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Born Exponent using Born Lande Equation Formula

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GoBorn Exponent using Born-Lande equation without Madelung Constant Formula

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

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

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

Born Exponent using Born Lande Equation Example

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Here is how the Born Exponent using Born Lande Equation equation looks like with Values.

Here is how the Born Exponent using Born Lande Equation equation looks like with Units.

Here is how the Born Exponent using Born Lande Equation equation looks like.

0.9926 = \frac{1}{1 - \frac{- 3500 \cdot 4 \cdot 3.1416 \cdot 8.9E-12 \cdot 60}{6E+23 \cdot 1.7 \cdot ({1.6E-19}^{2}) \cdot 4 \cdot 3}}

0.9926 = \frac{1}{1 - \frac{- 3500J/mol \cdot 4 \cdot 3.1416 \cdot 8.9E-12F/m \cdot 60A}{6E+23 \cdot 1.7 \cdot ({1.6E-19C}^{2}) \cdot 4C \cdot 3C}}

0.9926 = \frac{1}{1 - \frac{- 3500 \cdot 4 \cdot 3.1416 \cdot 8.9E-12 \cdot 60}{6E+23 \cdot 1.7 \cdot ({1.6E-19}^{2}) \cdot 4 \cdot 3}}

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Born Exponent using Born Lande Equation Solution

Follow our step by step solution on how to calculate Born Exponent using Born Lande Equation?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

n born = \frac{1}{1 - \frac{- 3500J/mol \cdot 4 \cdot π \cdot [Permitivity-vacuum] \cdot 60A}{[Avaga-no] \cdot 1.7 \cdot ({[Charge-e]}^{2}) \cdot 4C \cdot 3C}}

Next Step Substitute values of Constants

∴

n born = \frac{1}{1 - \frac{- 3500J/mol \cdot 4 \cdot 3.1416 \cdot 8.9E-12F/m \cdot 60A}{6E+23 \cdot 1.7 \cdot ({1.6E-19C}^{2}) \cdot 4C \cdot 3C}}

Next Step Convert Units

∴

n born = \frac{1}{1 - \frac{- 3500J/mol \cdot 4 \cdot 3.1416 \cdot 8.9E-12F/m \cdot 6E-9m}{6E+23 \cdot 1.7 \cdot ({1.6E-19C}^{2}) \cdot 4C \cdot 3C}}

Next Step Prepare to Evaluate

∴

n born = \frac{1}{1 - \frac{- 3500 \cdot 4 \cdot 3.1416 \cdot 8.9E-12 \cdot 6E-9}{6E+23 \cdot 1.7 \cdot ({1.6E-19}^{2}) \cdot 4 \cdot 3}}

Next Step Evaluate

∴

n born = 0.99264866619925

LAST Step Rounding Answer

∴

n born = 0.9926

Born Exponent using Born Lande Equation Formula Elements

Variables

Constants

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

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

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

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

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 Born Exponent

Go Born Exponent using Repulsive Interaction

n born = \frac{\log 10 (\frac{B}{E R})}{\log 10} (r 0)

Go Born Exponent using Born-Lande equation without Madelung Constant

n born = \frac{1}{1 - \frac{- U \cdot 4 \cdot π \cdot [Permitivity-vacuum] \cdot r 0}{[Avaga-no] \cdot N ions \cdot 0.88 \cdot ({[Charge-e]}^{2}) \cdot z + \cdot z -}}

Other formulas in Lattice Energy category

Go Lattice Energy using Born Lande Equation

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

Go Electrostatic Potential Energy between pair of Ions

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

Go Repulsive Interaction

E R = \frac{B}{{r 0}^{n born}}

Go Repulsive Interaction Constant

B = E R \cdot ({r 0}^{n born})

How to Evaluate Born Exponent using Born Lande Equation?

Born Exponent using Born Lande Equation evaluator uses 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)) to evaluate the Born Exponent, The Born exponent using Born Lande equation is typically a number between 5 and 12, determined experimentally by measuring the compressibility of the solid, or derived theoretically. Born Exponent is denoted by n_born symbol.

How to evaluate Born Exponent using Born Lande Equation using this online evaluator? To use this online evaluator for Born Exponent using Born Lande Equation, enter Lattice Energy (U), Distance of Closest Approach (r₀), Madelung Constant (M), Charge of Cation (z⁺) & Charge of Anion (z^-) and hit the calculate button.

FAQs on Born Exponent using Born Lande Equation

What is the formula to find Born Exponent using Born Lande Equation?

The formula of Born Exponent using Born Lande Equation is expressed as 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)). Here is an example- 0.992649 = 1/(1-(-3500*4*pi*[Permitivity-vacuum]*6E-09)/([Avaga-no]*1.7*([Charge-e]^2)*4*3)).

How to calculate Born Exponent using Born Lande Equation?

With Lattice Energy (U), Distance of Closest Approach (r₀), Madelung Constant (M), Charge of Cation (z⁺) & Charge of Anion (z^-) we can find Born Exponent using Born Lande Equation using the formula - 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)). This formula also uses Permittivity of vacuum, Avogadro’s number, Charge of electron, Archimedes' constant .

What are the other ways to Calculate Born Exponent?

Here are the different ways to Calculate Born Exponent-

Born Exponent=(log10(Repulsive Interaction Constant/Repulsive Interaction))/log10(Distance of Closest Approach)
Born Exponent=1/(1-(-Lattice Energy*4*pi*[Permitivity-vacuum]*Distance of Closest Approach)/([Avaga-no]*Number of Ions*0.88*([Charge-e]^2)*Charge of Cation*Charge of Anion))

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Born Exponent using Born Lande Equation Formula

​GoBorn Exponent using Repulsive Interaction Formula

​GoBorn Exponent using Born-Lande equation without Madelung Constant Formula

Born Exponent using Born Lande Equation Example

Born Exponent using Born Lande Equation Solution

Born Exponent using Born Lande Equation Formula Elements

Other Formulas to find Born Exponent

Other formulas in Lattice Energy category

How to Evaluate Born Exponent using Born Lande Equation?

FAQs on Born Exponent using Born Lande Equation

Variable Name

GoBorn Exponent using Repulsive Interaction Formula

GoBorn Exponent using Born-Lande equation without Madelung Constant Formula