Distance of Closest Approach using Madelung Energy 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%
✖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.ⓘ Madelung Energy [E_M]			+10% -10%

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

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Formula

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Distance of Closest Approach using Madelung Energy

Formula

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

Example

`"59.85591A"=-("1.7"*(("0.3C")^2)*("[Charge-e]"^2))/(4*pi*"[Permitivity-vacuum]"*"-5.9E^-21J")`

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Distance of Closest Approach using Madelung Energy Solution

STEP 0: Pre-Calculation Summary

Formula Used

Distance of Closest Approach = -(Madelung Constant*(Charge^2)*([Charge-e]^2))/(4*pi*[Permitivity-vacuum]*Madelung Energy)
r₀ = -(M*(q^2)*([Charge-e]^2))/(4*pi*[Permitivity-vacuum]*E_M)
This formula uses 3 Constants, 4 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

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 - (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 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

Madelung Constant: 1.7 --> No Conversion Required
Charge: 0.3 Coulomb --> 0.3 Coulomb 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

r₀ = -(M*(q^2)*([Charge-e]^2))/(4*pi*[Permitivity-vacuum]*E_M) --> -(1.7*(0.3^2)*([Charge-e]^2))/(4*pi*[Permitivity-vacuum]*(-5.9E-21))

Evaluating ... ...

r₀ = 5.98559136510753E-09

STEP 3: Convert Result to Output's Unit

5.98559136510753E-09 Meter -->59.8559136510753 Angstrom (Check conversion here)

FINAL ANSWER

59.8559136510753 ≈ 59.85591 Angstrom <-- Distance of Closest Approach

(Calculation completed in 00.004 seconds)

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Created by Prerana Bakli

University of Hawaiʻi at Mānoa (UH Manoa), Hawaii, USA

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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 Madelung Energy Formula

Distance of Closest Approach = -(Madelung Constant*(Charge^2)*([Charge-e]^2))/(4*pi*[Permitivity-vacuum]*Madelung Energy)
r₀ = -(M*(q^2)*([Charge-e]^2))/(4*pi*[Permitivity-vacuum]*E_M)

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 Madelung Energy?

Distance of Closest Approach using Madelung Energy calculator uses Distance of Closest Approach = -(Madelung Constant*(Charge^2)*([Charge-e]^2))/(4*pi*[Permitivity-vacuum]*Madelung Energy) to calculate the Distance of Closest Approach, The Distance of closest approach using Madelung Energy 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 Madelung Energy using this online calculator? To use this online calculator for Distance of Closest Approach using Madelung Energy, enter Madelung Constant (M), Charge (q) & Madelung Energy (E_M) and hit the calculate button. Here is how the Distance of Closest Approach using Madelung Energy calculation can be explained with given input values -> 6E+11 = -(1.7*(0.3^2)*([Charge-e]^2))/(4*pi*[Permitivity-vacuum]*(-5.9E-21)).

FAQ

What is Distance of Closest Approach using Madelung Energy?

The Distance of closest approach using Madelung Energy is the distance separating the ion centers in a lattice and is represented as r₀ = -(M*(q^2)*([Charge-e]^2))/(4*pi*[Permitivity-vacuum]*E_M) or Distance of Closest Approach = -(Madelung Constant*(Charge^2)*([Charge-e]^2))/(4*pi*[Permitivity-vacuum]*Madelung 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, A Charge is the fundamental property of forms of matter that exhibit electrostatic attraction or repulsion in the presence of other matter & 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 Distance of Closest Approach using Madelung Energy?

The Distance of closest approach using Madelung Energy is the distance separating the ion centers in a lattice is calculated using Distance of Closest Approach = -(Madelung Constant*(Charge^2)*([Charge-e]^2))/(4*pi*[Permitivity-vacuum]*Madelung Energy). To calculate Distance of Closest Approach using Madelung Energy, you need Madelung Constant (M), Charge (q) & Madelung Energy (E_M). With our tool, you need to enter the respective value for Madelung Constant, Charge & 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 Distance of Closest Approach?

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

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 = -([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)

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