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Distance of Closest Approach using Born Lande equation Calculator

Distance of Closest Approach Formula:

\[ r_0 = \frac{-N_A \cdot M \cdot z^+ \cdot z^- \cdot e^2 \cdot (1 - \frac{1}{n})}{4 \pi \varepsilon_0 \cdot U} \]

J/mol

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1. What is Distance of Closest Approach using Born Lande equation?

Definition: This calculator determines the equilibrium distance between ions in an ionic crystal using the Born-Lande equation.

Purpose: It helps in understanding ionic crystal structures and predicting lattice parameters in materials science.

2. How Does the Calculator Work?

The calculator uses the Born-Lande equation:

\[ r_0 = \frac{-N_A \cdot M \cdot z^+ \cdot z^- \cdot e^2 \cdot (1 - \frac{1}{n})}{4 \pi \varepsilon_0 \cdot U} \]

Where:

3. Importance of Distance of Closest Approach

Details: This calculation is fundamental in determining ionic radii, predicting crystal stability, and understanding material properties.

4. Using the Calculator

Tips: Enter the Madelung constant (default 1.7 for NaCl), cation charge, anion charge, Born exponent (default 8), and lattice energy. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is the Madelung constant?
A: It's a dimensionless constant that depends on the crystal structure geometry and accounts for the electrostatic interaction between ions.

Q2: Typical values for Born exponent?
A: It ranges from 5 to 12, with 8 being typical for many ionic crystals.

Q3: How to find lattice energy?
A: Lattice energy can be determined experimentally via Born-Haber cycles or calculated theoretically using other approaches.

Q4: What units does this calculator use?
A: All calculations are in SI units (meters, coulombs, joules).

Q5: Why is the result negative in the formula?
A: The negative sign indicates an attractive force between ions, but the distance itself is positive.

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