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Lattice Energy using Born-Lande equation using Kapustinskii approximation Solution

STEP 0: Pre-Calculation Summary
Formula Used
lattice_energy = -([Avaga-no]*Number of Ions*0.88 *Charge of Cation*Charge of Anion*([Charge-e]^2)*(1-(1/Born Exponent)))/(4*pi*[Permitivity-vacuum]*Distance of closest approach)
U = -([Avaga-no]*n*0.88 *z+*z-*([Charge-e]^2)*(1-(1/n)))/(4*pi*[Permitivity-vacuum]*r0)
This formula uses 5 Constants, 1 Functions, 5 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
e - Napier's constant Value Taken As 2.71828182845904523536028747135266249
[Avaga-no] - Avogadro’s number Value Taken As 6.02214076E23
[Charge-e] - Charge of electron Value Taken As 1.60217662E-19
[Permitivity-vacuum] - Permittivity of vacuum Value Taken As 8.85E-12
Functions Used
C - Binomial coefficient function, C(n,k)
Variables Used
Number of Ions- The Number of Ions is the number of ions formed from one formula unit of the substance.
Charge of Cation - The Charge of Cation is the positive charge over a cation with fewer electron than the respective atom. (Measured in Coulomb)
Charge of Anion - The Charge of Anion is the negative charge over an anion with more electron than the respective atom. (Measured in Coulomb)
Born Exponent- The Born Exponent is a number between 5 and 12, determined experimentally by measuring the compressibility of the solid, or derived theoretically.
Distance of closest approach - Distance of closest approach is the distance to which an alpha particle comes closer to the nucleus. (Measured in Meter)
STEP 1: Convert Input(s) to Base Unit
Number of Ions: 2 --> No Conversion Required
Charge of Cation: 1 Coulomb --> 1 Coulomb No Conversion Required
Charge of Anion: 1 Coulomb --> 1 Coulomb No Conversion Required
Born Exponent: 5 --> No Conversion Required
Distance of closest approach: 0.1 Meter --> 0.1 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
U = -([Avaga-no]*n*0.88 *z+*z-*([Charge-e]^2)*(1-(1/n)))/(4*pi*[Permitivity-vacuum]*r0) --> -([Avaga-no]*2*0.88 *1*1*([Charge-e]^2)*(1-(1/5)))/(4*pi*[Permitivity-vacuum]*0.1)
Evaluating ... ...
U = -0.00195713688699853
STEP 3: Convert Result to Output's Unit
-0.00195713688699853 Joule per Mole --> No Conversion Required
FINAL ANSWER
-0.00195713688699853 Joule per Mole <-- Lattice Energy
(Calculation completed in 00.000 seconds)

10+ Lattice Energy Calculators

Distance of closest approach using Born Lande equation
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) Go
Madelung constant using Born Landé equation
madelung_constant = (-Lattice Energy*4*pi*[Permitivity-vacuum]*Distance of closest approach)/((1-(1/Born Exponent))*([Charge-e]^2)*[Avaga-no]*Charge of Cation*Charge of Anion) Go
Lattice Energy using Born–Landé equation
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) Go
Born exponent using Born Landé equation
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)) Go
Distance of closest approach using Madelung Energy
distance_of_closest_approach = -(Madelung constant*(Charge^2)*([Charge-e]^2))/(4*pi*[Permitivity-vacuum]*Madelung Energy) Go
Madelung constant using Madelung Energy
madelung_constant = (-Madelung Energy*4*pi*[Permitivity-vacuum]*Distance of closest approach)/((Charge^2)*([Charge-e]^2)) Go
Madelung Energy
madelung_energy = -(Madelung constant*(Charge^2)*([Charge-e]^2))/(4*pi*[Permitivity-vacuum]*Distance of closest approach) Go
Distance of closest approach using Electrostatic potential
distance_of_closest_approach = (-(Charge^2)*([Charge-e]^2))/(4*pi*[Permitivity-vacuum]*Electrostatic Potential Energy between ion pair) Go
Electrostatic potential energy between a pair of ions
electrostatic_potential_energy_between_ion_pair = (-(Charge^2)*([Charge-e]^2))/(4*pi*[Permitivity-vacuum]*Distance of closest approach) Go
Repulsive Interaction
repulsive_interaction = Repulsive Interaction Constant/(Distance of closest approach^Born Exponent) Go

Lattice Energy using Born-Lande equation using Kapustinskii approximation Formula

lattice_energy = -([Avaga-no]*Number of Ions*0.88 *Charge of Cation*Charge of Anion*([Charge-e]^2)*(1-(1/Born Exponent)))/(4*pi*[Permitivity-vacuum]*Distance of closest approach)
U = -([Avaga-no]*n*0.88 *z+*z-*([Charge-e]^2)*(1-(1/n)))/(4*pi*[Permitivity-vacuum]*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 Lattice Energy using Born-Lande equation using Kapustinskii approximation?

Lattice Energy using Born-Lande equation using Kapustinskii approximation calculator uses lattice_energy = -([Avaga-no]*Number of Ions*0.88 *Charge of Cation*Charge of Anion*([Charge-e]^2)*(1-(1/Born Exponent)))/(4*pi*[Permitivity-vacuum]*Distance of closest approach) to calculate the Lattice Energy, The lattice energy using Born-Lande equation using Kapustinskii approximation of a crystalline solid is a measure of the energy released when ions are combined to make a compound. Lattice Energy is denoted by U symbol.

How to calculate Lattice Energy using Born-Lande equation using Kapustinskii approximation using this online calculator? To use this online calculator for Lattice Energy using Born-Lande equation using Kapustinskii approximation, enter Number of Ions (n), Charge of Cation (z+), Charge of Anion (z-), Born Exponent (n) & Distance of closest approach (r0) and hit the calculate button. Here is how the Lattice Energy using Born-Lande equation using Kapustinskii approximation calculation can be explained with given input values -> -0.001957 = -([Avaga-no]*2*0.88 *1*1*([Charge-e]^2)*(1-(1/5)))/(4*pi*[Permitivity-vacuum]*0.1).

FAQ

What is Lattice Energy using Born-Lande equation using Kapustinskii approximation?
The lattice energy using Born-Lande equation using Kapustinskii approximation of a crystalline solid is a measure of the energy released when ions are combined to make a compound and is represented as U = -([Avaga-no]*n*0.88 *z+*z-*([Charge-e]^2)*(1-(1/n)))/(4*pi*[Permitivity-vacuum]*r0) or lattice_energy = -([Avaga-no]*Number of Ions*0.88 *Charge of Cation*Charge of Anion*([Charge-e]^2)*(1-(1/Born Exponent)))/(4*pi*[Permitivity-vacuum]*Distance of closest approach). The Number of Ions is the number of ions formed from one formula unit of the substance, The Charge of Cation is the positive charge over a cation with fewer electron than the respective atom, The Charge of Anion is the negative charge over an anion with more electron than the respective atom, The Born Exponent is a number between 5 and 12, determined experimentally by measuring the compressibility of the solid, or derived theoretically & Distance of closest approach is the distance to which an alpha particle comes closer to the nucleus.
How to calculate Lattice Energy using Born-Lande equation using Kapustinskii approximation?
The lattice energy using Born-Lande equation using Kapustinskii approximation of a crystalline solid is a measure of the energy released when ions are combined to make a compound is calculated using lattice_energy = -([Avaga-no]*Number of Ions*0.88 *Charge of Cation*Charge of Anion*([Charge-e]^2)*(1-(1/Born Exponent)))/(4*pi*[Permitivity-vacuum]*Distance of closest approach). To calculate Lattice Energy using Born-Lande equation using Kapustinskii approximation, you need Number of Ions (n), Charge of Cation (z+), Charge of Anion (z-), Born Exponent (n) & Distance of closest approach (r0). With our tool, you need to enter the respective value for Number of Ions, Charge of Cation, Charge of Anion, Born Exponent & 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 Lattice Energy?
In this formula, Lattice Energy uses Number of Ions, Charge of Cation, Charge of Anion, Born Exponent & Distance of closest approach. We can use 10 other way(s) to calculate the same, which is/are as follows -
  • 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)
  • madelung_constant = (-Lattice Energy*4*pi*[Permitivity-vacuum]*Distance of closest approach)/((1-(1/Born Exponent))*([Charge-e]^2)*[Avaga-no]*Charge of Cation*Charge of Anion)
  • 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))
  • 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)
  • electrostatic_potential_energy_between_ion_pair = (-(Charge^2)*([Charge-e]^2))/(4*pi*[Permitivity-vacuum]*Distance of closest approach)
  • distance_of_closest_approach = (-(Charge^2)*([Charge-e]^2))/(4*pi*[Permitivity-vacuum]*Electrostatic Potential Energy between ion pair)
  • madelung_energy = -(Madelung constant*(Charge^2)*([Charge-e]^2))/(4*pi*[Permitivity-vacuum]*Distance of closest approach)
  • madelung_constant = (-Madelung Energy*4*pi*[Permitivity-vacuum]*Distance of closest approach)/((Charge^2)*([Charge-e]^2))
  • distance_of_closest_approach = -(Madelung constant*(Charge^2)*([Charge-e]^2))/(4*pi*[Permitivity-vacuum]*Madelung Energy)
  • repulsive_interaction = Repulsive Interaction Constant/(Distance of closest approach^Born Exponent)
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