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Brus Equation Formula

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Emission Energy of Quantum Dot refers to the production and discharge of energy or gas from Quantum Dot. Check FAQs

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}))

E_emission - Emission Energy of Quantum Dot?E_gap - Band Gap Energy?a - Radius of Quantum Dot?m_e - Effective Mass of Electron?m_h - Effective Mass of Hole?[hP] - Planck constant?[Mass-e] - Mass of electron?[Mass-e] - Mass of electron?

Brus Equation Example

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With units

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Here is how the Brus Equation equation looks like with Values.

Here is how the Brus Equation equation looks like with Units.

Here is how the Brus Equation equation looks like.

1.9905 = 1.74 + (\frac{{6.6E-34}^{2}}{8 \cdot (3^{2})}) \cdot ((\frac{1}{9.1E-31 \cdot 0.21}) + (\frac{1}{9.1E-31 \cdot 0.81}))

1.9905eV = 1.74eV + (\frac{{6.6E-34}^{2}}{8 \cdot ({3nm}^{2})}) \cdot ((\frac{1}{9.1E-31kg \cdot 0.21}) + (\frac{1}{9.1E-31kg \cdot 0.81}))

1.9905 = 1.74 + (\frac{{6.6E-34}^{2}}{8 \cdot (3^{2})}) \cdot ((\frac{1}{9.1E-31 \cdot 0.21}) + (\frac{1}{9.1E-31 \cdot 0.81}))

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Brus Equation Solution

Follow our step by step solution on how to calculate Brus Equation?

FIRST Step Consider the formula

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}))

Next Step Substitute values of Variables

∴

E emission = 1.74eV + (\frac{{[hP]}^{2}}{8 \cdot ({3nm}^{2})}) \cdot ((\frac{1}{[Mass-e] \cdot 0.21}) + (\frac{1}{[Mass-e] \cdot 0.81}))

Next Step Substitute values of Constants

∴

E emission = 1.74eV + (\frac{{6.6E-34}^{2}}{8 \cdot ({3nm}^{2})}) \cdot ((\frac{1}{9.1E-31kg \cdot 0.21}) + (\frac{1}{9.1E-31kg \cdot 0.81}))

Next Step Convert Units

∴

E emission = 2.8E-19J + (\frac{{6.6E-34}^{2}}{8 \cdot ({3E-9m}^{2})}) \cdot ((\frac{1}{9.1E-31kg \cdot 0.21}) + (\frac{1}{9.1E-31kg \cdot 0.81}))

Next Step Prepare to Evaluate

∴

E emission = 2.8E-19 + (\frac{{6.6E-34}^{2}}{8 \cdot ({3E-9}^{2})}) \cdot ((\frac{1}{9.1E-31 \cdot 0.21}) + (\frac{1}{9.1E-31 \cdot 0.81}))

Next Step Evaluate

∴

E emission = 3.18919691801901E-19J

Next Step Convert to Output's Unit

∴

E emission = 1.99053928569754eV

LAST Step Rounding Answer

∴

E emission = 1.9905eV

Brus Equation Formula Elements

Variables

Constants

Emission Energy of Quantum Dot

Emission Energy of Quantum Dot refers to the production and discharge of energy or gas from Quantum Dot.

Symbol: E_emission

Measurement: EnergyUnit: eV

Note: Value can be positive or negative.

Formulas to find Emission Energy of Quantum Dot

Band Gap Energy

The Band Gap Energy is the minimum amount of energy required for an exciton to break free of its bound state.

Symbol: E_gap

Measurement: EnergyUnit: eV

Note: Value can be positive or negative.

Formulas to find Band Gap 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

Effective Mass of Electron

Effective Mass of Electron is usually stated as a factor multiplying the rest mass of an electron.

Symbol: m_e

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Effective Mass of Electron

Effective Mass of Hole

Effective Mass of Hole is the mass that it seems to have when responding to forces.

Symbol: m_h

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Effective Mass of Hole

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

Mass of electron

Mass of electron is a fundamental physical constant, representing the amount of matter contained within an electron, an elementary particle with a negative electric charge.

Symbol: [Mass-e]

Value: 9.10938356E-31 kg

Mass of electron

Mass of electron is a fundamental physical constant, representing the amount of matter contained within an electron, an elementary particle with a negative electric charge.

Symbol: [Mass-e]

Value: 9.10938356E-31 kg

Other formulas in Quantum Dots category

Go Quantum Capacitance of Quantum Dot

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

Go Confinement Energy

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

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}

How to Evaluate Brus Equation?

Brus Equation evaluator uses Emission Energy of Quantum Dot = Band Gap Energy+(([hP]^2)/(8*(Radius of Quantum Dot^2)))*((1/([Mass-e]*Effective Mass of Electron))+(1/([Mass-e]*Effective Mass of Hole))) to evaluate the Emission Energy of Quantum Dot, The Brus Equation formula is defined as the emission energy of quantum dot semiconductor nanocrystals (such as CdSe nanocrystals). This is useful for calculating the radius of a quantum dot from experimentally determined parameters. Emission Energy of Quantum Dot is denoted by E_emission symbol.

How to evaluate Brus Equation using this online evaluator? To use this online evaluator for Brus Equation, enter Band Gap Energy (E_gap), Radius of Quantum Dot (a), Effective Mass of Electron (m_e) & Effective Mass of Hole (m_h) and hit the calculate button.

FAQs on Brus Equation

What is the formula to find Brus Equation?

The formula of Brus Equation is expressed as Emission Energy of Quantum Dot = Band Gap Energy+(([hP]^2)/(8*(Radius of Quantum Dot^2)))*((1/([Mass-e]*Effective Mass of Electron))+(1/([Mass-e]*Effective Mass of Hole))). Here is an example- 1.2E+19 = 2.78778855420001E-19+(([hP]^2)/(8*(3E-09^2)))*((1/([Mass-e]*0.21))+(1/([Mass-e]*0.81))).

How to calculate Brus Equation?

With Band Gap Energy (E_gap), Radius of Quantum Dot (a), Effective Mass of Electron (m_e) & Effective Mass of Hole (m_h) we can find Brus Equation using the formula - Emission Energy of Quantum Dot = Band Gap Energy+(([hP]^2)/(8*(Radius of Quantum Dot^2)))*((1/([Mass-e]*Effective Mass of Electron))+(1/([Mass-e]*Effective Mass of Hole))). This formula also uses Planck constant, Mass of electron, Mass of electron constant(s).

Can the Brus Equation be negative?

Yes, the Brus Equation, measured in Energy can be negative.

Which unit is used to measure Brus Equation?

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

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Brus Equation Formula

Brus Equation Example

Brus Equation Solution

Brus Equation Formula Elements

Other formulas in Quantum Dots category

How to Evaluate Brus Equation?

FAQs on Brus Equation

Variable Name