LCM of two numbers

Total Energy of Ion in Lattice Calculator

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Lattice Energy

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Distance of Closest Approach Madelung Constant

✖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%
✖The Repulsive Interaction is between atoms acts over a very short range, but is very large when distances are short.ⓘ Repulsive Interaction [E_R]			+10% -10%

✖The Total Energy of Ion in the lattice is the sum of Madelung Energy and Repulsive potential energy.ⓘ Total Energy of Ion in Lattice [E_total]

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Total Energy of Ion in Lattice Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Energy of Ion = Madelung Energy+Repulsive Interaction
E_total = E_M+E_R
This formula uses 3 Variables

Variables Used

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.
Repulsive Interaction - (Measured in Joule) - The Repulsive Interaction is between atoms acts over a very short range, but is very large when distances are short.

STEP 1: Convert Input(s) to Base Unit

Madelung Energy: -5.9E-21 Joule --> -5.9E-21 Joule No Conversion Required
Repulsive Interaction: 5800000000000 Joule --> 5800000000000 Joule No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

E_total = E_M+E_R --> (-5.9E-21)+5800000000000

Evaluating ... ...

E_total = 5800000000000

STEP 3: Convert Result to Output's Unit

5800000000000 Joule --> No Conversion Required

FINAL ANSWER

5800000000000 ≈ 5.8E+12 Joule <-- Total Energy of Ion

(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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National Institute of Information Technology (NIIT), Neemrana

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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)

Total Energy of Ion in Lattice Formula

LaTeX Go

Total Energy of Ion = Madelung Energy+Repulsive Interaction
E_total = E_M+E_R

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 Total Energy of Ion in Lattice?

Total Energy of Ion in Lattice calculator uses Total Energy of Ion = Madelung Energy+Repulsive Interaction to calculate the Total Energy of Ion, The Total Energy of Ion in lattice is the sum of Madelung Energy and Repulsive potential energy. Total Energy of Ion is denoted by E_total symbol.

How to calculate Total Energy of Ion in Lattice using this online calculator? To use this online calculator for Total Energy of Ion in Lattice, enter Madelung Energy (E_M) & Repulsive Interaction (E_R) and hit the calculate button. Here is how the Total Energy of Ion in Lattice calculation can be explained with given input values -> 5.8E+12 = (-5.9E-21)+5800000000000.

FAQ

What is Total Energy of Ion in Lattice?

The Total Energy of Ion in lattice is the sum of Madelung Energy and Repulsive potential energy and is represented as E_total = E_M+E_R or Total Energy of Ion = Madelung Energy+Repulsive Interaction. 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 & The Repulsive Interaction is between atoms acts over a very short range, but is very large when distances are short.

How to calculate Total Energy of Ion in Lattice?

The Total Energy of Ion in lattice is the sum of Madelung Energy and Repulsive potential energy is calculated using Total Energy of Ion = Madelung Energy+Repulsive Interaction. To calculate Total Energy of Ion in Lattice, you need Madelung Energy (E_M) & Repulsive Interaction (E_R). With our tool, you need to enter the respective value for Madelung Energy & Repulsive Interaction 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 Total Energy of Ion?

In this formula, Total Energy of Ion uses Madelung Energy & Repulsive Interaction. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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