is the correct sum of the energy stored in the interactions of anyone ion, but the final equation multiplies this by the Avogadro constant:

e4e1219b20a6dffdd490de8fe82c9f08.png


I would have thought that this would have counted every interaction twice, by following this equation for the energy stored in a charge configuration:

Chapter2604.gif
 
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  • #2
This would mean that the electrostatic potential for the ionic lattice needs to be halved before it can be used in the Born-Landé equation.However, I'm not sure if this is correct, as the Wikipedia page on the Born-Landé equation does not mention halving the electrostatic potential.Can someone explain to me how the Born-Landé equation can be applied to find the electrostatic potential for an ionic lattice without halving it?
 

1. What is the Born-Landé equation?

The Born-Landé equation is a mathematical formula used in physics to calculate the electrostatic energy between two charged particles. It takes into account the charges and distances of the particles, as well as the dielectric constant of the medium they are in.

2. How is the Born-Landé equation derived?

The Born-Landé equation is derived from the Coulomb's law, which states that the electrostatic force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

3. Why is the Born-Landé equation sometimes referred to as the "double energy equation"?

The Born-Landé equation is sometimes referred to as the "double energy equation" because it takes into account the energy of both the positively charged and negatively charged particles. This is in contrast to other equations, such as the Coulomb's law, which only consider the energy of one of the particles.

4. How is the Born-Landé equation used in practical applications?

The Born-Landé equation is used in various fields of science, including chemistry, physics, and material science. It is often used to calculate the energy changes in chemical reactions, the stability of molecules, and the properties of materials.

5. Are there any limitations to the Born-Landé equation?

While the Born-Landé equation is a useful tool for calculating electrostatic energy, it does have its limitations. It assumes that the particles are point charges and that the medium they are in is homogeneous and isotropic. In reality, this may not always be the case, and the equation may not accurately predict the energy in these situations.

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