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Minimum Potential Energy of Ion Formula

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The Minimum Potential Energy of Ion is a means of calculating the lattice energy of a crystalline ionic compound. Check FAQs

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

E_min - Minimum Potential Energy of Ion?q - Charge?M - Madelung Constant?r₀ - Distance of Closest Approach?B - Repulsive Interaction Constant?n_born - Born Exponent?[Charge-e] - Charge of electron?[Permitivity-vacuum] - Permittivity of vacuum?π - Archimedes' constant?

Minimum Potential Energy of Ion Example

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Here is how the Minimum Potential Energy of Ion equation looks like with Values.

Here is how the Minimum Potential Energy of Ion equation looks like with Units.

Here is how the Minimum Potential Energy of Ion equation looks like.

5.8E+12 = (\frac{- ({0.3}^{2}) \cdot ({1.6E-19}^{2}) \cdot 1.7}{4 \cdot 3.1416 \cdot 8.9E-12 \cdot 60}) + (\frac{40000}{60^{0.9926}})

5.8E+12J = (\frac{- ({0.3C}^{2}) \cdot ({1.6E-19C}^{2}) \cdot 1.7}{4 \cdot 3.1416 \cdot 8.9E-12F/m \cdot 60A}) + (\frac{40000}{{60A}^{0.9926}})

5.8E+12 = (\frac{- ({0.3}^{2}) \cdot ({1.6E-19}^{2}) \cdot 1.7}{4 \cdot 3.1416 \cdot 8.9E-12 \cdot 60}) + (\frac{40000}{60^{0.9926}})

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Minimum Potential Energy of Ion Solution

Follow our step by step solution on how to calculate Minimum Potential Energy of Ion?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

E min = (\frac{- ({0.3C}^{2}) \cdot ({[Charge-e]}^{2}) \cdot 1.7}{4 \cdot π \cdot [Permitivity-vacuum] \cdot 60A}) + (\frac{40000}{{60A}^{0.9926}})

Next Step Substitute values of Constants

∴

E min = (\frac{- ({0.3C}^{2}) \cdot ({1.6E-19C}^{2}) \cdot 1.7}{4 \cdot 3.1416 \cdot 8.9E-12F/m \cdot 60A}) + (\frac{40000}{{60A}^{0.9926}})

Next Step Convert Units

∴

E min = (\frac{- ({0.3C}^{2}) \cdot ({1.6E-19C}^{2}) \cdot 1.7}{4 \cdot 3.1416 \cdot 8.9E-12F/m \cdot 6E-9m}) + (\frac{40000}{{6E-9m}^{0.9926}})

Next Step Prepare to Evaluate

∴

E min = (\frac{- ({0.3}^{2}) \cdot ({1.6E-19}^{2}) \cdot 1.7}{4 \cdot 3.1416 \cdot 8.9E-12 \cdot 6E-9}) + (\frac{40000}{{6E-9}^{0.9926}})

Next Step Evaluate

∴

E min = 5795181739688.58J

LAST Step Rounding Answer

∴

E min = 5.8E+12J

Minimum Potential Energy of Ion Formula Elements

Variables

Constants

Minimum Potential Energy of Ion

The Minimum Potential Energy of Ion is a means of calculating the lattice energy of a crystalline ionic compound.

Symbol: E_min

Measurement: EnergyUnit: J

Note: Value can be positive or negative.

Formulas to find Minimum Potential Energy of Ion

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

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

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

Repulsive Interaction Constant

The Repulsive Interaction Constant is the constant scaling the strength of the repulsive interaction.

Symbol: B

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Repulsive Interaction Constant

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 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 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 Born Exponent using Born Lande Equation

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 -}}

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}}

How to Evaluate Minimum Potential Energy of Ion?

Minimum Potential Energy of Ion evaluator uses Minimum Potential 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 evaluate the Minimum Potential Energy of Ion, The Minimum Potential Energy of Ion is a means of calculating the lattice energy of a crystalline ionic compound. Minimum Potential Energy of Ion is denoted by E_min symbol.

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

FAQs on Minimum Potential Energy of Ion

What is the formula to find Minimum Potential Energy of Ion?

The formula of Minimum Potential Energy of Ion is expressed as Minimum Potential 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)). Here is an example- 5.8E+12 = ((-(0.3^2)*([Charge-e]^2)*1.7)/(4*pi*[Permitivity-vacuum]*6E-09))+(40000/(6E-09^0.9926)).

How to calculate Minimum Potential Energy of Ion?

With Charge (q), Madelung Constant (M), Distance of Closest Approach (r₀), Repulsive Interaction Constant (B) & Born Exponent (n_born) we can find Minimum Potential Energy of Ion using the formula - Minimum Potential 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)). This formula also uses Charge of electron, Permittivity of vacuum, Archimedes' constant .

Can the Minimum Potential Energy of Ion be negative?

Yes, the Minimum Potential Energy of Ion, measured in Energy can be negative.

Which unit is used to measure Minimum Potential Energy of Ion?

Minimum Potential Energy of Ion is usually measured using the Joule[J] for Energy. Kilojoule[J], Gigajoule[J], Megajoule[J] are the few other units in which Minimum Potential Energy of Ion can be measured.

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Minimum Potential Energy of Ion Formula

Minimum Potential Energy of Ion Example

Minimum Potential Energy of Ion Solution

Minimum Potential Energy of Ion Formula Elements

Other formulas in Lattice Energy category

How to Evaluate Minimum Potential Energy of Ion?

FAQs on Minimum Potential Energy of Ion

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