Repulsive Interaction Constant given Madelung constant 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 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%
✖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%
✖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 given M, (where M= Madelung Constant) is the constant scaling the strength of the repulsive interaction.ⓘ Repulsive Interaction Constant given Madelung constant [B_M]

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Formula

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Repulsive Interaction Constant given Madelung constant

Formula

`"B"_{"M"} = ("M"*("q"^2)*("[Charge-e]"^2)*("r"_{"0"}^("n"_{"born"}-1)))/(4*pi*"[Permitivity-vacuum]"*"n"_{"born"})`

Example

`"4.1E^-29"=("1.7"*(("0.3C")^2)*("[Charge-e]"^2)*(("60A")^("0.9926"-1)))/(4*pi*"[Permitivity-vacuum]"*"0.9926")`

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Repulsive Interaction Constant given Madelung constant Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
B_M = (M*(q^2)*([Charge-e]^2)*(r₀^(n_born-1)))/(4*pi*[Permitivity-vacuum]*n_born)
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 Constant given M - The Repulsive Interaction Constant given M, (where M= Madelung Constant) is the constant scaling the strength of the repulsive interaction.
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.
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.
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

Madelung Constant: 1.7 --> No Conversion Required
Charge: 0.3 Coulomb --> 0.3 Coulomb 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_M = (M*(q^2)*([Charge-e]^2)*(r₀^(n_born-1)))/(4*pi*[Permitivity-vacuum]*n_born) --> (1.7*(0.3^2)*([Charge-e]^2)*(6E-09^(0.9926-1)))/(4*pi*[Permitivity-vacuum]*0.9926)

Evaluating ... ...

B_M = 4.09285619643233E-29

STEP 3: Convert Result to Output's Unit

4.09285619643233E-29 --> No Conversion Required

FINAL ANSWER

4.09285619643233E-29 ≈ 4.1E-29 <-- Repulsive Interaction Constant given M

(Calculation completed in 00.004 seconds)

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< 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 Constant given Madelung constant 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 Constant given Madelung constant?

Repulsive Interaction Constant given Madelung constant calculator uses 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) to calculate the Repulsive Interaction Constant given M, The Repulsive Interaction Constant given Madelung constant is the constant scaling the strength of the repulsive interaction. Repulsive Interaction Constant given M is denoted by B_M symbol.

How to calculate Repulsive Interaction Constant given Madelung constant using this online calculator? To use this online calculator for Repulsive Interaction Constant given Madelung constant, enter Madelung Constant (M), Charge (q), Distance of Closest Approach (r₀) & Born Exponent (n_born) and hit the calculate button. Here is how the Repulsive Interaction Constant given Madelung constant calculation can be explained with given input values -> 4.1E-29 = (1.7*(0.3^2)*([Charge-e]^2)*(6E-09^(0.9926-1)))/(4*pi*[Permitivity-vacuum]*0.9926).

FAQ

What is Repulsive Interaction Constant given Madelung constant?

The Repulsive Interaction Constant given Madelung constant is the constant scaling the strength of the repulsive interaction and is represented as B_M = (M*(q^2)*([Charge-e]^2)*(r₀^(n_born-1)))/(4*pi*[Permitivity-vacuum]*n_born) or 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). The Madelung constant is used in determining the electrostatic potential of a single ion in a crystal by approximating the ions by point charges, A Charge is the fundamental property of forms of matter that exhibit electrostatic attraction or repulsion in the presence of other matter, 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 Madelung constant?

The Repulsive Interaction Constant given Madelung constant is the constant scaling the strength of the repulsive interaction is calculated using 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). To calculate Repulsive Interaction Constant given Madelung constant, you need Madelung Constant (M), Charge (q), Distance of Closest Approach (r₀) & Born Exponent (n_born). With our tool, you need to enter the respective value for Madelung Constant, Charge, 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.

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