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Madelung Constant using Born-Mayer equation Calculator

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Madelung Constant Distance of Closest Approach

✖The Lattice Energy of a crystalline solid is a measure of the energy released when ions are combined to make a compound.ⓘ Lattice Energy [U]			+10% -10%
✖Distance of Closest Approach is the distance to which an alpha particle comes closer to the nucleus.ⓘ Distance of Closest Approach [r₀]			+10% -10%
✖The Charge of Cation is the positive charge over a cation with fewer electron than the respective atom.ⓘ Charge of Cation [z⁺]			+10% -10%
✖The Charge of Anion is the negative charge over an anion with more electron than the respective atom.ⓘ Charge of Anion [z^-]			+10% -10%
✖The Constant Depending on Compressibility is a constant dependent on the compressibility of the crystal, 30 pm works well for all alkali metal halides.ⓘ Constant Depending on Compressibility [ρ]			+10% -10%

✖The Madelung constant is used in determining the electrostatic potential of a single ion in a crystal by approximating the ions by point charges.ⓘ Madelung Constant using Born-Mayer equation [M]

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Madelung Constant using Born-Mayer equation Solution

STEP 0: Pre-Calculation Summary

Formula Used

Madelung Constant = (-Lattice Energy*4*pi*[Permitivity-vacuum]*Distance of Closest Approach)/([Avaga-no]*Charge of Cation*Charge of Anion*([Charge-e]^2)*(1-(Constant Depending on Compressibility/Distance of Closest Approach)))
M = (-U*4*pi*[Permitivity-vacuum]*r₀)/([Avaga-no]*z⁺*z^-*([Charge-e]^2)*(1-(ρ/r₀)))
This formula uses 4 Constants, 6 Variables

Constants Used

[Permitivity-vacuum] - Permittivity of vacuum Value Taken As 8.85E-12
[Avaga-no] - Avogadro’s number Value Taken As 6.02214076E+23
[Charge-e] - Charge of electron Value Taken As 1.60217662E-19
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Madelung Constant - The Madelung constant is used in determining the electrostatic potential of a single ion in a crystal by approximating the ions by point charges.
Lattice Energy - (Measured in Joule per Mole) - The Lattice Energy of a crystalline solid is a measure of the energy released when ions are combined to make a compound.
Distance of Closest Approach - (Measured in Meter) - Distance of Closest Approach is the distance to which an alpha particle comes closer to the nucleus.
Charge of Cation - (Measured in Coulomb) - The Charge of Cation is the positive charge over a cation with fewer electron than the respective atom.
Charge of Anion - (Measured in Coulomb) - The Charge of Anion is the negative charge over an anion with more electron than the respective atom.
Constant Depending on Compressibility - (Measured in Meter) - The Constant Depending on Compressibility is a constant dependent on the compressibility of the crystal, 30 pm works well for all alkali metal halides.

STEP 1: Convert Input(s) to Base Unit

Lattice Energy: 3500 Joule per Mole --> 3500 Joule per Mole No Conversion Required
Distance of Closest Approach: 60 Angstrom --> 6E-09 Meter (Check conversion here)
Charge of Cation: 4 Coulomb --> 4 Coulomb No Conversion Required
Charge of Anion: 3 Coulomb --> 3 Coulomb No Conversion Required
Constant Depending on Compressibility: 60.44 Angstrom --> 6.044E-09 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

M = (-U*4*pi*[Permitivity-vacuum]*r₀)/([Avaga-no]*z⁺*z^-*([Charge-e]^2)*(1-(ρ/r₀))) --> (-3500*4*pi*[Permitivity-vacuum]*6E-09)/([Avaga-no]*4*3*([Charge-e]^2)*(1-(6.044E-09/6E-09)))

Evaluating ... ...

M = 1.71679355814139

STEP 3: Convert Result to Output's Unit

1.71679355814139 --> No Conversion Required

FINAL ANSWER

1.71679355814139 ≈ 1.716794 <-- Madelung Constant

(Calculation completed in 00.020 seconds)

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University of Hawaiʻi at Mānoa (UH Manoa), Hawaii, USA

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< Madelung Constant Calculators

Madelung Constant using Born-Mayer equation

LaTeX Go Madelung Constant = (-Lattice Energy*4*pi*[Permitivity-vacuum]*Distance of Closest Approach)/([Avaga-no]*Charge of Cation*Charge of Anion*([Charge-e]^2)*(1-(Constant Depending on Compressibility/Distance of Closest Approach)))

Madelung Constant using Born Lande Equation

LaTeX Go Madelung Constant = (-Lattice Energy*4*pi*[Permitivity-vacuum]*Distance of Closest Approach)/((1-(1/Born Exponent))*([Charge-e]^2)*[Avaga-no]*Charge of Cation*Charge of Anion)

Madelung Constant given Repulsive Interaction Constant

LaTeX Go Madelung Constant = (Repulsive Interaction Constant given M*4*pi*[Permitivity-vacuum]*Born Exponent)/((Charge^2)*([Charge-e]^2)*(Distance of Closest Approach^(Born Exponent-1)))

Madelung Constant using Kapustinskii Approximation

LaTeX Go Madelung Constant = 0.88*Number of Ions

Madelung Constant using Born-Mayer equation Formula

LaTeX Go

What is Born–Landé equation?

The Born–Landé equation is a means of calculating the lattice energy of a crystalline ionic compound. In 1918 Max Born and Alfred Landé proposed that the lattice energy could be derived from the electrostatic potential of the ionic lattice and a repulsive potential energy term. The ionic lattice is modeled as an assembly of hard elastic spheres which are compressed together by the mutual attraction of the electrostatic charges on the ions. They achieve the observed equilibrium distance apart due to a balancing short range repulsion.

How to Calculate Madelung Constant using Born-Mayer equation?

Madelung Constant using Born-Mayer equation calculator uses Madelung Constant = (-Lattice Energy*4*pi*[Permitivity-vacuum]*Distance of Closest Approach)/([Avaga-no]*Charge of Cation*Charge of Anion*([Charge-e]^2)*(1-(Constant Depending on Compressibility/Distance of Closest Approach))) to calculate the Madelung Constant, The Madelung constant using Born-Mayer equation is used in determining the electrostatic potential of a single ion in a crystal by approximating the ions by point charges. Madelung Constant is denoted by M symbol.

How to calculate Madelung Constant using Born-Mayer equation using this online calculator? To use this online calculator for Madelung Constant using Born-Mayer equation, enter Lattice Energy (U), Distance of Closest Approach (r₀), Charge of Cation (z⁺), Charge of Anion (z^-) & Constant Depending on Compressibility (ρ) and hit the calculate button. Here is how the Madelung Constant using Born-Mayer equation calculation can be explained with given input values -> 1.716794 = (-3500*4*pi*[Permitivity-vacuum]*6E-09)/([Avaga-no]*4*3*([Charge-e]^2)*(1-(6.044E-09/6E-09))).

FAQ

What is Madelung Constant using Born-Mayer equation?

The Madelung constant using Born-Mayer equation is used in determining the electrostatic potential of a single ion in a crystal by approximating the ions by point charges and is represented as M = (-U*4*pi*[Permitivity-vacuum]*r₀)/([Avaga-no]*z⁺*z^-*([Charge-e]^2)*(1-(ρ/r₀))) or Madelung Constant = (-Lattice Energy*4*pi*[Permitivity-vacuum]*Distance of Closest Approach)/([Avaga-no]*Charge of Cation*Charge of Anion*([Charge-e]^2)*(1-(Constant Depending on Compressibility/Distance of Closest Approach))). The Lattice Energy of a crystalline solid is a measure of the energy released when ions are combined to make a compound, Distance of Closest Approach is the distance to which an alpha particle comes closer to the nucleus, The Charge of Cation is the positive charge over a cation with fewer electron than the respective atom, The Charge of Anion is the negative charge over an anion with more electron than the respective atom & The Constant Depending on Compressibility is a constant dependent on the compressibility of the crystal, 30 pm works well for all alkali metal halides.

How to calculate Madelung Constant using Born-Mayer equation?

The Madelung constant using Born-Mayer equation is used in determining the electrostatic potential of a single ion in a crystal by approximating the ions by point charges is calculated using Madelung Constant = (-Lattice Energy*4*pi*[Permitivity-vacuum]*Distance of Closest Approach)/([Avaga-no]*Charge of Cation*Charge of Anion*([Charge-e]^2)*(1-(Constant Depending on Compressibility/Distance of Closest Approach))). To calculate Madelung Constant using Born-Mayer equation, you need Lattice Energy (U), Distance of Closest Approach (r₀), Charge of Cation (z⁺), Charge of Anion (z^-) & Constant Depending on Compressibility (ρ). With our tool, you need to enter the respective value for Lattice Energy, Distance of Closest Approach, Charge of Cation, Charge of Anion & Constant Depending on Compressibility and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Madelung Constant?

In this formula, Madelung Constant uses Lattice Energy, Distance of Closest Approach, Charge of Cation, Charge of Anion & Constant Depending on Compressibility. We can use 3 other way(s) to calculate the same, which is/are as follows -

Madelung Constant = (Repulsive Interaction Constant given M*4*pi*[Permitivity-vacuum]*Born Exponent)/((Charge^2)*([Charge-e]^2)*(Distance of Closest Approach^(Born Exponent-1)))
Madelung Constant = (-Lattice Energy*4*pi*[Permitivity-vacuum]*Distance of Closest Approach)/((1-(1/Born Exponent))*([Charge-e]^2)*[Avaga-no]*Charge of Cation*Charge of Anion)
Madelung Constant = 0.88*Number of Ions

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