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Confinement Energy Formula

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Confinement Energy in the particle in a box model is also used in modeling the exciton. Variance of particle size allows for control of the confinement energy. Check FAQs

E confinement = \frac{({[hP]}^{2}) \cdot (π^{2})}{2 \cdot (a^{2}) \cdot μ ex}

E_confinement - Confinement Energy?a - Radius of Quantum Dot?μ_ex - Reduced Mass of Exciton?[hP] - Planck constant?π - Archimedes' constant?

Confinement Energy Example

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Here is how the Confinement Energy equation looks like with Values.

Here is how the Confinement Energy equation looks like with Units.

Here is how the Confinement Energy equation looks like.

9.7027 = \frac{({6.6E-34}^{2}) \cdot ({3.1416}^{2})}{2 \cdot (3^{2}) \cdot 0.17}

9.7027eV = \frac{({6.6E-34}^{2}) \cdot ({3.1416}^{2})}{2 \cdot ({3nm}^{2}) \cdot 0.17me}

9.7027 = \frac{({6.6E-34}^{2}) \cdot ({3.1416}^{2})}{2 \cdot (3^{2}) \cdot 0.17}

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Confinement Energy Solution

Follow our step by step solution on how to calculate Confinement Energy?

FIRST Step Consider the formula

E confinement = \frac{({[hP]}^{2}) \cdot (π^{2})}{2 \cdot (a^{2}) \cdot μ ex}

Next Step Substitute values of Variables

∴

E confinement = \frac{({[hP]}^{2}) \cdot (π^{2})}{2 \cdot ({3nm}^{2}) \cdot 0.17me}

Next Step Substitute values of Constants

∴

E confinement = \frac{({6.6E-34}^{2}) \cdot ({3.1416}^{2})}{2 \cdot ({3nm}^{2}) \cdot 0.17me}

Next Step Convert Units

∴

E confinement = \frac{({6.6E-34}^{2}) \cdot ({3.1416}^{2})}{2 \cdot ({3E-9m}^{2}) \cdot 1.5E-31kg}

Next Step Prepare to Evaluate

∴

E confinement = \frac{({6.6E-34}^{2}) \cdot ({3.1416}^{2})}{2 \cdot ({3E-9}^{2}) \cdot 1.5E-31}

Next Step Evaluate

∴

E confinement = 1.55453706487244E-18J

Next Step Convert to Output's Unit

∴

E confinement = 9.70265298206678eV

LAST Step Rounding Answer

∴

E confinement = 9.7027eV

Confinement Energy Formula Elements

Variables

Constants

Confinement Energy

Confinement Energy in the particle in a box model is also used in modeling the exciton. Variance of particle size allows for control of the confinement energy.

Symbol: E_confinement

Measurement: EnergyUnit: eV

Note: Value can be positive or negative.

Formulas to find Confinement Energy

Radius of Quantum Dot

Radius of Quantum Dot is the distance from the center to any point on the boundary of Quantum dots.

Symbol: a

Measurement: LengthUnit: nm

Note: Value can be positive or negative.

Formulas to find Radius of Quantum Dot

Reduced Mass of Exciton

Reduced Mass of Exciton is the reduced mass of an electron and a hole that are attracted to each other by the Coulomb force which can form a bound state called exciton.

Symbol: μ_ex

Measurement: WeightUnit: me

Note: Value can be positive or negative.

Formulas to find Reduced Mass of Exciton

Planck constant

Planck constant is a fundamental universal constant that defines the quantum nature of energy and relates the energy of a photon to its frequency.

Symbol: [hP]

Value: 6.626070040E-34

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 Quantum Dots category

Go Quantum Capacitance of Quantum Dot

C N = \frac{{[Charge-e]}^{2}}{IP N - EA N}

Go Coulombic Attraction Energy

E coulombic = - \frac{1.8 \cdot ({[Charge-e]}^{2})}{2 \cdot π \cdot [Permeability-vacuum] \cdot ε r \cdot a}

Go Reduced Mass of Exciton

μ ex = \frac{[Mass-e] \cdot (m e \cdot m h)}{m e + m h}

Go Brus Equation

E emission = E gap + (\frac{{[hP]}^{2}}{8 \cdot (a^{2})}) \cdot ((\frac{1}{[Mass-e] \cdot m e}) + (\frac{1}{[Mass-e] \cdot m h}))

How to Evaluate Confinement Energy?

Confinement Energy evaluator uses Confinement Energy = (([hP]^2)*(pi^2))/(2*(Radius of Quantum Dot^2)*Reduced Mass of Exciton) to evaluate the Confinement Energy, The Confinement Energy formula in as particle in a box model is also used in modelling the exciton. Confinement energy is a term used to explain the confinement effect inside the nanospace. Variance of particle size allows for control of the confinement energy. Confinement Energy is denoted by E_confinement symbol.

How to evaluate Confinement Energy using this online evaluator? To use this online evaluator for Confinement Energy, enter Radius of Quantum Dot (a) & Reduced Mass of Exciton (μ_ex) and hit the calculate button.

FAQs on Confinement Energy

What is the formula to find Confinement Energy?

The formula of Confinement Energy is expressed as Confinement Energy = (([hP]^2)*(pi^2))/(2*(Radius of Quantum Dot^2)*Reduced Mass of Exciton). Here is an example- 6.1E+19 = (([hP]^2)*(pi^2))/(2*(3E-09^2)*1.54859625024252E-31).

How to calculate Confinement Energy?

With Radius of Quantum Dot (a) & Reduced Mass of Exciton (μ_ex) we can find Confinement Energy using the formula - Confinement Energy = (([hP]^2)*(pi^2))/(2*(Radius of Quantum Dot^2)*Reduced Mass of Exciton). This formula also uses Planck constant, Archimedes' constant .

Can the Confinement Energy be negative?

Yes, the Confinement Energy, measured in Energy can be negative.

Which unit is used to measure Confinement Energy?

Confinement Energy is usually measured using the Electron-Volt[eV] for Energy. Joule[eV], Kilojoule[eV], Gigajoule[eV] are the few other units in which Confinement Energy can be measured.

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Confinement Energy Formula

Confinement Energy Example

Confinement Energy Solution

Confinement Energy Formula Elements

Other formulas in Quantum Dots category

How to Evaluate Confinement Energy?

FAQs on Confinement Energy

Variable Name