To calculate the Born-Mayer potential, multiply the constant A by the exponential function of the negative ratio of ion distance (R) to the repulsion parameter (ρ).
Born Mayer Potential Calculator
Enter any 3 values to calculate the missing variable
The Born Mayer Potential Calculator is used to calculate the potential energy between ions in a lattice structure. This potential plays an important role in understanding ionic crystals and lattice energy.
The Born-Mayer equation is used to calculate the repulsive energy component of the total potential energy in ionic solids, complementing the Coulombic (attractive) potential. The formula includes constants related to the specific crystal structure and ion distances, making it useful in fields like solid-state physics and chemistry.
Formula
V = A × e^(-R / ρ)
| Variable | Description |
|---|---|
| V | Born-Mayer potential energy (in joules) |
| A | Constant based on material properties |
| R | Distance between ions (in meters) |
| ρ | Repulsion parameter or range parameter (in meters) |
How to Calculate ?
- Determine the constant A, specific to the material.
- Measure the distance between ions (R) in meters.
- Identify the repulsion parameter (ρ) in meters.
- Use the formula: Multiply A by the exponential of (-R / ρ).
- The result will give you the Born-Mayer potential energy between the ions.
Example 1
| Step | Calculation |
|---|---|
| Given A | 1.0 × 10⁻¹² J |
| Distance between ions (R) | 0.2 × 10⁻⁹ m |
| Repulsion parameter (ρ) | 0.03 × 10⁻⁹ m |
| V Calculation | 1.0 × 10⁻¹² × e^(-0.2 / 0.03) |
| Result | V ≈ 2.06 × 10⁻¹³ J |
Answer: The Born-Mayer potential is approximately 2.06 × 10⁻¹³ J.
Example 2
| Step | Calculation |
|---|---|
| Given A | 2.5 × 10⁻¹² J |
| Distance between ions (R) | 0.15 × 10⁻⁹ m |
| Repulsion parameter (ρ) | 0.05 × 10⁻⁹ m |
| V Calculation | 2.5 × 10⁻¹² × e^(-0.15 / 0.05) |
| Result | V ≈ 4.11 × 10⁻¹³ J |
Answer: The Born-Mayer potential is approximately 4.11 × 10⁻¹³ J.
What is Born Mayer Potential Calculator ?
The Born-Mayer potential is used to calculate the lattice energy in ionic crystals, providing insights into the strength of the ionic bonds. The formula for the Born-Mayer potential is: V(r) = A * exp(-r/ρ) – C/r^n
Here, A is a constant related to the repulsion between ions, r is the distance between ions, ρ is a parameter that defines how quickly the repulsive forces decrease with distance, and C is the Coulomb constant related to the attraction between oppositely charged ions.
The Born-Mayer equation is often combined with the Madelung constant to determine lattice energies in a more comprehensive way.
Using a Born-Mayer potential calculator, you can estimate the lattice energy of a crystal by inputting values for these constants. This calculation is often part of the Born-Haber cycle, which assesses the energy changes in the formation of an ionic compound.
For detailed lattice energy calculations, you can reference a Madelung constant calculator, which is essential for determining how ionic charges interact within the crystal structure.
