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Minimum Potential Energy of Ion 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

✖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 Constant is the constant scaling the strength of the repulsive interaction.ⓘ Repulsive Interaction Constant [B]			+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 Minimum Potential Energy of Ion is a means of calculating the lattice energy of a crystalline ionic compound.ⓘ Minimum Potential Energy of Ion [E_min]

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Minimum Potential Energy of Ion Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
E_min = ((-(q^2)*([Charge-e]^2)*M)/(4*pi*[Permitivity-vacuum]*r₀))+(B/(r₀^n_born))
This formula uses 3 Constants, 6 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

Minimum Potential Energy of Ion - (Measured in Joule) - The Minimum Potential Energy of Ion is a means of calculating the lattice energy of a crystalline ionic compound.
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.
Repulsive Interaction Constant - The Repulsive Interaction Constant is the constant scaling the strength of the repulsive interaction.
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

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)
Repulsive Interaction Constant: 40000 --> No Conversion Required
Born Exponent: 0.9926 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

E_min = ((-(q^2)*([Charge-e]^2)*M)/(4*pi*[Permitivity-vacuum]*r₀))+(B/(r₀^n_born)) --> ((-(0.3^2)*([Charge-e]^2)*1.7)/(4*pi*[Permitivity-vacuum]*6E-09))+(40000/(6E-09^0.9926))

Evaluating ... ...

E_min = 5795181739688.58

STEP 3: Convert Result to Output's Unit

5795181739688.58 Joule --> No Conversion Required

FINAL ANSWER

5795181739688.58 ≈ 5.8E+12 Joule <-- Minimum Potential Energy of Ion

(Calculation completed in 00.020 seconds)

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

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< Lattice Energy Calculators

Lattice Energy using Born Lande Equation

LaTeX 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

LaTeX 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))

Electrostatic Potential Energy between pair of Ions

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

Repulsive Interaction

LaTeX Go Repulsive Interaction = Repulsive Interaction Constant/(Distance of Closest Approach^Born Exponent)

Minimum Potential Energy of Ion Formula

LaTeX Go

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 Minimum Potential Energy of Ion?

Minimum Potential Energy of Ion calculator uses 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)) to calculate the Minimum Potential Energy of Ion, The Minimum Potential Energy of Ion is a means of calculating the lattice energy of a crystalline ionic compound. Minimum Potential Energy of Ion is denoted by E_min symbol.

How to calculate Minimum Potential Energy of Ion using this online calculator? To use this online calculator for Minimum Potential Energy of Ion, enter Charge (q), Madelung Constant (M), Distance of Closest Approach (r₀), Repulsive Interaction Constant (B) & Born Exponent (n_born) and hit the calculate button. Here is how the Minimum Potential Energy of Ion calculation can be explained with given input values -> 5.8E+12 = ((-(0.3^2)*([Charge-e]^2)*1.7)/(4*pi*[Permitivity-vacuum]*6E-09))+(40000/(6E-09^0.9926)).

FAQ

What is Minimum Potential Energy of Ion?

The Minimum Potential Energy of Ion is a means of calculating the lattice energy of a crystalline ionic compound and is represented as E_min = ((-(q^2)*([Charge-e]^2)*M)/(4*pi*[Permitivity-vacuum]*r₀))+(B/(r₀^n_born)) or 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)). 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, The Repulsive Interaction Constant is the constant scaling the strength of the repulsive interaction & 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 Minimum Potential Energy of Ion?

The Minimum Potential Energy of Ion is a means of calculating the lattice energy of a crystalline ionic compound is calculated using 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)). To calculate Minimum Potential Energy of Ion, you need Charge (q), Madelung Constant (M), Distance of Closest Approach (r₀), Repulsive Interaction Constant (B) & Born Exponent (n_born). With our tool, you need to enter the respective value for Charge, Madelung Constant, Distance of Closest Approach, Repulsive Interaction Constant & 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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