Madelung Energy Calculator

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Madelung Constant

Distance of Closest Approach

✖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 [M]			+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%
✖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 Madelung Energy for a simple lattice consisting ions with equal and opposite charge in a 1:1 ratio is the sum of interactions between one ion and all other lattice ions.ⓘ Madelung Energy [E_M]

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Formula

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Madelung Energy

Formula

`"E"_{"M"} = -("M"*("q"^2)*("[Charge-e]"^2))/(4*pi*"[Permitivity-vacuum]"*"r"_{"0"})`

Example

`"-5.9E^-21J"=-("1.7"*(("0.3C")^2)*("[Charge-e]"^2))/(4*pi*"[Permitivity-vacuum]"*"60A")`

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Download Madelung Constant Formulas PDF

Madelung Energy Solution

STEP 0: Pre-Calculation Summary

Formula Used

Madelung Energy = -(Madelung Constant*(Charge^2)*([Charge-e]^2))/(4*pi*[Permitivity-vacuum]*Distance of Closest Approach)
E_M = -(M*(q^2)*([Charge-e]^2))/(4*pi*[Permitivity-vacuum]*r₀)
This formula uses 3 Constants, 4 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 Energy - (Measured in Joule) - The Madelung Energy for a simple lattice consisting ions with equal and opposite charge in a 1:1 ratio is the sum of interactions between one ion and all other lattice ions.
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.
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.
Distance of Closest Approach - (Measured in Meter) - Distance of Closest Approach is the distance to which an alpha particle comes closer to the nucleus.

STEP 1: Convert Input(s) to Base Unit

Madelung Constant: 1.7 --> No Conversion Required
Charge: 0.3 Coulomb --> 0.3 Coulomb No Conversion Required
Distance of Closest Approach: 60 Angstrom --> 6E-09 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

E_M = -(M*(q^2)*([Charge-e]^2))/(4*pi*[Permitivity-vacuum]*r₀) --> -(1.7*(0.3^2)*([Charge-e]^2))/(4*pi*[Permitivity-vacuum]*6E-09)

Evaluating ... ...

E_M = -5.88583150902241E-21

STEP 3: Convert Result to Output's Unit

-5.88583150902241E-21 Joule --> No Conversion Required

FINAL ANSWER

-5.88583150902241E-21 ≈ -5.9E-21 Joule <-- Madelung Energy

(Calculation completed in 00.004 seconds)

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Created by Prerana Bakli

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

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< 10+ Madelung Constant Calculators

Madelung Constant using Born-Mayer equation

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 Total Energy of Ion

Go 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))

Madelung Constant using Born Lande Equation

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

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 Total Energy of Ion given Repulsive Interaction

Go Madelung Constant = ((Total energy of Ion in an Ionic Crystal-Repulsive Interaction between Ions)*4*pi*[Permitivity-vacuum]*Distance of Closest Approach)/(-(Charge^2)*([Charge-e]^2))

Madelung Constant using Madelung Energy

Go Madelung Constant = (-(Madelung Energy)*4*pi*[Permitivity-vacuum]*Distance of Closest Approach)/((Charge^2)*([Charge-e]^2))

Madelung Energy

Go Madelung Energy = -(Madelung Constant*(Charge^2)*([Charge-e]^2))/(4*pi*[Permitivity-vacuum]*Distance of Closest Approach)

Madelung Energy using Total Energy of Ion given Distance

Go Madelung Energy = Total energy of Ion in an Ionic Crystal-(Repulsive Interaction Constant given M/(Distance of Closest Approach^Born Exponent))

Madelung Energy using Total Energy of Ion

Go Madelung Energy = Total energy of Ion in an Ionic Crystal-Repulsive Interaction between Ions

Madelung Constant using Kapustinskii Approximation

Go Madelung Constant = 0.88*Number of Ions

Madelung Energy Formula

Madelung Energy = -(Madelung Constant*(Charge^2)*([Charge-e]^2))/(4*pi*[Permitivity-vacuum]*Distance of Closest Approach)
E_M = -(M*(q^2)*([Charge-e]^2))/(4*pi*[Permitivity-vacuum]*r₀)

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 Energy?

Madelung Energy calculator uses Madelung Energy = -(Madelung Constant*(Charge^2)*([Charge-e]^2))/(4*pi*[Permitivity-vacuum]*Distance of Closest Approach) to calculate the Madelung Energy, The Madelung Energy for a simple lattice consisting ions with equal and opposite charge in a 1:1 ratio is the sum of interactions between one ion and all other lattice ions. Madelung Energy is denoted by E_M symbol.

How to calculate Madelung Energy using this online calculator? To use this online calculator for Madelung Energy, enter Madelung Constant (M), Charge (q) & Distance of Closest Approach (r₀) and hit the calculate button. Here is how the Madelung Energy calculation can be explained with given input values -> -5.9E-21 = -(1.7*(0.3^2)*([Charge-e]^2))/(4*pi*[Permitivity-vacuum]*6E-09).

FAQ

What is Madelung Energy?

The Madelung Energy for a simple lattice consisting ions with equal and opposite charge in a 1:1 ratio is the sum of interactions between one ion and all other lattice ions and is represented as E_M = -(M*(q^2)*([Charge-e]^2))/(4*pi*[Permitivity-vacuum]*r₀) or Madelung Energy = -(Madelung Constant*(Charge^2)*([Charge-e]^2))/(4*pi*[Permitivity-vacuum]*Distance of Closest Approach). The Madelung constant is used in determining the electrostatic potential of a single ion in a crystal by approximating the ions by point charges, A Charge is the fundamental property of forms of matter that exhibit electrostatic attraction or repulsion in the presence of other matter & Distance of Closest Approach is the distance to which an alpha particle comes closer to the nucleus.

How to calculate Madelung Energy?

The Madelung Energy for a simple lattice consisting ions with equal and opposite charge in a 1:1 ratio is the sum of interactions between one ion and all other lattice ions is calculated using Madelung Energy = -(Madelung Constant*(Charge^2)*([Charge-e]^2))/(4*pi*[Permitivity-vacuum]*Distance of Closest Approach). To calculate Madelung Energy, you need Madelung Constant (M), Charge (q) & Distance of Closest Approach (r₀). With our tool, you need to enter the respective value for Madelung Constant, Charge & Distance of Closest Approach 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 Energy?

In this formula, Madelung Energy uses Madelung Constant, Charge & Distance of Closest Approach. We can use 2 other way(s) to calculate the same, which is/are as follows -

Madelung Energy = Total energy of Ion in an Ionic Crystal-Repulsive Interaction between Ions
Madelung Energy = Total energy of Ion in an Ionic Crystal-(Repulsive Interaction Constant given M/(Distance of Closest Approach^Born Exponent))

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