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Total Energy of Ion given Charges and Distances Calculator

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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 Total Energy of Ion in the lattice is the sum of Madelung Energy and Repulsive potential energy.ⓘ Total Energy of Ion given Charges and Distances [E_total]

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Total Energy of Ion given Charges and Distances Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
E_total = ((-(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

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.
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_total = ((-(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_total = 5795181739688.58

STEP 3: Convert Result to Output's Unit

5795181739688.58 Joule --> No Conversion Required

FINAL ANSWER

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

(Calculation completed in 00.004 seconds)

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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)

Total Energy of Ion given Charges and Distances 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 Total Energy of Ion given Charges and Distances?

Total Energy of Ion given Charges and Distances calculator uses 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)) to calculate the Total Energy of Ion, The Total Energy of ion given charges and distances in the lattice is the sum of Madelung Energy and Repulsive potential energy. Total Energy of Ion is denoted by E_total symbol.

How to calculate Total Energy of Ion given Charges and Distances using this online calculator? To use this online calculator for Total Energy of Ion given Charges and Distances, 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 Total Energy of Ion given Charges and Distances 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 Total Energy of Ion given Charges and Distances?

The Total Energy of ion given charges and distances in the lattice is the sum of Madelung Energy and Repulsive potential energy and is represented as E_total = ((-(q^2)*([Charge-e]^2)*M)/(4*pi*[Permitivity-vacuum]*r₀))+(B/(r₀^n_born)) or 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)). 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 Total Energy of Ion given Charges and Distances?

The Total Energy of ion given charges and distances in the lattice is the sum of Madelung Energy and Repulsive potential energy is calculated using 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)). To calculate Total Energy of Ion given Charges and Distances, 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.

How many ways are there to calculate Total Energy of Ion?

In this formula, Total Energy of Ion uses Charge, Madelung Constant, Distance of Closest Approach, Repulsive Interaction Constant & Born Exponent. We can use 1 other way(s) to calculate the same, which is/are as follows -

Total Energy of Ion = Madelung Energy+Repulsive Interaction

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