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Total Energy of Ion given Charges and Distances Formula

GoTotal Energy of Ion in Lattice Formula

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

E total = (\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_total - Total 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?

Total Energy of Ion given Charges and Distances Example

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Here is how the Total Energy of Ion given Charges and Distances equation looks like with Values.

Here is how the Total Energy of Ion given Charges and Distances equation looks like with Units.

Here is how the Total Energy of Ion given Charges and Distances 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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Total Energy of Ion given Charges and Distances Solution

Follow our step by step solution on how to calculate Total Energy of Ion given Charges and Distances?

FIRST Step Consider the formula

E total = (\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 total = (\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 total = (\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 total = (\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 total = (\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 total = 5795181739688.58J

LAST Step Rounding Answer

∴

E total = 5.8E+12J

Total Energy of Ion given Charges and Distances Formula Elements

Variables

Constants

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

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 to find Total Energy of Ion

Go Total Energy of Ion in Lattice

E total = E M + E R

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 Total Energy of Ion given Charges and Distances?

Total Energy of Ion given Charges and Distances evaluator uses Total 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 Total Energy of Ion, The Total Energy of ion given charges and distances in the lattice is the sum of Madelung Energy and Repulsive potential energy. Total Energy of Ion is denoted by E_total symbol.

How to evaluate Total Energy of Ion given Charges and Distances using this online evaluator? To use this online evaluator for Total Energy of Ion given Charges and Distances, 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 Total Energy of Ion given Charges and Distances

What is the formula to find Total Energy of Ion given Charges and Distances?

The formula of Total Energy of Ion given Charges and Distances is expressed as Total 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 Total Energy of Ion given Charges and Distances?

With Charge (q), Madelung Constant (M), Distance of Closest Approach (r₀), Repulsive Interaction Constant (B) & Born Exponent (n_born) we can find Total Energy of Ion given Charges and Distances using the formula - Total 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 .

What are the other ways to Calculate Total Energy of Ion?

Here are the different ways to Calculate Total Energy of Ion-

Total Energy of Ion=Madelung Energy+Repulsive Interaction

Can the Total Energy of Ion given Charges and Distances be negative?

Yes, the Total Energy of Ion given Charges and Distances, measured in Energy can be negative.

Which unit is used to measure Total Energy of Ion given Charges and Distances?

Total Energy of Ion given Charges and Distances is usually measured using the Joule[J] for Energy. Kilojoule[J], Gigajoule[J], Megajoule[J] are the few other units in which Total Energy of Ion given Charges and Distances can be measured.

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Total Energy of Ion given Charges and Distances Formula

​GoTotal Energy of Ion in Lattice Formula

Total Energy of Ion given Charges and Distances Example

Total Energy of Ion given Charges and Distances Solution

Total Energy of Ion given Charges and Distances Formula Elements

Other Formulas to find Total Energy of Ion

Other formulas in Lattice Energy category

How to Evaluate Total Energy of Ion given Charges and Distances?

FAQs on Total Energy of Ion given Charges and Distances

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GoTotal Energy of Ion in Lattice Formula