असंतृप्तता की डिग्री कैलकुलेटर — सूत्र

Born-Landé Equation for Lattice Energy

Formula

U = −(A × N_A × e² × z⁺ × z⁻) / (4πε₀ × r₀) × (1 − 1/n)

Simplified with constants combined: U = −(A × 1389.4 × z⁺ × z⁻ / r₀) × (1 − 1/n)

Where r₀ is in angstroms (pm/100), and 1389.4 kJ·Å/mol combines N_A, e², and 4πε₀.

Where:

  • A = Madelung constant (depends on crystal structure)
  • z⁺, z⁻ = ion charges
  • r₀ = interionic distance
  • n = Born exponent (5-12 depending on electron configuration)

    • हल किया गया उदाहरण

    NaCl: z⁺ = 1, z⁻ = 1, r₀ = 281 pm, A = 1.748, n = 8.

    1. U = -(A × 1389.4 × z⁺ × z⁻ / r₀) × (1 - 1/n)
    2. r₀ = 281 pm = 2.81 Å
    3. U = -(1.748 × 1389.4 × 1 × 1 / 2.81) × (1 - 1/8)
    4. U = -(864.2) × (0.875)
    5. U = -756 kJ/mol