Distance of Closest Approach using Born Lande equation Calculator

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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%
✖The Charge of Cation is the positive charge over a cation with fewer electron than the respective atom.ⓘ Charge of Cation [z⁺]			+10% -10%
✖The Charge of Anion is the negative charge over an anion with more electron than the respective atom.ⓘ Charge of Anion [z^-]			+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 Lattice Energy of a crystalline solid is a measure of the energy released when ions are combined to make a compound.ⓘ Lattice Energy [U]			+10% -10%

✖Distance of Closest Approach is the distance to which an alpha particle comes closer to the nucleus.ⓘ Distance of Closest Approach using Born Lande equation [r₀]

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Formula

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Distance of Closest Approach using Born Lande equation

Formula

`"r"_{"0"} = -("[Avaga-no]"*"M"*"z"^{"+"}*"z"^{"-"}*("[Charge-e]"^2)*(1-(1/"n"_{"born"})))/(4*pi*"[Permitivity-vacuum]"*"U")`

Example

`"60.40016A"=-("[Avaga-no]"*"1.7"*"4C"*"3C"*("[Charge-e]"^2)*(1-(1/"0.9926")))/(4*pi*"[Permitivity-vacuum]"*"3500J/mol")`

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Distance of Closest Approach using Born Lande equation Solution

STEP 0: Pre-Calculation Summary

Formula Used

Distance of Closest Approach = -([Avaga-no]*Madelung Constant*Charge of Cation*Charge of Anion*([Charge-e]^2)*(1-(1/Born Exponent)))/(4*pi*[Permitivity-vacuum]*Lattice Energy)
r₀ = -([Avaga-no]*M*z⁺*z^-*([Charge-e]^2)*(1-(1/n_born)))/(4*pi*[Permitivity-vacuum]*U)
This formula uses 4 Constants, 6 Variables

Constants Used

[Permitivity-vacuum] - Permittivity of vacuum Value Taken As 8.85E-12
[Avaga-no] - Avogadro’s number Value Taken As 6.02214076E+23
[Charge-e] - Charge of electron Value Taken As 1.60217662E-19
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Distance of Closest Approach - (Measured in Meter) - Distance of Closest Approach is the distance to which an alpha particle comes closer to the nucleus.
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 of Cation - (Measured in Coulomb) - The Charge of Cation is the positive charge over a cation with fewer electron than the respective atom.
Charge of Anion - (Measured in Coulomb) - The Charge of Anion is the negative charge over an anion with more electron than the respective atom.
Born Exponent - The Born Exponent is a number between 5 and 12, determined experimentally by measuring the compressibility of the solid, or derived theoretically.
Lattice Energy - (Measured in Joule per Mole) - The Lattice Energy of a crystalline solid is a measure of the energy released when ions are combined to make a compound.

STEP 1: Convert Input(s) to Base Unit

Madelung Constant: 1.7 --> No Conversion Required
Charge of Cation: 4 Coulomb --> 4 Coulomb No Conversion Required
Charge of Anion: 3 Coulomb --> 3 Coulomb No Conversion Required
Born Exponent: 0.9926 --> No Conversion Required
Lattice Energy: 3500 Joule per Mole --> 3500 Joule per Mole No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r₀ = -([Avaga-no]*M*z⁺*z^-*([Charge-e]^2)*(1-(1/n_born)))/(4*pi*[Permitivity-vacuum]*U) --> -([Avaga-no]*1.7*4*3*([Charge-e]^2)*(1-(1/0.9926)))/(4*pi*[Permitivity-vacuum]*3500)

Evaluating ... ...

r₀ = 6.04001642309941E-09

STEP 3: Convert Result to Output's Unit

6.04001642309941E-09 Meter -->60.4001642309941 Angstrom (Check conversion here)

FINAL ANSWER

60.4001642309941 ≈ 60.40016 Angstrom <-- Distance of Closest Approach

(Calculation completed in 00.020 seconds)

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< 4 Distance of Closest Approach Calculators

Distance of Closest Approach using Born-Lande Equation without Madelung Constant

Go Distance of Closest Approach = -([Avaga-no]*Number of Ions*0.88*Charge of Cation*Charge of Anion*([Charge-e]^2)*(1-(1/Born Exponent)))/(4*pi*[Permitivity-vacuum]*Lattice Energy)

Distance of Closest Approach using Born Lande equation

Go Distance of Closest Approach = -([Avaga-no]*Madelung Constant*Charge of Cation*Charge of Anion*([Charge-e]^2)*(1-(1/Born Exponent)))/(4*pi*[Permitivity-vacuum]*Lattice Energy)

Distance of Closest Approach using Madelung Energy

Go Distance of Closest Approach = -(Madelung Constant*(Charge^2)*([Charge-e]^2))/(4*pi*[Permitivity-vacuum]*Madelung Energy)

Distance of Closest Approach using Electrostatic Potential

Go Distance of Closest Approach = (-(Charge^2)*([Charge-e]^2))/(4*pi*[Permitivity-vacuum]*Electrostatic Potential Energy between Ion Pair)

Distance of Closest Approach using Born Lande equation 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 Distance of Closest Approach using Born Lande equation?

Distance of Closest Approach using Born Lande equation calculator uses Distance of Closest Approach = -([Avaga-no]*Madelung Constant*Charge of Cation*Charge of Anion*([Charge-e]^2)*(1-(1/Born Exponent)))/(4*pi*[Permitivity-vacuum]*Lattice Energy) to calculate the Distance of Closest Approach, The Distance of closest approach using Born Lande equation is the distance separating the ion centers in a lattice. Distance of Closest Approach is denoted by r₀ symbol.

How to calculate Distance of Closest Approach using Born Lande equation using this online calculator? To use this online calculator for Distance of Closest Approach using Born Lande equation, enter Madelung Constant (M), Charge of Cation (z⁺), Charge of Anion (z^-), Born Exponent (n_born) & Lattice Energy (U) and hit the calculate button. Here is how the Distance of Closest Approach using Born Lande equation calculation can be explained with given input values -> 6E+11 = -([Avaga-no]*1.7*4*3*([Charge-e]^2)*(1-(1/0.9926)))/(4*pi*[Permitivity-vacuum]*3500).

FAQ

What is Distance of Closest Approach using Born Lande equation?

The Distance of closest approach using Born Lande equation is the distance separating the ion centers in a lattice and is represented as r₀ = -([Avaga-no]*M*z⁺*z^-*([Charge-e]^2)*(1-(1/n_born)))/(4*pi*[Permitivity-vacuum]*U) or Distance of Closest Approach = -([Avaga-no]*Madelung Constant*Charge of Cation*Charge of Anion*([Charge-e]^2)*(1-(1/Born Exponent)))/(4*pi*[Permitivity-vacuum]*Lattice Energy). The Madelung constant is used in determining the electrostatic potential of a single ion in a crystal by approximating the ions by point charges, The Charge of Cation is the positive charge over a cation with fewer electron than the respective atom, The Charge of Anion is the negative charge over an anion with more electron than the respective atom, The Born Exponent is a number between 5 and 12, determined experimentally by measuring the compressibility of the solid, or derived theoretically & The Lattice Energy of a crystalline solid is a measure of the energy released when ions are combined to make a compound.

How to calculate Distance of Closest Approach using Born Lande equation?

The Distance of closest approach using Born Lande equation is the distance separating the ion centers in a lattice is calculated using Distance of Closest Approach = -([Avaga-no]*Madelung Constant*Charge of Cation*Charge of Anion*([Charge-e]^2)*(1-(1/Born Exponent)))/(4*pi*[Permitivity-vacuum]*Lattice Energy). To calculate Distance of Closest Approach using Born Lande equation, you need Madelung Constant (M), Charge of Cation (z⁺), Charge of Anion (z^-), Born Exponent (n_born) & Lattice Energy (U). With our tool, you need to enter the respective value for Madelung Constant, Charge of Cation, Charge of Anion, Born Exponent & Lattice 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 Distance of Closest Approach?

In this formula, Distance of Closest Approach uses Madelung Constant, Charge of Cation, Charge of Anion, Born Exponent & Lattice Energy. We can use 3 other way(s) to calculate the same, which is/are as follows -

Distance of Closest Approach = -([Avaga-no]*Number of Ions*0.88*Charge of Cation*Charge of Anion*([Charge-e]^2)*(1-(1/Born Exponent)))/(4*pi*[Permitivity-vacuum]*Lattice Energy)
Distance of Closest Approach = (-(Charge^2)*([Charge-e]^2))/(4*pi*[Permitivity-vacuum]*Electrostatic Potential Energy between Ion Pair)
Distance of Closest Approach = -(Madelung Constant*(Charge^2)*([Charge-e]^2))/(4*pi*[Permitivity-vacuum]*Madelung Energy)

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