Potential energy between two oppositely charged ions in a crystal

In summary, The conversation discusses the concept of equilibrium between two ions, with one person having trouble understanding how equilibrium is achieved when the ions are attracted to each other. The other person explains that the point of equilibrium is where the sum of the forces is zero and where the potential has a minimum value. They suggest plotting the potential to better understand the concept.
  • #1
geoffreythelm
11
0
Hi, I am having trouble with the following:

attachment.php?attachmentid=20081&stc=1&d=1250100045.jpg


All I have really done is differentiate the function to give an expression for F(r), but I am a bit clueless about the rest. How can there be equilibrium if the two ions are attracted to each other?

Cheers,
GeoffreyThelm
 

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  • #2
Your potential has two terms, are they both attractive?
 
  • #3
I see.. So one (the first term?) is due to the attractive force from one ion, and vice versa for the other? So c is going to end up being something which looks like electric potential should. So is the point of equilibrium the point between the ions where the first term= the second term?
 
  • #4
The point of equilibrium is where the sum of the forces is zero. When you have a potential, it is where dU/dx = 0, i.e. where the potential has an extremum (maximum or minimum). In this case it had better be a minimum. Consider plotting this potential to see what it looks like.
 

1. What is potential energy between two oppositely charged ions in a crystal?

The potential energy between two oppositely charged ions in a crystal refers to the amount of energy that is required to bring the ions to a specific distance from each other in the crystal lattice. This energy is a result of the attractive force between the ions due to their opposite charges.

2. How is the potential energy between two oppositely charged ions in a crystal calculated?

The potential energy between two oppositely charged ions in a crystal is calculated using Coulomb's law, which states that the energy is directly proportional to the magnitude of the charges and inversely proportional to the distance between them. It can be represented by the equation E = k(q1q2)/r, where E is the potential energy, k is a constant, q1 and q2 are the charges of the ions, and r is the distance between them.

3. How does the distance between the ions affect the potential energy in a crystal?

The distance between the ions has a significant impact on the potential energy in a crystal. As the distance between the ions decreases, the potential energy increases, and as the distance increases, the potential energy decreases. This is because the closer the ions are, the stronger the attraction between them and the more energy is required to separate them.

4. What is the role of lattice energy in the potential energy between two oppositely charged ions in a crystal?

Lattice energy is the energy released when ions are brought together to form a crystal lattice. This energy is a result of the potential energy between the ions and plays a crucial role in determining the overall potential energy between the ions in the crystal. It is also a major factor in determining the stability and strength of the crystal lattice.

5. How does the type of crystal affect the potential energy between two oppositely charged ions?

The type of crystal can have a significant impact on the potential energy between two oppositely charged ions. In ionic crystals, where ions of opposite charges are held together by electrostatic forces, the potential energy is high due to the strong attraction between the ions. In covalent crystals, where atoms are held together by shared electrons, the potential energy is lower as there is less of an attraction between the ions. Metallic crystals, where electrons are delocalized and shared among all atoms, have even lower potential energy as there is no specific attraction between individual ions.

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