Born Exponent Using Born-Lande Equation Without Madelung Constant Calculator

Born-Lande Equation Without Madelung Constant:

\[ n_{born} = \frac{1}{1 - \frac{-U \cdot 4\pi \cdot \varepsilon_0 \cdot r_0}{N_A \cdot N_{ions} \cdot 0.88 \cdot e^2 \cdot z^+ \cdot z^-}} \]

Lattice Energy (U):

J/mol

Distance of Closest Approach (r₀):

Number of Ions (N_ions):

Charge of Cation (z⁺):

Charge of Anion (z⁻):

Born Exponent (n_born):

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1. What is the Born Exponent?

The Born Exponent is a parameter in the Born-Lande equation that characterizes the repulsive forces between ions in a crystal lattice. It typically ranges between 5 and 12 and is determined experimentally by measuring the compressibility of solids or derived theoretically.

2. How Does the Calculator Work?

The calculator uses the Born-Lande equation without Madelung constant:

\[ n_{born} = \frac{1}{1 - \frac{-U \cdot 4\pi \cdot \varepsilon_0 \cdot r_0}{N_A \cdot N_{ions} \cdot 0.88 \cdot e^2 \cdot z^+ \cdot z^-}} \]

Where:

\( U \) — Lattice Energy (J/mol)
\( r_0 \) — Distance of Closest Approach (m)
\( N_{ions} \) — Number of Ions
\( z^+ \) — Charge of Cation
\( z^- \) — Charge of Anion
\( \varepsilon_0 \) — Permittivity of vacuum (8.85×10⁻¹² F/m)
\( N_A \) — Avogadro's number (6.022×10²³ mol⁻¹)
\( e \) — Charge of electron (1.602×10⁻¹⁹ C)

Explanation: The equation calculates the Born exponent based on the balance between attractive Coulomb forces and repulsive forces in ionic crystals.

3. Importance of Born Exponent Calculation

Details: The Born exponent is crucial for understanding the stability and compressibility of ionic compounds. It helps in predicting material properties and behavior under different conditions.

4. Using the Calculator

Tips: Enter lattice energy in J/mol, distance in meters, number of ions, and charges of cation and anion. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for Born exponent values?
A: Born exponent values typically range between 5 and 12 for most ionic compounds.

Q2: How is the Born exponent determined experimentally?
A: The Born exponent is determined by measuring the compressibility of solid materials under pressure.

Q3: Why is the Madelung constant not included in this calculation?
A: This specific formulation focuses on the fundamental ionic interactions without considering the specific crystal structure geometry represented by the Madelung constant.

Q4: What factors influence the Born exponent value?
A: The Born exponent is influenced by the size of ions, their electronic configurations, and the nature of ionic bonding in the compound.

Q5: Can this calculator be used for all ionic compounds?
A: This calculator provides a theoretical estimation based on fundamental principles, but experimental validation is recommended for specific compounds.