Repulsive Interaction using Total Energy of Ion Solution

STEP 0: Pre-Calculation Summary
Formula Used
Repulsive Interaction = Total Energy of Ion-(Madelung Energy)
ER = Etotal-(EM)
This formula uses 3 Variables
Variables Used
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.
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.
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
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ER = Etotal-(EM) --> 5790000000000-((-5.9E-21))
Evaluating ... ...
ER = 5790000000000
STEP 3: Convert Result to Output's Unit
5790000000000 Joule --> No Conversion Required
FINAL ANSWER
5790000000000 5.8E+12 Joule <-- Repulsive Interaction
(Calculation completed in 00.004 seconds)

Credits

Created by Prerana Bakli
University of Hawaiʻi at Mānoa (UH Manoa), Hawaii, USA
Prerana Bakli has created this Calculator and 800+ more calculators!
Verified by Akshada Kulkarni
National Institute of Information Technology (NIIT), Neemrana
Akshada Kulkarni has verified this Calculator and 900+ more calculators!

25 Lattice Energy Calculators

Lattice Energy using Born-Mayer equation
Go Lattice Energy = (-[Avaga-no]*Madelung Constant*Charge of Cation*Charge of Anion*([Charge-e]^2)*(1-(Constant Depending on Compressibility/Distance of Closest Approach)))/(4*pi*[Permitivity-vacuum]*Distance of Closest Approach)
Constant depending on compressibility using Born-Mayer equation
Go Constant Depending on Compressibility = (((Lattice Energy*4*pi*[Permitivity-vacuum]*Distance of Closest Approach)/([Avaga-no]*Madelung Constant*Charge of Cation*Charge of Anion*([Charge-e]^2)))+1)*Distance of Closest Approach
Minimum Potential Energy of Ion
Go Minimum Potential 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))
Repulsive Interaction Constant using Total Energy of Ion
Go 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)
Total Energy of Ion given Charges and Distances
Go 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))
Lattice Energy using Born-Lande equation using Kapustinskii Approximation
Go Lattice Energy = -([Avaga-no]*Number of Ions*0.88 *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 without Madelung Constant
Go Born Exponent = 1/(1-(-Lattice Energy*4*pi*[Permitivity-vacuum]*Distance of Closest Approach)/([Avaga-no]*Number of Ions*0.88*([Charge-e]^2)*Charge of Cation*Charge of Anion))
Lattice Energy using Born Lande Equation
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
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))
Lattice Energy using Kapustinskii equation
Go Lattice Energy for Kapustinskii Equation = (1.20200*(10^(-4))*Number of Ions*Charge of Cation*Charge of Anion*(1-((3.45*(10^(-11)))/(Radius of Cation+Radius of Anion))))/(Radius of Cation+Radius of Anion)
Repulsive Interaction Constant given Madelung constant
Go Repulsive Interaction Constant given M = (Madelung Constant*(Charge^2)*([Charge-e]^2)*(Distance of Closest Approach^(Born Exponent-1)))/(4*pi*[Permitivity-vacuum]*Born Exponent)
Lattice Energy using Original Kapustinskii equation
Go Lattice Energy for Kapustinskii Equation = ((([Kapustinskii_C]/1.20200)*1.079) *Number of Ions*Charge of Cation*Charge of Anion)/(Radius of Cation+Radius of Anion)
Repulsive Interaction using Total Energy of ion given charges and distances
Go Repulsive Interaction = Total Energy of Ion-(-(Charge^2)*([Charge-e]^2)*Madelung Constant)/(4*pi*[Permitivity-vacuum]*Distance of Closest Approach)
Born Exponent using Repulsive Interaction
Go Born Exponent = (log10(Repulsive Interaction Constant/Repulsive Interaction))/log10(Distance of Closest Approach)
Electrostatic Potential Energy between pair of Ions
Go Electrostatic Potential Energy between Ion Pair = (-(Charge^2)*([Charge-e]^2))/(4*pi*[Permitivity-vacuum]*Distance of Closest Approach)
Repulsive Interaction Constant given Total Energy of Ion and Madelung Energy
Go Repulsive Interaction Constant = (Total Energy of Ion-(Madelung Energy))*(Distance of Closest Approach^Born Exponent)
Repulsive Interaction Constant
Go Repulsive Interaction Constant = Repulsive Interaction*(Distance of Closest Approach^Born Exponent)
Repulsive Interaction
Go Repulsive Interaction = Repulsive Interaction Constant/(Distance of Closest Approach^Born Exponent)
Lattice Energy using Lattice Enthalpy
Go Lattice Energy = Lattice Enthalpy-(Pressure Lattice Energy*Molar Volume Lattice Energy)
Lattice Enthalpy using Lattice Energy
Go Lattice Enthalpy = Lattice Energy+(Pressure Lattice Energy*Molar Volume Lattice Energy)
Outer Pressure of Lattice
Go Pressure Lattice Energy = (Lattice Enthalpy-Lattice Energy)/Molar Volume Lattice Energy
Volume change of lattice
Go Molar Volume Lattice Energy = (Lattice Enthalpy-Lattice Energy)/Pressure Lattice Energy
Repulsive Interaction using Total Energy of Ion
Go Repulsive Interaction = Total Energy of Ion-(Madelung Energy)
Total Energy of Ion in Lattice
Go Total Energy of Ion = Madelung Energy+Repulsive Interaction
Number of Ions using Kapustinskii Approximation
Go Number of Ions = Madelung Constant/0.88

Repulsive Interaction using Total Energy of Ion Formula

Repulsive Interaction = Total Energy of Ion-(Madelung Energy)
ER = Etotal-(EM)

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 using Total Energy of Ion?

Repulsive Interaction using Total Energy of Ion calculator uses Repulsive Interaction = Total Energy of Ion-(Madelung Energy) to calculate the Repulsive Interaction, The Repulsive Interaction using Total Energy of Ion is between atoms acts over a very short range, but is very large when distances are short. Repulsive Interaction is denoted by ER symbol.

How to calculate Repulsive Interaction using Total Energy of Ion using this online calculator? To use this online calculator for Repulsive Interaction using Total Energy of Ion, enter Total Energy of Ion (Etotal) & Madelung Energy (EM) and hit the calculate button. Here is how the Repulsive Interaction using Total Energy of Ion calculation can be explained with given input values -> 5.8E+12 = 5790000000000-((-5.9E-21)).

FAQ

What is Repulsive Interaction using Total Energy of Ion?
The Repulsive Interaction using Total Energy of Ion is between atoms acts over a very short range, but is very large when distances are short and is represented as ER = Etotal-(EM) or Repulsive Interaction = Total Energy of Ion-(Madelung Energy). 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.
How to calculate Repulsive Interaction using Total Energy of Ion?
The Repulsive Interaction using Total Energy of Ion is between atoms acts over a very short range, but is very large when distances are short is calculated using Repulsive Interaction = Total Energy of Ion-(Madelung Energy). To calculate Repulsive Interaction using Total Energy of Ion, you need Total Energy of Ion (Etotal) & Madelung Energy (EM). With our tool, you need to enter the respective value for Total Energy of Ion & Madelung Energy 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?
In this formula, Repulsive Interaction uses Total Energy of Ion & Madelung Energy. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Repulsive Interaction = Repulsive Interaction Constant/(Distance of Closest Approach^Born Exponent)
  • Repulsive Interaction = Total Energy of Ion-(-(Charge^2)*([Charge-e]^2)*Madelung Constant)/(4*pi*[Permitivity-vacuum]*Distance of Closest Approach)
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