Repulsive Interaction using Total Energy of ion given charges and distances Calculator

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Ionic Bonding

Covalent Bonding

Electronegativity

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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%
✖A Charge is the fundamental property of forms of matter that exhibit electrostatic attraction or repulsion in the presence of other matter.ⓘ Charge [q]			+10% -10%
✖The Madelung constant is used in determining the electrostatic potential of a single ion in a crystal by approximating the ions by point charges.ⓘ Madelung Constant [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 Repulsive Interaction is between atoms acts over a very short range, but is very large when distances are short.ⓘ Repulsive Interaction using Total Energy of ion given charges and distances [E_R]

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Formula

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Repulsive Interaction using Total Energy of ion given charges and distances

Formula

`"E"_{"R"} = "E"_{"total"}-(-("q"^2)*("[Charge-e]"^2)*"M")/(4*pi*"[Permitivity-vacuum]"*"r"_{"0"})`

Example

`"5.8E^12J"="5.79E^12J"-(-(("0.3C")^2)*("[Charge-e]"^2)*"1.7")/(4*pi*"[Permitivity-vacuum]"*"60A")`

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Repulsive Interaction using Total Energy of ion given charges and distances Solution

STEP 0: Pre-Calculation Summary

Formula Used

Repulsive Interaction = Total Energy of Ion-(-(Charge^2)*([Charge-e]^2)*Madelung Constant)/(4*pi*[Permitivity-vacuum]*Distance of Closest Approach)
E_R = E_total-(-(q^2)*([Charge-e]^2)*M)/(4*pi*[Permitivity-vacuum]*r₀)
This formula uses 3 Constants, 5 Variables

Constants Used

[Permitivity-vacuum] - Permittivity of vacuum Value Taken As 8.85E-12
[Charge-e] - Charge of electron Value Taken As 1.60217662E-19
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

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.
Charge - (Measured in Coulomb) - A Charge is the fundamental property of forms of matter that exhibit electrostatic attraction or repulsion in the presence of other matter.
Madelung Constant - The Madelung constant is used in determining the electrostatic potential of a single ion in a crystal by approximating the ions by point charges.
Distance of Closest Approach - (Measured in Meter) - Distance of Closest Approach is the distance to which an alpha particle comes closer to the nucleus.

STEP 1: Convert Input(s) to Base Unit

Total Energy of Ion: 5790000000000 Joule --> 5790000000000 Joule No Conversion Required
Charge: 0.3 Coulomb --> 0.3 Coulomb No Conversion Required
Madelung Constant: 1.7 --> No Conversion Required
Distance of Closest Approach: 60 Angstrom --> 6E-09 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

E_R = E_total-(-(q^2)*([Charge-e]^2)*M)/(4*pi*[Permitivity-vacuum]*r₀) --> 5790000000000-(-(0.3^2)*([Charge-e]^2)*1.7)/(4*pi*[Permitivity-vacuum]*6E-09)

Evaluating ... ...

E_R = 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)

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Home » Chemistry » Chemical Bonding » Ionic Bonding » Lattice Energy » Repulsive Interaction using Total Energy of ion given charges and distances

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 given charges and distances Formula

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 given charges and distances?

Repulsive Interaction using Total Energy of ion given charges and distances calculator uses Repulsive Interaction = Total Energy of Ion-(-(Charge^2)*([Charge-e]^2)*Madelung Constant)/(4*pi*[Permitivity-vacuum]*Distance of Closest Approach) to calculate the Repulsive Interaction, The Repulsive Interaction using Total Energy of ion given charges and distances is between atoms acts over a very short range, but is very large when distances are short. Repulsive Interaction is denoted by E_R symbol.

How to calculate Repulsive Interaction using Total Energy of ion given charges and distances using this online calculator? To use this online calculator for Repulsive Interaction using Total Energy of ion given charges and distances, enter Total Energy of Ion (E_total), Charge (q), Madelung Constant (M) & Distance of Closest Approach (r₀) and hit the calculate button. Here is how the Repulsive Interaction using Total Energy of ion given charges and distances calculation can be explained with given input values -> 5.8E+12 = 5790000000000-(-(0.3^2)*([Charge-e]^2)*1.7)/(4*pi*[Permitivity-vacuum]*6E-09).

FAQ

What is Repulsive Interaction using Total Energy of ion given charges and distances?

The Repulsive Interaction using Total Energy of ion given charges and distances is between atoms acts over a very short range, but is very large when distances are short and is represented as E_R = E_total-(-(q^2)*([Charge-e]^2)*M)/(4*pi*[Permitivity-vacuum]*r₀) or Repulsive Interaction = Total Energy of Ion-(-(Charge^2)*([Charge-e]^2)*Madelung Constant)/(4*pi*[Permitivity-vacuum]*Distance of Closest Approach). The Total Energy of Ion in the lattice is the sum of Madelung Energy and Repulsive potential energy, A Charge is the fundamental property of forms of matter that exhibit electrostatic attraction or repulsion in the presence of other matter, The Madelung constant is used in determining the electrostatic potential of a single ion in a crystal by approximating the ions by point charges & Distance of Closest Approach is the distance to which an alpha particle comes closer to the nucleus.

How to calculate Repulsive Interaction using Total Energy of ion given charges and distances?

The Repulsive Interaction using Total Energy of ion given charges and distances 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-(-(Charge^2)*([Charge-e]^2)*Madelung Constant)/(4*pi*[Permitivity-vacuum]*Distance of Closest Approach). To calculate Repulsive Interaction using Total Energy of ion given charges and distances, you need Total Energy of Ion (E_total), Charge (q), Madelung Constant (M) & Distance of Closest Approach (r₀). With our tool, you need to enter the respective value for Total Energy of Ion, Charge, Madelung Constant & Distance of Closest Approach 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, Charge, Madelung Constant & Distance of Closest Approach. 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-(Madelung Energy)

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