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Madelung Constant using Born-Mayer equation Formula

GoMadelung Constant given Repulsive Interaction Constant Formula

GoMadelung Constant using Born Lande 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{- 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}))}

M - Madelung Constant?U - Lattice Energy?r₀ - Distance of Closest Approach?z⁺ - Charge of Cation?z^- - Charge of Anion?ρ - Constant Depending on Compressibility?[Permitivity-vacuum] - Permittivity of vacuum?[Avaga-no] - Avogadro’s number?[Charge-e] - Charge of electron?π - Archimedes' constant?

Madelung Constant using Born-Mayer equation Example

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Here is how the Madelung Constant using Born-Mayer equation equation looks like with Values.

Here is how the Madelung Constant using Born-Mayer equation equation looks like with Units.

Here is how the Madelung Constant using Born-Mayer equation equation looks like.

1.7168 = \frac{- 3500 \cdot 4 \cdot 3.1416 \cdot 8.9E-12 \cdot 60}{6E+23 \cdot 4 \cdot 3 \cdot ({1.6E-19}^{2}) \cdot (1 - (\frac{60.44}{60}))}

1.7168 = \frac{- 3500J/mol \cdot 4 \cdot 3.1416 \cdot 8.9E-12F/m \cdot 60A}{6E+23 \cdot 4C \cdot 3C \cdot ({1.6E-19C}^{2}) \cdot (1 - (\frac{60.44A}{60A}))}

1.7168 = \frac{- 3500 \cdot 4 \cdot 3.1416 \cdot 8.9E-12 \cdot 60}{6E+23 \cdot 4 \cdot 3 \cdot ({1.6E-19}^{2}) \cdot (1 - (\frac{60.44}{60}))}

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Madelung Constant using Born-Mayer equation Solution

Follow our step by step solution on how to calculate Madelung Constant using Born-Mayer equation?

FIRST Step Consider the formula

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}))}

Next Step Substitute values of Variables

∴

M = \frac{- 3500J/mol \cdot 4 \cdot π \cdot [Permitivity-vacuum] \cdot 60A}{[Avaga-no] \cdot 4C \cdot 3C \cdot ({[Charge-e]}^{2}) \cdot (1 - (\frac{60.44A}{60A}))}

Next Step Substitute values of Constants

∴

M = \frac{- 3500J/mol \cdot 4 \cdot 3.1416 \cdot 8.9E-12F/m \cdot 60A}{6E+23 \cdot 4C \cdot 3C \cdot ({1.6E-19C}^{2}) \cdot (1 - (\frac{60.44A}{60A}))}

Next Step Convert Units

∴

M = \frac{- 3500J/mol \cdot 4 \cdot 3.1416 \cdot 8.9E-12F/m \cdot 6E-9m}{6E+23 \cdot 4C \cdot 3C \cdot ({1.6E-19C}^{2}) \cdot (1 - (\frac{6E-9m}{6E-9m}))}

Next Step Prepare to Evaluate

∴

M = \frac{- 3500 \cdot 4 \cdot 3.1416 \cdot 8.9E-12 \cdot 6E-9}{6E+23 \cdot 4 \cdot 3 \cdot ({1.6E-19}^{2}) \cdot (1 - (\frac{6E-9}{6E-9}))}

Next Step Evaluate

∴

M = 1.71679355814139

LAST Step Rounding Answer

∴

M = 1.7168

Madelung Constant using Born-Mayer equation 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

Lattice Energy

The Lattice Energy of a crystalline solid is a measure of the energy released when ions are combined to make a compound.

Symbol: U

Measurement: Molar EnthalpyUnit: J/mol

Note: Value can be positive or negative.

Formulas to find Lattice Energy

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

Charge of Cation

The Charge of Cation is the positive charge over a cation with fewer electron than the respective atom.

Symbol: z⁺

Measurement: Electric ChargeUnit: C

Note: Value can be positive or negative.

Formulas to find Charge of Cation

Charge of Anion

The Charge of Anion is the negative charge over an anion with more electron than the respective atom.

Symbol: z^-

Measurement: Electric ChargeUnit: C

Note: Value can be positive or negative.

Formulas to find Charge of Anion

Constant Depending on Compressibility

The Constant Depending on Compressibility is a constant dependent on the compressibility of the crystal, 30 pm works well for all alkali metal halides.

Symbol: ρ

Measurement: LengthUnit: A

Note: Value can be positive or negative.

Formulas to find Constant Depending on Compressibility

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

Avogadro’s number

Avogadro’s number represents the number of entities (atoms, molecules, ions, etc.) in one mole of a substance.

Symbol: [Avaga-no]

Value: 6.02214076E+23

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 given Repulsive Interaction Constant

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})}

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 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 using Born-Mayer equation?

Madelung Constant using Born-Mayer equation evaluator uses 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))) to evaluate the Madelung Constant, The Madelung constant using Born-Mayer equation 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 using Born-Mayer equation using this online evaluator? To use this online evaluator for Madelung Constant using Born-Mayer equation, enter Lattice Energy (U), Distance of Closest Approach (r₀), Charge of Cation (z⁺), Charge of Anion (z^-) & Constant Depending on Compressibility (ρ) and hit the calculate button.

FAQs on Madelung Constant using Born-Mayer equation

What is the formula to find Madelung Constant using Born-Mayer equation?

The formula of Madelung Constant using Born-Mayer equation is expressed as 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))). Here is an example- 1.716794 = (-3500*4*pi*[Permitivity-vacuum]*6E-09)/([Avaga-no]*4*3*([Charge-e]^2)*(1-(6.044E-09/6E-09))).

How to calculate Madelung Constant using Born-Mayer equation?

With Lattice Energy (U), Distance of Closest Approach (r₀), Charge of Cation (z⁺), Charge of Anion (z^-) & Constant Depending on Compressibility (ρ) we can find Madelung Constant using Born-Mayer equation using the formula - 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))). This formula also uses Permittivity of vacuum, Avogadro’s number, 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=(Repulsive Interaction Constant given M*4*pi*[Permitivity-vacuum]*Born Exponent)/((Charge^2)*([Charge-e]^2)*(Distance of Closest Approach^(Born Exponent-1)))
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=0.88*Number of Ions

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Madelung Constant using Born-Mayer equation Formula

​GoMadelung Constant given Repulsive Interaction Constant Formula

​GoMadelung Constant using Born Lande Equation Formula

Madelung Constant using Born-Mayer equation Example

Madelung Constant using Born-Mayer equation Solution

Madelung Constant using Born-Mayer equation Formula Elements

Other Formulas to find Madelung Constant

Other formulas in Madelung Constant category

How to Evaluate Madelung Constant using Born-Mayer equation?

FAQs on Madelung Constant using Born-Mayer equation

Variable Name

GoMadelung Constant given Repulsive Interaction Constant Formula

GoMadelung Constant using Born Lande Equation Formula