Born–Landé Lattice Energy Calculator
🔥 Thermochemistry & Bonding. Use the Born–Landé lattice energy formula to find lattice energy, madelung constant, cation charge |z⁺|, anion charge |z⁻|, ion distance r₀, born exponent n: pick the value you want, type the others, and the answer updates as you go.
Enter the charge sizes (both positive). Default: NaCl, about −755 kJ/mol.
Pick the ○ next to the value you want to find, fill in the others, and it solves as you type.
What each letter means
| Quantity | Unit |
|---|---|
| Lattice energy | kJ/mol |
| Madelung constant | no unit |
| Cation charge |z⁺| | no unit |
| Anion charge |z⁻| | no unit |
| Ion distance r₀ | pm |
| Born exponent n | no unit |
Worked example
Find the lattice energy when Madelung constant = 1.748, Cation charge |z⁺| = 1, Anion charge |z⁻| = 1, Ion distance r₀ = 282 pm, Born exponent n = 8.
Using E = -(NA M z^+ z^- e²)/(4πε0 r0)(1 - 1/n): Lattice energy = -753.55 kJ/mol.
Frequently asked questions
What is the formula for Born–Landé lattice energy?
E = -(NA M z^+ z^- e²)/(4πε0 r0)(1 - 1/n). Enter the charge sizes (both positive). Default: NaCl, about −755 kJ/mol.
What do the letters stand for, and what units are used?
Lattice energy in kJ/mol, Madelung constant, Cation charge |z⁺|, Anion charge |z⁻|, Ion distance r₀ in pm, Born exponent n.
How do you calculate lattice energy?
Put the values into E = -(NA M z^+ z^- e²)/(4πε0 r0)(1 - 1/n). For example, with Madelung constant = 1.748, Cation charge |z⁺| = 1, Anion charge |z⁻| = 1, Ion distance r₀ = 282 pm, Born exponent n = 8, lattice energy = -753.55 kJ/mol.
Can I solve for a different value?
Yes. In the calculator above, pick the circle next to any value (lattice energy, madelung constant, cation charge |z⁺|, anion charge |z⁻|, ion distance r₀, born exponent n) and fill in the others: it rearranges the formula for you.
