1. What is the Born Exponent?

Definition: The Born Exponent is a number between 5 and 12, determined experimentally by measuring the compressibility of the solid, or derived theoretically.

Purpose: It's used in the Born-Landé equation to calculate lattice energy of ionic crystals, accounting for repulsive forces between ions.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( n_{born} \) — Born Exponent (unitless)
• \( U \) — Lattice Energy (J/mol)
• \( \epsilon_0 \) — Permittivity of vacuum (8.854×10⁻¹² F/m)
• \( r_0 \) — Distance of closest approach (m)
• \( N_A \) — Avogadro's number (6.022×10²³ mol⁻¹)
• \( M \) — Madelung constant (unitless)
• \( e \) — Elementary charge (1.602×10⁻¹⁹ C)
• \( z^+ \) — Charge of cation (unitless)
• \( z^- \) — Charge of anion (unitless)

3. Importance of Born Exponent

Details: The Born exponent is crucial for accurate lattice energy calculations, which are fundamental in understanding ionic crystal stability, solubility, and melting points.

4. Using the Calculator

Tips: Enter all required values with proper units. The Madelung constant defaults to 1.7 (typical for NaCl structure). Charges should be entered as whole numbers representing ionic charges.

5. Frequently Asked Questions (FAQ)

Q1: What's a typical range for Born exponent?
A: Most ionic compounds have Born exponents between 5 and 12, with 8 being a common average value.

Q2: How do I determine the Madelung constant?
A: It depends on crystal structure: 1.748 for NaCl, 1.638 for CsCl, 5.039 for fluorite (CaF₂).

Q3: What units should I use for distance?
A: The distance should be in meters (typically in the range of 2-3×10⁻¹⁰ m for ionic crystals).

Q4: Can I use this for covalent compounds?
A: No, the Born-Landé equation and Born exponent are specifically for ionic compounds.

Q5: Why is lattice energy negative in the formula?
A: The negative sign accounts for the exothermic nature of lattice formation (energy is released).