Repulsive Interaction Constant given Madelung constant Formula

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The Repulsive Interaction Constant given M, (where M= Madelung Constant) is the constant scaling the strength of the repulsive interaction. Check FAQs
BM=M(q2)([Charge-e]2)(r0nborn-1)4π[Permitivity-vacuum]nborn
BM - Repulsive Interaction Constant given M?M - Madelung Constant?q - Charge?r0 - Distance of Closest Approach?nborn - Born Exponent?[Charge-e] - Charge of electron?[Permitivity-vacuum] - Permittivity of vacuum?π - Archimedes' constant?

Repulsive Interaction Constant given Madelung constant Example

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Here is how the Repulsive Interaction Constant given Madelung constant equation looks like with Values.

Here is how the Repulsive Interaction Constant given Madelung constant equation looks like with Units.

Here is how the Repulsive Interaction Constant given Madelung constant equation looks like.

4.1E-29Edit=1.7Edit(0.3Edit2)(1.6E-192)(60Edit0.9926Edit-1)43.14168.9E-120.9926Edit
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Repulsive Interaction Constant given Madelung constant Solution

Follow our step by step solution on how to calculate Repulsive Interaction Constant given Madelung constant?

FIRST Step Consider the formula
BM=M(q2)([Charge-e]2)(r0nborn-1)4π[Permitivity-vacuum]nborn
Next Step Substitute values of Variables
BM=1.7(0.3C2)([Charge-e]2)(60A0.9926-1)4π[Permitivity-vacuum]0.9926
Next Step Substitute values of Constants
BM=1.7(0.3C2)(1.6E-19C2)(60A0.9926-1)43.14168.9E-12F/m0.9926
Next Step Convert Units
BM=1.7(0.3C2)(1.6E-19C2)(6E-9m0.9926-1)43.14168.9E-12F/m0.9926
Next Step Prepare to Evaluate
BM=1.7(0.32)(1.6E-192)(6E-90.9926-1)43.14168.9E-120.9926
Next Step Evaluate
BM=4.09285619643233E-29
LAST Step Rounding Answer
BM=4.1E-29

Repulsive Interaction Constant given Madelung constant Formula Elements

Variables
Constants
Repulsive Interaction Constant given M
The Repulsive Interaction Constant given M, (where M= Madelung Constant) is the constant scaling the strength of the repulsive interaction.
Symbol: BM
Measurement: NAUnit: Unitless
Note: Value can be positive or negative.
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.
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.
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.
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: nborn
Measurement: NAUnit: Unitless
Note: Value can be positive or negative.
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=-[Avaga-no]Mz+z-([Charge-e]2)(1-(1nborn))4π[Permitivity-vacuum]r0
​Go Born Exponent using Born Lande Equation
nborn=11--U4π[Permitivity-vacuum]r0[Avaga-no]M([Charge-e]2)z+z-
​Go Electrostatic Potential Energy between pair of Ions
EPair=-(q2)([Charge-e]2)4π[Permitivity-vacuum]r0
​Go Repulsive Interaction
ER=Br0nborn

How to Evaluate Repulsive Interaction Constant given Madelung constant?

Repulsive Interaction Constant given Madelung constant evaluator uses Repulsive Interaction Constant given M = (Madelung Constant*(Charge^2)*([Charge-e]^2)*(Distance of Closest Approach^(Born Exponent-1)))/(4*pi*[Permitivity-vacuum]*Born Exponent) to evaluate the Repulsive Interaction Constant given M, The Repulsive Interaction Constant given Madelung constant is the constant scaling the strength of the repulsive interaction. Repulsive Interaction Constant given M is denoted by BM symbol.

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

FAQs on Repulsive Interaction Constant given Madelung constant

What is the formula to find Repulsive Interaction Constant given Madelung constant?
The formula of Repulsive Interaction Constant given Madelung constant is expressed as Repulsive Interaction Constant given M = (Madelung Constant*(Charge^2)*([Charge-e]^2)*(Distance of Closest Approach^(Born Exponent-1)))/(4*pi*[Permitivity-vacuum]*Born Exponent). Here is an example- 4.1E-29 = (1.7*(0.3^2)*([Charge-e]^2)*(6E-09^(0.9926-1)))/(4*pi*[Permitivity-vacuum]*0.9926).
How to calculate Repulsive Interaction Constant given Madelung constant?
With Madelung Constant (M), Charge (q), Distance of Closest Approach (r0) & Born Exponent (nborn) we can find Repulsive Interaction Constant given Madelung constant using the formula - Repulsive Interaction Constant given M = (Madelung Constant*(Charge^2)*([Charge-e]^2)*(Distance of Closest Approach^(Born Exponent-1)))/(4*pi*[Permitivity-vacuum]*Born Exponent). This formula also uses Charge of electron, Permittivity of vacuum, Archimedes' constant .
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