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Born-Landé Lattice Energy Calculator — result sheet
Estimate ionic lattice energy per mole from charges, interionic distance, Madelung constant, and Born exponent.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: U = −NₐM|z₊z₋|e²/(4πε₀r₀) × (1−1/n).
The Born-Landé model estimates the electrostatic lattice energy with a repulsion correction for an ideal ionic crystal.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Madelung constant — minimum 1.0E-6; maximum 100
- Cation charge magnitude — e; minimum 1.0E-6; maximum 20
- Anion charge magnitude — e; minimum 1.0E-6; maximum 20
- Closest ion distance — pm; minimum 1.0E-6; maximum 1000000
- Born exponent n — minimum 1.000001; maximum 100
Worked example
| Input | Value |
|---|---|
| Madelung constant | 1.74756 |
| Cation charge magnitude | 1 |
| Anion charge magnitude | 1 |
| Closest ion distance | 281 |
| Born exponent n | 9 |
Lattice energy ≈ −768 kJ/mol.
Assumptions and limits
- Charges are entered as magnitudes in elementary-charge units and distance is the nearest-ion separation.
- The Madelung constant and Born exponent describe the chosen crystal structure and ion pair.
- Crystal defects, polarization, covalency, hydration, and enthalpy-of-solution effects are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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