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Distance of Closest Approach using Born Lande equation Formula

GoDistance of Closest Approach using Born-Lande Equation without Madelung Constant Formula

GoDistance of Closest Approach using Electrostatic Potential Formula

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

r 0 = - \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 U}

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

Distance of Closest Approach using Born Lande equation Example

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Here is how the Distance of Closest Approach using Born Lande equation equation looks like with Values.

Here is how the Distance of Closest Approach using Born Lande equation equation looks like with Units.

Here is how the Distance of Closest Approach using Born Lande equation equation looks like.

60.4002 = - \frac{6E+23 \cdot 1.7 \cdot 4 \cdot 3 \cdot ({1.6E-19}^{2}) \cdot (1 - (\frac{1}{0.9926}))}{4 \cdot 3.1416 \cdot 8.9E-12 \cdot 3500}

60.4002A = - \frac{6E+23 \cdot 1.7 \cdot 4C \cdot 3C \cdot ({1.6E-19C}^{2}) \cdot (1 - (\frac{1}{0.9926}))}{4 \cdot 3.1416 \cdot 8.9E-12F/m \cdot 3500J/mol}

60.4002 = - \frac{6E+23 \cdot 1.7 \cdot 4 \cdot 3 \cdot ({1.6E-19}^{2}) \cdot (1 - (\frac{1}{0.9926}))}{4 \cdot 3.1416 \cdot 8.9E-12 \cdot 3500}

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Distance of Closest Approach using Born Lande equation Solution

Follow our step by step solution on how to calculate Distance of Closest Approach using Born Lande equation?

FIRST Step Consider the formula

r 0 = - \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 U}

Next Step Substitute values of Variables

∴

r 0 = - \frac{[Avaga-no] \cdot 1.7 \cdot 4C \cdot 3C \cdot ({[Charge-e]}^{2}) \cdot (1 - (\frac{1}{0.9926}))}{4 \cdot π \cdot [Permitivity-vacuum] \cdot 3500J/mol}

Next Step Substitute values of Constants

∴

r 0 = - \frac{6E+23 \cdot 1.7 \cdot 4C \cdot 3C \cdot ({1.6E-19C}^{2}) \cdot (1 - (\frac{1}{0.9926}))}{4 \cdot 3.1416 \cdot 8.9E-12F/m \cdot 3500J/mol}

Next Step Prepare to Evaluate

∴

r 0 = - \frac{6E+23 \cdot 1.7 \cdot 4 \cdot 3 \cdot ({1.6E-19}^{2}) \cdot (1 - (\frac{1}{0.9926}))}{4 \cdot 3.1416 \cdot 8.9E-12 \cdot 3500}

Next Step Evaluate

∴

r 0 = 6.04001642309941E-09m

Next Step Convert to Output's Unit

∴

r 0 = 60.4001642309941A

LAST Step Rounding Answer

∴

r 0 = 60.4002A

Distance of Closest Approach using Born Lande equation Formula Elements

Variables

Constants

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

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

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

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

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 Distance of Closest Approach

Go Distance of Closest Approach using Born-Lande Equation without Madelung Constant

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

Go Distance of Closest Approach using Electrostatic Potential

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

Go Distance of Closest Approach using Madelung Energy

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

How to Evaluate Distance of Closest Approach using Born Lande equation?

Distance of Closest Approach using Born Lande equation evaluator uses Distance of Closest Approach = -([Avaga-no]*Madelung Constant*Charge of Cation*Charge of Anion*([Charge-e]^2)*(1-(1/Born Exponent)))/(4*pi*[Permitivity-vacuum]*Lattice Energy) to evaluate the Distance of Closest Approach, The Distance of closest approach using Born Lande equation is the distance separating the ion centers in a lattice. Distance of Closest Approach is denoted by r₀ symbol.

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

FAQs on Distance of Closest Approach using Born Lande equation

What is the formula to find Distance of Closest Approach using Born Lande equation?

The formula of Distance of Closest Approach using Born Lande equation is expressed as Distance of Closest Approach = -([Avaga-no]*Madelung Constant*Charge of Cation*Charge of Anion*([Charge-e]^2)*(1-(1/Born Exponent)))/(4*pi*[Permitivity-vacuum]*Lattice Energy). Here is an example- 6E+11 = -([Avaga-no]*1.7*4*3*([Charge-e]^2)*(1-(1/0.9926)))/(4*pi*[Permitivity-vacuum]*3500).

How to calculate Distance of Closest Approach using Born Lande equation?

With Madelung Constant (M), Charge of Cation (z⁺), Charge of Anion (z^-), Born Exponent (n_born) & Lattice Energy (U) we can find Distance of Closest Approach using Born Lande equation using the formula - Distance of Closest Approach = -([Avaga-no]*Madelung Constant*Charge of Cation*Charge of Anion*([Charge-e]^2)*(1-(1/Born Exponent)))/(4*pi*[Permitivity-vacuum]*Lattice Energy). This formula also uses Avogadro’s number, Charge of electron, Permittivity of vacuum, Archimedes' constant .

What are the other ways to Calculate Distance of Closest Approach?

Here are the different ways to Calculate Distance of Closest Approach-

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

Can the Distance of Closest Approach using Born Lande equation be negative?

Yes, the Distance of Closest Approach using Born Lande equation, measured in Length can be negative.

Which unit is used to measure Distance of Closest Approach using Born Lande equation?

Distance of Closest Approach using Born Lande equation is usually measured using the Angstrom[A] for Length. Meter[A], Millimeter[A], Kilometer[A] are the few other units in which Distance of Closest Approach using Born Lande equation can be measured.

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Distance of Closest Approach using Born Lande equation Formula

​GoDistance of Closest Approach using Born-Lande Equation without Madelung Constant Formula

​GoDistance of Closest Approach using Electrostatic Potential Formula

Distance of Closest Approach using Born Lande equation Example

Distance of Closest Approach using Born Lande equation Solution

Distance of Closest Approach using Born Lande equation Formula Elements

Other Formulas to find Distance of Closest Approach

How to Evaluate Distance of Closest Approach using Born Lande equation?

FAQs on Distance of Closest Approach using Born Lande equation

Variable Name

GoDistance of Closest Approach using Born-Lande Equation without Madelung Constant Formula

GoDistance of Closest Approach using Electrostatic Potential Formula