Madelung Energy using Total Energy of Ion Solution

STEP 0: Pre-Calculation Summary
Formula Used
Madelung Energy = Total energy of Ion in an Ionic Crystal-Repulsive Interaction between Ions
EM = Etot-E
This formula uses 3 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 between Ions - (Measured in Joule) - The Repulsive Interaction between Ions 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
Total energy of Ion in an Ionic Crystal: 7.02E-23 Joule --> 7.02E-23 Joule No Conversion Required
Repulsive Interaction between Ions: 5.93E-21 Joule --> 5.93E-21 Joule No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
EM = Etot-E --> 7.02E-23-5.93E-21
Evaluating ... ...
EM = -5.8598E-21
STEP 3: Convert Result to Output's Unit
-5.8598E-21 Joule --> No Conversion Required
FINAL ANSWER
-5.8598E-21 -5.9E-21 Joule <-- Madelung Energy
(Calculation completed in 00.020 seconds)

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National Institute of Information Technology (NIIT), Neemrana
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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 Formula

​LaTeX ​Go
Madelung Energy = Total energy of Ion in an Ionic Crystal-Repulsive Interaction between Ions
EM = Etot-E

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?

Madelung Energy using Total Energy of Ion calculator uses Madelung Energy = Total energy of Ion in an Ionic Crystal-Repulsive Interaction between Ions to calculate the Madelung Energy, The Madelung Energy using Total Energy of Ion 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 EM symbol.

How to calculate Madelung Energy using Total Energy of Ion using this online calculator? To use this online calculator for Madelung Energy using Total Energy of Ion, enter Total energy of Ion in an Ionic Crystal (Etot) & Repulsive Interaction between Ions (E) and hit the calculate button. Here is how the Madelung Energy using Total Energy of Ion calculation can be explained with given input values -> -5.9E-21 = 7.02E-23-5.93E-21.

FAQ

What is Madelung Energy using Total Energy of Ion?
The Madelung Energy using Total Energy of Ion 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 EM = Etot-E or Madelung Energy = Total energy of Ion in an Ionic Crystal-Repulsive Interaction between Ions. 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 between Ions is between atoms acts over a very short range, but is very large when distances are short.
How to calculate Madelung Energy using Total Energy of Ion?
The Madelung Energy using Total Energy of Ion 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 between Ions. To calculate Madelung Energy using Total Energy of Ion, you need Total energy of Ion in an Ionic Crystal (Etot) & Repulsive Interaction between Ions (E). With our tool, you need to enter the respective value for Total energy of Ion in an Ionic Crystal & Repulsive Interaction between Ions 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 between Ions. 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 Constant given M/(Distance of Closest Approach^Born Exponent))
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