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Born Exponent using Repulsive Interaction Calculator

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Ionic Bonding Covalent Bonding Electronegativity

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Lattice Energy

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Distance of Closest Approach Madelung Constant

✖The Repulsive Interaction Constant is the constant scaling the strength of the repulsive interaction.ⓘ Repulsive Interaction Constant [B]			+10% -10%
✖The Repulsive Interaction is between atoms acts over a very short range, but is very large when distances are short.ⓘ Repulsive Interaction [E_R]			+10% -10%
✖Distance of Closest Approach is the distance to which an alpha particle comes closer to the nucleus.ⓘ Distance of Closest Approach [r₀]			+10% -10%

✖The Born Exponent is a number between 5 and 12, determined experimentally by measuring the compressibility of the solid, or derived theoretically.ⓘ Born Exponent using Repulsive Interaction [n_born]

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Formula

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Born Exponent using Repulsive Interaction

Formula

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

Example

0.992644 = \frac{\log 10 (\frac{40000}{5.8E+12 J})}{\log 10} (60 A)

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Born Exponent using Repulsive Interaction Solution

STEP 0: Pre-Calculation Summary

Formula Used

Born Exponent = (log10(Repulsive Interaction Constant/Repulsive Interaction))/log10(Distance of Closest Approach)
n_born = (log10(B/E_R))/log10(r₀)
This formula uses 1 Functions, 4 Variables

Functions Used

log10 - The common logarithm, also known as the base-10 logarithm or the decimal logarithm, is a mathematical function that is the inverse of the exponential function., log10(Number)

Variables Used

Born Exponent - The Born Exponent is a number between 5 and 12, determined experimentally by measuring the compressibility of the solid, or derived theoretically.
Repulsive Interaction Constant - The Repulsive Interaction Constant is the constant scaling the strength of the repulsive interaction.
Repulsive Interaction - (Measured in Joule) - The Repulsive Interaction is between atoms acts over a very short range, but is very large when distances are short.
Distance of Closest Approach - (Measured in Meter) - Distance of Closest Approach is the distance to which an alpha particle comes closer to the nucleus.

STEP 1: Convert Input(s) to Base Unit

Repulsive Interaction Constant: 40000 --> No Conversion Required
Repulsive Interaction: 5800000000000 Joule --> 5800000000000 Joule No Conversion Required
Distance of Closest Approach: 60 Angstrom --> 6E-09 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

n_born = (log10(B/E_R))/log10(r₀) --> (log10(40000/5800000000000))/log10(6E-09)

Evaluating ... ...

n_born = 0.992643899295252

STEP 3: Convert Result to Output's Unit

0.992643899295252 --> No Conversion Required

FINAL ANSWER

0.992643899295252 ≈ 0.992644 <-- Born Exponent

(Calculation completed in 00.004 seconds)

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Created by Prerana Bakli

University of Hawaiʻi at Mānoa (UH Manoa), Hawaii, USA

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National Institute of Information Technology (NIIT), Neemrana

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< Lattice Energy Calculators

Lattice Energy using Born Lande Equation

Go Lattice Energy = -([Avaga-no]*Madelung Constant*Charge of Cation*Charge of Anion*([Charge-e]^2)*(1-(1/Born Exponent)))/(4*pi*[Permitivity-vacuum]*Distance of Closest Approach)

Born Exponent using Born Lande Equation

Go 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))

Electrostatic Potential Energy between pair of Ions

Go Electrostatic Potential Energy between Ion Pair = (-(Charge^2)*([Charge-e]^2))/(4*pi*[Permitivity-vacuum]*Distance of Closest Approach)

Repulsive Interaction

Go Repulsive Interaction = Repulsive Interaction Constant/(Distance of Closest Approach^Born Exponent)

Born Exponent using Repulsive Interaction Formula

Born Exponent = (log10(Repulsive Interaction Constant/Repulsive Interaction))/log10(Distance of Closest Approach)
n_born = (log10(B/E_R))/log10(r₀)

What is Born–Landé equation?

The Born–Landé equation is a means of calculating the lattice energy of a crystalline ionic compound. In 1918 Max Born and Alfred Landé proposed that the lattice energy could be derived from the electrostatic potential of the ionic lattice and a repulsive potential energy term. The ionic lattice is modeled as an assembly of hard elastic spheres which are compressed together by the mutual attraction of the electrostatic charges on the ions. They achieve the observed equilibrium distance apart due to a balancing short range repulsion.

How to Calculate Born Exponent using Repulsive Interaction?

Born Exponent using Repulsive Interaction calculator uses Born Exponent = (log10(Repulsive Interaction Constant/Repulsive Interaction))/log10(Distance of Closest Approach) to calculate the Born Exponent, The Born exponent using Repulsive Interaction 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 calculate Born Exponent using Repulsive Interaction using this online calculator? To use this online calculator for Born Exponent using Repulsive Interaction, enter Repulsive Interaction Constant (B), Repulsive Interaction (E_R) & Distance of Closest Approach (r₀) and hit the calculate button. Here is how the Born Exponent using Repulsive Interaction calculation can be explained with given input values -> 0.992644 = (log10(40000/5800000000000))/log10(6E-09).

FAQ

What is Born Exponent using Repulsive Interaction?

The Born exponent using Repulsive Interaction is typically a number between 5 and 12, determined experimentally by measuring the compressibility of the solid, or derived theoretically and is represented as n_born = (log10(B/E_R))/log10(r₀) or Born Exponent = (log10(Repulsive Interaction Constant/Repulsive Interaction))/log10(Distance of Closest Approach). The Repulsive Interaction Constant is the constant scaling the strength of the repulsive interaction, The Repulsive Interaction is between atoms acts over a very short range, but is very large when distances are short & Distance of Closest Approach is the distance to which an alpha particle comes closer to the nucleus.

How to calculate Born Exponent using Repulsive Interaction?

The Born exponent using Repulsive Interaction is typically a number between 5 and 12, determined experimentally by measuring the compressibility of the solid, or derived theoretically is calculated using Born Exponent = (log10(Repulsive Interaction Constant/Repulsive Interaction))/log10(Distance of Closest Approach). To calculate Born Exponent using Repulsive Interaction, you need Repulsive Interaction Constant (B), Repulsive Interaction (E_R) & Distance of Closest Approach (r₀). With our tool, you need to enter the respective value for Repulsive Interaction Constant, Repulsive Interaction & Distance of Closest Approach and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Born Exponent?

In this formula, Born Exponent uses Repulsive Interaction Constant, Repulsive Interaction & Distance of Closest Approach. We can use 2 other way(s) to calculate the same, which is/are as follows -

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))
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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