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Repulsive Interaction Constant using Total Energy of Ion Formula

GoRepulsive Interaction Constant Formula

GoRepulsive Interaction Constant given Total Energy of Ion and Madelung Energy Formula

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

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

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

Repulsive Interaction Constant using Total Energy of Ion Example

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Here is how the Repulsive Interaction Constant using Total Energy of Ion equation looks like with Values.

Here is how the Repulsive Interaction Constant using Total Energy of Ion equation looks like with Units.

Here is how the Repulsive Interaction Constant using Total Energy of Ion equation looks like.

39964.2342 = (5.8E+12 - (- \frac{1.7 \cdot ({0.3}^{2}) \cdot ({1.6E-19}^{2})}{4 \cdot 3.1416 \cdot 8.9E-12 \cdot 60})) \cdot (60^{0.9926})

39964.2342 = (5.8E+12J - (- \frac{1.7 \cdot ({0.3C}^{2}) \cdot ({1.6E-19C}^{2})}{4 \cdot 3.1416 \cdot 8.9E-12F/m \cdot 60A})) \cdot ({60A}^{0.9926})

39964.2342 = (5.8E+12 - (- \frac{1.7 \cdot ({0.3}^{2}) \cdot ({1.6E-19}^{2})}{4 \cdot 3.1416 \cdot 8.9E-12 \cdot 60})) \cdot (60^{0.9926})

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Repulsive Interaction Constant using Total Energy of Ion Solution

Follow our step by step solution on how to calculate Repulsive Interaction Constant using Total Energy of Ion?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

B = (5.8E+12J - (- \frac{1.7 \cdot ({0.3C}^{2}) \cdot ({[Charge-e]}^{2})}{4 \cdot π \cdot [Permitivity-vacuum] \cdot 60A})) \cdot ({60A}^{0.9926})

Next Step Substitute values of Constants

∴

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

Next Step Convert Units

∴

B = (5.8E+12J - (- \frac{1.7 \cdot ({0.3C}^{2}) \cdot ({1.6E-19C}^{2})}{4 \cdot 3.1416 \cdot 8.9E-12F/m \cdot 6E-9m})) \cdot ({6E-9m}^{0.9926})

Next Step Prepare to Evaluate

∴

B = (5.8E+12 - (- \frac{1.7 \cdot ({0.3}^{2}) \cdot ({1.6E-19}^{2})}{4 \cdot 3.1416 \cdot 8.9E-12 \cdot 6E-9})) \cdot ({6E-9}^{0.9926})

Next Step Evaluate

∴

B = 39964.2341522917

LAST Step Rounding Answer

∴

B = 39964.2342

Repulsive Interaction Constant using Total Energy of Ion Formula Elements

Variables

Constants

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

Total Energy of Ion

The Total Energy of Ion in the lattice is the sum of Madelung Energy and Repulsive potential energy.

Symbol: E_total

Measurement: EnergyUnit: J

Note: Value can be positive or negative.

Formulas to find Total Energy of Ion

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

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

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 to find Repulsive Interaction Constant

Go Repulsive Interaction Constant

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

Go Repulsive Interaction Constant given Total Energy of Ion and Madelung Energy

B = (E total - (E M)) \cdot ({r 0}^{n born})

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 Repulsive Interaction Constant using Total Energy of Ion?

Repulsive Interaction Constant using Total Energy of Ion evaluator uses Repulsive Interaction Constant = (Total Energy of Ion-(-(Madelung Constant*(Charge^2)*([Charge-e]^2))/(4*pi*[Permitivity-vacuum]*Distance of Closest Approach)))*(Distance of Closest Approach^Born Exponent) to evaluate the Repulsive Interaction Constant, The Repulsive Interaction Constant using Total Energy of Ion is the constant scaling the strength of the repulsive interaction. Repulsive Interaction Constant is denoted by B symbol.

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

FAQs on Repulsive Interaction Constant using Total Energy of Ion

What is the formula to find Repulsive Interaction Constant using Total Energy of Ion?

The formula of Repulsive Interaction Constant using Total Energy of Ion is expressed as Repulsive Interaction Constant = (Total Energy of Ion-(-(Madelung Constant*(Charge^2)*([Charge-e]^2))/(4*pi*[Permitivity-vacuum]*Distance of Closest Approach)))*(Distance of Closest Approach^Born Exponent). Here is an example- 39964.23 = (5790000000000-(-(1.7*(0.3^2)*([Charge-e]^2))/(4*pi*[Permitivity-vacuum]*6E-09)))*(6E-09^0.9926).

How to calculate Repulsive Interaction Constant using Total Energy of Ion?

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

What are the other ways to Calculate Repulsive Interaction Constant?

Here are the different ways to Calculate Repulsive Interaction Constant-

Repulsive Interaction Constant=Repulsive Interaction*(Distance of Closest Approach^Born Exponent)
Repulsive Interaction Constant=(Total Energy of Ion-(Madelung Energy))*(Distance of Closest Approach^Born Exponent)

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Repulsive Interaction Constant using Total Energy of Ion Formula

​GoRepulsive Interaction Constant Formula

​GoRepulsive Interaction Constant given Total Energy of Ion and Madelung Energy Formula

Repulsive Interaction Constant using Total Energy of Ion Example

Repulsive Interaction Constant using Total Energy of Ion Solution

Repulsive Interaction Constant using Total Energy of Ion Formula Elements

Other Formulas to find Repulsive Interaction Constant

Other formulas in Lattice Energy category

How to Evaluate Repulsive Interaction Constant using Total Energy of Ion?

FAQs on Repulsive Interaction Constant using Total Energy of Ion

Variable Name

GoRepulsive Interaction Constant Formula

GoRepulsive Interaction Constant given Total Energy of Ion and Madelung Energy Formula