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Repulsive Interaction Constant given Total Energy of Ion and Madelung Energy Calculator

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Lattice Energy

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Distance of Closest Approach Madelung Constant

✖The Total Energy of Ion in the lattice is the sum of Madelung Energy and Repulsive potential energy.ⓘ Total Energy of Ion [E_total]			+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]			+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 Repulsive Interaction Constant is the constant scaling the strength of the repulsive interaction.ⓘ Repulsive Interaction Constant given Total Energy of Ion and Madelung Energy [B]

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Repulsive Interaction Constant given Total Energy of Ion and Madelung Energy Solution

STEP 0: Pre-Calculation Summary

Formula Used

Repulsive Interaction Constant = (Total Energy of Ion-(Madelung Energy))*(Distance of Closest Approach^Born Exponent)
B = (E_total-(E_M))*(r₀^n_born)
This formula uses 5 Variables

Variables Used

Repulsive Interaction Constant - The Repulsive Interaction Constant is the constant scaling the strength of the repulsive interaction.
Total Energy of Ion - (Measured in Joule) - The Total Energy of Ion in the lattice is the sum of Madelung Energy and Repulsive potential energy.
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.
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: 5790000000000 Joule --> 5790000000000 Joule No Conversion Required
Madelung Energy: -5.9E-21 Joule --> -5.9E-21 Joule 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

B = (E_total-(E_M))*(r₀^n_born) --> (5790000000000-((-5.9E-21)))*(6E-09^0.9926)

Evaluating ... ...

B = 39964.2341522917

STEP 3: Convert Result to Output's Unit

39964.2341522917 --> No Conversion Required

FINAL ANSWER

39964.2341522917 ≈ 39964.23 <-- Repulsive Interaction Constant

(Calculation completed in 00.004 seconds)

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< Lattice Energy Calculators

Lattice Energy using Born Lande Equation

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

Born Exponent using Born Lande Equation

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

Electrostatic Potential Energy between pair of Ions

LaTeX Go Electrostatic Potential Energy between Ion Pair = (-(Charge^2)*([Charge-e]^2))/(4*pi*[Permitivity-vacuum]*Distance of Closest Approach)

Repulsive Interaction

LaTeX Go Repulsive Interaction = Repulsive Interaction Constant/(Distance of Closest Approach^Born Exponent)

Repulsive Interaction Constant given Total Energy of Ion and Madelung Energy Formula

LaTeX Go

Repulsive Interaction Constant = (Total Energy of Ion-(Madelung Energy))*(Distance of Closest Approach^Born Exponent)
B = (E_total-(E_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 Repulsive Interaction Constant given Total Energy of Ion and Madelung Energy?

Repulsive Interaction Constant given Total Energy of Ion and Madelung Energy calculator uses Repulsive Interaction Constant = (Total Energy of Ion-(Madelung Energy))*(Distance of Closest Approach^Born Exponent) to calculate the Repulsive Interaction Constant, The Repulsive Interaction Constant given Total Energy of ion and Madelung Energy is the constant scaling the strength of the repulsive interaction. Repulsive Interaction Constant is denoted by B symbol.

How to calculate Repulsive Interaction Constant given Total Energy of Ion and Madelung Energy using this online calculator? To use this online calculator for Repulsive Interaction Constant given Total Energy of Ion and Madelung Energy, enter Total Energy of Ion (E_total), Madelung Energy (E_M), Distance of Closest Approach (r₀) & Born Exponent (n_born) and hit the calculate button. Here is how the Repulsive Interaction Constant given Total Energy of Ion and Madelung Energy calculation can be explained with given input values -> 39964.23 = (5790000000000-((-5.9E-21)))*(6E-09^0.9926).

FAQ

What is Repulsive Interaction Constant given Total Energy of Ion and Madelung Energy?

The Repulsive Interaction Constant given Total Energy of ion and Madelung Energy is the constant scaling the strength of the repulsive interaction and is represented as B = (E_total-(E_M))*(r₀^n_born) or Repulsive Interaction Constant = (Total Energy of Ion-(Madelung Energy))*(Distance of Closest Approach^Born Exponent). The Total Energy of Ion in the lattice is the sum of Madelung Energy and Repulsive potential 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, 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 Repulsive Interaction Constant given Total Energy of Ion and Madelung Energy?

The Repulsive Interaction Constant given Total Energy of ion and Madelung Energy is the constant scaling the strength of the repulsive interaction is calculated using Repulsive Interaction Constant = (Total Energy of Ion-(Madelung Energy))*(Distance of Closest Approach^Born Exponent). To calculate Repulsive Interaction Constant given Total Energy of Ion and Madelung Energy, you need Total Energy of Ion (E_total), Madelung Energy (E_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, Madelung Energy, 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 Repulsive Interaction Constant?

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

Repulsive Interaction Constant = Repulsive Interaction*(Distance of Closest Approach^Born Exponent)
Repulsive Interaction Constant = (Total Energy of Ion-(-(Madelung Constant*(Charge^2)*([Charge-e]^2))/(4*pi*[Permitivity-vacuum]*Distance of Closest Approach)))*(Distance of Closest Approach^Born Exponent)

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