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Madelung Constant using Total Energy of Ion Calculator

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Madelung Constant Distance of Closest Approach

✖The Total energy of Ion in an Ionic Crystal in the lattice is the sum of Madelung Energy and Repulsive potential energy.ⓘ Total energy of Ion in an Ionic Crystal [E_tot]			+10% -10%
✖The Repulsive Interaction Constant given M, (where M= Madelung Constant) is the constant scaling the strength of the repulsive interaction.ⓘ Repulsive Interaction Constant given M [B_M]			+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 Born Exponent is a number between 5 and 12, determined experimentally by measuring the compressibility of the solid, or derived theoretically.ⓘ Born Exponent [n_born]			+10% -10%
✖A Charge is the fundamental property of forms of matter that exhibit electrostatic attraction or repulsion in the presence of other matter.ⓘ Charge [q]			+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 Total Energy of Ion [M]

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Madelung Constant using Total Energy of Ion Solution

STEP 0: Pre-Calculation Summary

Formula Used

Madelung Constant = ((Total energy of Ion in an Ionic Crystal-(Repulsive Interaction Constant given M/(Distance of Closest Approach^Born Exponent)))*4*pi*[Permitivity-vacuum]*Distance of Closest Approach)/(-(Charge^2)*([Charge-e]^2))
M = ((E_tot-(B_M/(r₀^n_born)))*4*pi*[Permitivity-vacuum]*r₀)/(-(q^2)*([Charge-e]^2))
This formula uses 3 Constants, 6 Variables

Constants Used

[Permitivity-vacuum] - Permittivity of vacuum Value Taken As 8.85E-12
[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.
Total energy of Ion in an Ionic Crystal - (Measured in Joule) - The Total energy of Ion in an Ionic Crystal in the lattice is the sum of Madelung Energy and Repulsive potential energy.
Repulsive Interaction Constant given M - The Repulsive Interaction Constant given M, (where M= Madelung Constant) is the constant scaling the strength of the repulsive interaction.
Distance of Closest Approach - (Measured in Meter) - Distance of Closest Approach is the distance to which an alpha particle comes closer to the nucleus.
Born Exponent - The Born Exponent is a number between 5 and 12, determined experimentally by measuring the compressibility of the solid, or derived theoretically.
Charge - (Measured in Coulomb) - A Charge is the fundamental property of forms of matter that exhibit electrostatic attraction or repulsion in the presence of other matter.

STEP 1: Convert Input(s) to Base Unit

Total energy of Ion in an Ionic Crystal: 7.02E-23 Joule --> 7.02E-23 Joule No Conversion Required
Repulsive Interaction Constant given M: 4.1E-29 --> No Conversion Required
Distance of Closest Approach: 60 Angstrom --> 6E-09 Meter (Check conversion here)
Born Exponent: 0.9926 --> No Conversion Required
Charge: 0.3 Coulomb --> 0.3 Coulomb No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

M = ((E_tot-(B_M/(r₀^n_born)))*4*pi*[Permitivity-vacuum]*r₀)/(-(q^2)*([Charge-e]^2)) --> ((7.02E-23-(4.1E-29/(6E-09^0.9926)))*4*pi*[Permitivity-vacuum]*6E-09)/(-(0.3^2)*([Charge-e]^2))

Evaluating ... ...

M = 1.69538733246286

STEP 3: Convert Result to Output's Unit

1.69538733246286 --> No Conversion Required

FINAL ANSWER

1.69538733246286 ≈ 1.695387 <-- 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 Total Energy of Ion 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 Total Energy of Ion?

Madelung Constant using Total Energy of Ion calculator uses Madelung Constant = ((Total energy of Ion in an Ionic Crystal-(Repulsive Interaction Constant given M/(Distance of Closest Approach^Born Exponent)))*4*pi*[Permitivity-vacuum]*Distance of Closest Approach)/(-(Charge^2)*([Charge-e]^2)) to calculate the Madelung Constant, The Madelung constant using Total Energy of Ion 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 Total Energy of Ion using this online calculator? To use this online calculator for Madelung Constant using Total Energy of Ion, enter Total energy of Ion in an Ionic Crystal (E_tot), Repulsive Interaction Constant given M (B_M), Distance of Closest Approach (r₀), Born Exponent (n_born) & Charge (q) and hit the calculate button. Here is how the Madelung Constant using Total Energy of Ion calculation can be explained with given input values -> 1.695387 = ((7.02E-23-(4.1E-29/(6E-09^0.9926)))*4*pi*[Permitivity-vacuum]*6E-09)/(-(0.3^2)*([Charge-e]^2)).

FAQ

What is Madelung Constant using Total Energy of Ion?

The Madelung constant using Total Energy of Ion 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 = ((E_tot-(B_M/(r₀^n_born)))*4*pi*[Permitivity-vacuum]*r₀)/(-(q^2)*([Charge-e]^2)) or Madelung Constant = ((Total energy of Ion in an Ionic Crystal-(Repulsive Interaction Constant given M/(Distance of Closest Approach^Born Exponent)))*4*pi*[Permitivity-vacuum]*Distance of Closest Approach)/(-(Charge^2)*([Charge-e]^2)). The Total energy of Ion in an Ionic Crystal in the lattice is the sum of Madelung Energy and Repulsive potential energy, The Repulsive Interaction Constant given M, (where M= Madelung Constant) is the constant scaling the strength of the repulsive interaction, Distance of Closest Approach is the distance to which an alpha particle comes closer to the nucleus, The Born Exponent is a number between 5 and 12, determined experimentally by measuring the compressibility of the solid, or derived theoretically & A Charge is the fundamental property of forms of matter that exhibit electrostatic attraction or repulsion in the presence of other matter.

How to calculate Madelung Constant using Total Energy of Ion?

The Madelung constant using Total Energy of Ion 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 = ((Total energy of Ion in an Ionic Crystal-(Repulsive Interaction Constant given M/(Distance of Closest Approach^Born Exponent)))*4*pi*[Permitivity-vacuum]*Distance of Closest Approach)/(-(Charge^2)*([Charge-e]^2)). To calculate Madelung Constant using Total Energy of Ion, you need Total energy of Ion in an Ionic Crystal (E_tot), Repulsive Interaction Constant given M (B_M), Distance of Closest Approach (r₀), Born Exponent (n_born) & Charge (q). With our tool, you need to enter the respective value for Total energy of Ion in an Ionic Crystal, Repulsive Interaction Constant given M, Distance of Closest Approach, Born Exponent & Charge 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 Total energy of Ion in an Ionic Crystal, Repulsive Interaction Constant given M, Distance of Closest Approach, Born Exponent & Charge. 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 = (-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)))

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