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Madelung Constant given Repulsive Interaction Constant Formula

GoMadelung Constant using Born Lande Equation Formula

GoMadelung Constant using Born-Mayer equation Formula

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The Madelung constant is used in determining the electrostatic potential of a single ion in a crystal by approximating the ions by point charges. Check FAQs

M = \frac{B M \cdot 4 \cdot π \cdot [Permitivity-vacuum] \cdot n born}{(q^{2}) \cdot ({[Charge-e]}^{2}) \cdot ({r 0}^{n born - 1})}

M - Madelung Constant?B_M - Repulsive Interaction Constant given M?n_born - Born Exponent?q - Charge?r₀ - Distance of Closest Approach?[Permitivity-vacuum] - Permittivity of vacuum?[Charge-e] - Charge of electron?π - Archimedes' constant?

Madelung Constant given Repulsive Interaction Constant Example

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Here is how the Madelung Constant given Repulsive Interaction Constant equation looks like with Values.

Here is how the Madelung Constant given Repulsive Interaction Constant equation looks like with Units.

Here is how the Madelung Constant given Repulsive Interaction Constant equation looks like.

1.703 = \frac{4.1E-29 \cdot 4 \cdot 3.1416 \cdot 8.9E-12 \cdot 0.9926}{({0.3}^{2}) \cdot ({1.6E-19}^{2}) \cdot (60^{0.9926 - 1})}

1.703 = \frac{4.1E-29 \cdot 4 \cdot 3.1416 \cdot 8.9E-12F/m \cdot 0.9926}{({0.3C}^{2}) \cdot ({1.6E-19C}^{2}) \cdot ({60A}^{0.9926 - 1})}

1.703 = \frac{4.1E-29 \cdot 4 \cdot 3.1416 \cdot 8.9E-12 \cdot 0.9926}{({0.3}^{2}) \cdot ({1.6E-19}^{2}) \cdot (60^{0.9926 - 1})}

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Madelung Constant given Repulsive Interaction Constant Solution

Follow our step by step solution on how to calculate Madelung Constant given Repulsive Interaction Constant?

FIRST Step Consider the formula

M = \frac{B M \cdot 4 \cdot π \cdot [Permitivity-vacuum] \cdot n born}{(q^{2}) \cdot ({[Charge-e]}^{2}) \cdot ({r 0}^{n born - 1})}

Next Step Substitute values of Variables

∴

M = \frac{4.1E-29 \cdot 4 \cdot π \cdot [Permitivity-vacuum] \cdot 0.9926}{({0.3C}^{2}) \cdot ({[Charge-e]}^{2}) \cdot ({60A}^{0.9926 - 1})}

Next Step Substitute values of Constants

∴

M = \frac{4.1E-29 \cdot 4 \cdot 3.1416 \cdot 8.9E-12F/m \cdot 0.9926}{({0.3C}^{2}) \cdot ({1.6E-19C}^{2}) \cdot ({60A}^{0.9926 - 1})}

Next Step Convert Units

∴

M = \frac{4.1E-29 \cdot 4 \cdot 3.1416 \cdot 8.9E-12F/m \cdot 0.9926}{({0.3C}^{2}) \cdot ({1.6E-19C}^{2}) \cdot ({6E-9m}^{0.9926 - 1})}

Next Step Prepare to Evaluate

∴

M = \frac{4.1E-29 \cdot 4 \cdot 3.1416 \cdot 8.9E-12 \cdot 0.9926}{({0.3}^{2}) \cdot ({1.6E-19}^{2}) \cdot ({6E-9}^{0.9926 - 1})}

Next Step Evaluate

∴

M = 1.70296723497777

LAST Step Rounding Answer

∴

M = 1.703

Madelung Constant given Repulsive Interaction Constant Formula Elements

Variables

Constants

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.

Symbol: M

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Madelung Constant

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.

Symbol: B_M

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Repulsive Interaction Constant given M

Born Exponent

The Born Exponent is a number between 5 and 12, determined experimentally by measuring the compressibility of the solid, or derived theoretically.

Symbol: n_born

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Born Exponent

Charge

A Charge is the fundamental property of forms of matter that exhibit electrostatic attraction or repulsion in the presence of other matter.

Symbol: q

Measurement: Electric ChargeUnit: C

Note: Value can be positive or negative.

Formulas to find Charge

Distance of Closest Approach

Distance of Closest Approach is the distance to which an alpha particle comes closer to the nucleus.

Symbol: r₀

Measurement: LengthUnit: A

Note: Value can be positive or negative.

Formulas to find Distance of Closest Approach

Permittivity of vacuum

Permittivity of vacuum is a fundamental physical constant that describes the ability of a vacuum to permit the transmission of electric field lines.

Symbol: [Permitivity-vacuum]

Value: 8.85E-12 F/m

Charge of electron

Charge of electron is a fundamental physical constant, representing the electric charge carried by an electron, which is the elementary particle with a negative electric charge.

Symbol: [Charge-e]

Value: 1.60217662E-19 C

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other Formulas to find Madelung Constant

Go Madelung Constant using Born Lande Equation

M = \frac{- U \cdot 4 \cdot π \cdot [Permitivity-vacuum] \cdot r 0}{(1 - (\frac{1}{n born})) \cdot ({[Charge-e]}^{2}) \cdot [Avaga-no] \cdot z + \cdot z -}

Go Madelung Constant using Born-Mayer equation

M = \frac{- U \cdot 4 \cdot π \cdot [Permitivity-vacuum] \cdot r 0}{[Avaga-no] \cdot z + \cdot z - \cdot ({[Charge-e]}^{2}) \cdot (1 - (\frac{ρ}{r 0}))}

Go Madelung Constant using Kapustinskii Approximation

M = 0.88 \cdot N ions

Go Madelung Constant using Madelung Energy

M = \frac{- (E M) \cdot 4 \cdot π \cdot [Permitivity-vacuum] \cdot r 0}{(q^{2}) \cdot ({[Charge-e]}^{2})}

Other formulas in Madelung Constant category

Go Madelung Energy

E M = - \frac{M \cdot (q^{2}) \cdot ({[Charge-e]}^{2})}{4 \cdot π \cdot [Permitivity-vacuum] \cdot r 0}

Go Madelung Energy using Total Energy of Ion

E M = E tot - E

Go Madelung Energy using Total Energy of Ion given Distance

E M = E tot - (\frac{B M}{{r 0}^{n born}})

How to Evaluate Madelung Constant given Repulsive Interaction Constant?

Madelung Constant given Repulsive Interaction Constant evaluator uses Madelung Constant = (Repulsive Interaction Constant given M*4*pi*[Permitivity-vacuum]*Born Exponent)/((Charge^2)*([Charge-e]^2)*(Distance of Closest Approach^(Born Exponent-1))) to evaluate the Madelung Constant, The Madelung constant given Repulsive Interaction Constant is used in determining the electrostatic potential of a single ion in a crystal by approximating the ions by point charges. Madelung Constant is denoted by M symbol.

How to evaluate Madelung Constant given Repulsive Interaction Constant using this online evaluator? To use this online evaluator for Madelung Constant given Repulsive Interaction Constant, enter Repulsive Interaction Constant given M (B_M), Born Exponent (n_born), Charge (q) & Distance of Closest Approach (r₀) and hit the calculate button.

FAQs on Madelung Constant given Repulsive Interaction Constant

What is the formula to find Madelung Constant given Repulsive Interaction Constant?

The formula of Madelung Constant given Repulsive Interaction Constant is expressed as Madelung Constant = (Repulsive Interaction Constant given M*4*pi*[Permitivity-vacuum]*Born Exponent)/((Charge^2)*([Charge-e]^2)*(Distance of Closest Approach^(Born Exponent-1))). Here is an example- 1.702967 = (4.1E-29*4*pi*[Permitivity-vacuum]*0.9926)/((0.3^2)*([Charge-e]^2)*(6E-09^(0.9926-1))).

How to calculate Madelung Constant given Repulsive Interaction Constant?

With Repulsive Interaction Constant given M (B_M), Born Exponent (n_born), Charge (q) & Distance of Closest Approach (r₀) we can find Madelung Constant given Repulsive Interaction Constant using the formula - Madelung Constant = (Repulsive Interaction Constant given M*4*pi*[Permitivity-vacuum]*Born Exponent)/((Charge^2)*([Charge-e]^2)*(Distance of Closest Approach^(Born Exponent-1))). This formula also uses Permittivity of vacuum, Charge of electron, Archimedes' constant .

What are the other ways to Calculate Madelung Constant?

Here are the different ways to Calculate Madelung Constant-

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

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Madelung Constant given Repulsive Interaction Constant Formula

​GoMadelung Constant using Born Lande Equation Formula

​GoMadelung Constant using Born-Mayer equation Formula

Madelung Constant given Repulsive Interaction Constant Example

Madelung Constant given Repulsive Interaction Constant Solution

Madelung Constant given Repulsive Interaction Constant Formula Elements

Other Formulas to find Madelung Constant

Other formulas in Madelung Constant category

How to Evaluate Madelung Constant given Repulsive Interaction Constant?

FAQs on Madelung Constant given Repulsive Interaction Constant

Variable Name

GoMadelung Constant using Born Lande Equation Formula

GoMadelung Constant using Born-Mayer equation Formula