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Madelung Energy using Total Energy of Ion given Distance 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%

✖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 using Total Energy of Ion given Distance [E_M]

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Madelung Energy using Total Energy of Ion given Distance Solution

STEP 0: Pre-Calculation Summary

Formula Used

Madelung Energy = Total energy of Ion in an Ionic Crystal-(Repulsive Interaction Constant given M/(Distance of Closest Approach^Born Exponent))
E_M = E_tot-(B_M/(r₀^n_born))
This formula uses 5 Variables

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.
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.

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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

E_M = E_tot-(B_M/(r₀^n_born)) --> 7.02E-23-(4.1E-29/(6E-09^0.9926))

Evaluating ... ...

E_M = -5.8698612831808E-21

STEP 3: Convert Result to Output's Unit

-5.8698612831808E-21 Joule --> No Conversion Required

FINAL ANSWER

-5.8698612831808E-21 ≈ -5.9E-21 Joule <-- Madelung Energy

(Calculation completed in 00.004 seconds)

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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 Energy using Total Energy of Ion given Distance Formula

LaTeX Go

Madelung Energy = Total energy of Ion in an Ionic Crystal-(Repulsive Interaction Constant given M/(Distance of Closest Approach^Born Exponent))
E_M = E_tot-(B_M/(r₀^n_born))

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 using Total Energy of Ion given Distance?

Madelung Energy using Total Energy of Ion given Distance calculator uses Madelung Energy = Total energy of Ion in an Ionic Crystal-(Repulsive Interaction Constant given M/(Distance of Closest Approach^Born Exponent)) to calculate the Madelung Energy, The Madelung Energy using Total Energy of Ion given Distance 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 Total Energy of Ion given Distance using this online calculator? To use this online calculator for Madelung Energy using Total Energy of Ion given Distance, 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) and hit the calculate button. Here is how the Madelung Energy using Total Energy of Ion given Distance calculation can be explained with given input values -> -5.9E-21 = 7.02E-23-(4.1E-29/(6E-09^0.9926)).

FAQ

What is Madelung Energy using Total Energy of Ion given Distance?

The Madelung Energy using Total Energy of Ion given Distance 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 = E_tot-(B_M/(r₀^n_born)) or Madelung Energy = Total energy of Ion in an Ionic Crystal-(Repulsive Interaction Constant given M/(Distance of Closest Approach^Born Exponent)). 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.

How to calculate Madelung Energy using Total Energy of Ion given Distance?

The Madelung Energy using Total Energy of Ion given Distance 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 = Total energy of Ion in an Ionic Crystal-(Repulsive Interaction Constant given M/(Distance of Closest Approach^Born Exponent)). To calculate Madelung Energy using Total Energy of Ion given Distance, 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). 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 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 Total energy of Ion in an Ionic Crystal, Repulsive Interaction Constant given M, Distance of Closest Approach & Born Exponent. We can use 2 other way(s) to calculate the same, which is/are as follows -

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

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