Brus Equation Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)))
Eemission = Egap+(([hP]^2)/(8*(a^2)))*((1/([Mass-e]*me))+(1/([Mass-e]*mh)))
This formula uses 2 Constants, 5 Variables
Constants Used
[Mass-e] - Mass of electron Value Taken As 9.10938356E-31 Kilogram
[hP] - Planck constant Value Taken As 6.626070040E-34 Kilogram Meter² / Second
Variables Used
Emission Energy of Quantum Dot - (Measured in Joule) - Emission Energy of Quantum Dot refers to the production and discharge of energy or gas from Quantum Dot.
Band Gap Energy - (Measured in Joule) - The Band Gap Energy is the minimum amount of energy required for an exciton to break free of its bound state.
Radius of Quantum Dot - (Measured in Meter) - Radius of Quantum Dot is the distance from the center to any point on the boundary of Quantum dots.
Effective Mass of Electron - Effective Mass of Electron is usually stated as a factor multiplying the rest mass of an electron.
Effective Mass of Hole - Effective Mass of Hole is the mass that it seems to have when responding to forces.
STEP 1: Convert Input(s) to Base Unit
Band Gap Energy: 1.74 Electron-Volt --> 2.78778855420001E-19 Joule (Check conversion here)
Radius of Quantum Dot: 3 Nanometer --> 3E-09 Meter (Check conversion here)
Effective Mass of Electron: 0.21 --> No Conversion Required
Effective Mass of Hole: 0.81 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Eemission = Egap+(([hP]^2)/(8*(a^2)))*((1/([Mass-e]*me))+(1/([Mass-e]*mh))) --> 2.78778855420001E-19+(([hP]^2)/(8*(3E-09^2)))*((1/([Mass-e]*0.21))+(1/([Mass-e]*0.81)))
Evaluating ... ...
Eemission = 3.18919691801901E-19
STEP 3: Convert Result to Output's Unit
3.18919691801901E-19 Joule -->1.99053928569754 Electron-Volt (Check conversion here)
FINAL ANSWER
1.99053928569754 1.990539 Electron-Volt <-- Emission Energy of Quantum Dot
(Calculation completed in 00.004 seconds)
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Credits

Created by Sangita Kalita
National Institute of Technology, Manipur (NIT Manipur), Imphal, Manipur
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7 Quantum Dots Calculators

Exciton Bohr Radius
Go Exciton Bohr Radius = Dielectric Constant of Bulk Material*(Effective Mass of Electron/((Effective Mass of Electron*Effective Mass of Hole)/(Effective Mass of Electron+Effective Mass of Hole)))*[Bohr-r]
Brus Equation
Go 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)))
Reduced Mass of Exciton
Go Reduced Mass of Exciton = ([Mass-e]*(Effective Mass of Electron*Effective Mass of Hole))/(Effective Mass of Electron+Effective Mass of Hole)
Coulombic Attraction Energy
Go Coulombic Attraction Energy = -(1.8*([Charge-e]^2))/(2*pi*[Permeability-vacuum]*Dielectric Constant of Bulk Material*Radius of Quantum Dot)
Total Energy of Particle in Quantum Dot
Go Total Energy of a Particle in Quantum Dot = Band Gap Energy+Confinement Energy+(Coulombic Attraction Energy)
Quantum Capacitance of Quantum Dot
Go Quantum Capacitance of Quantum Dot = ([Charge-e]^2)/(Ionization Potential of N Particle-Electron Affinity of N Particle System)
Confinement Energy
Go Confinement Energy = (([hP]^2)*(pi^2))/(2*(Radius of Quantum Dot^2)*Reduced Mass of Exciton)

Brus Equation 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)))
Eemission = Egap+(([hP]^2)/(8*(a^2)))*((1/([Mass-e]*me))+(1/([Mass-e]*mh)))

Who identified Brus Equation?

It was first identified by Alexey Ekimov and Alexander Efros while studying quantum dots for the first time in the 1980s. The equation was named after Louis E. Brus who independently discovered it a few years later.

How to Calculate Brus Equation?

Brus Equation calculator 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 calculate 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 Eemission symbol.

How to calculate Brus Equation using this online calculator? To use this online calculator for Brus Equation, enter Band Gap Energy (Egap), Radius of Quantum Dot (a), Effective Mass of Electron (me) & Effective Mass of Hole (mh) and hit the calculate button. Here is how the Brus Equation calculation can be explained with given input values -> 1.2E+19 = 2.78778855420001E-19+(([hP]^2)/(8*(3E-09^2)))*((1/([Mass-e]*0.21))+(1/([Mass-e]*0.81))).

FAQ

What is Brus Equation?
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 and is represented as Eemission = Egap+(([hP]^2)/(8*(a^2)))*((1/([Mass-e]*me))+(1/([Mass-e]*mh))) or 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))). The Band Gap Energy is the minimum amount of energy required for an exciton to break free of its bound state, Radius of Quantum Dot is the distance from the center to any point on the boundary of Quantum dots, Effective Mass of Electron is usually stated as a factor multiplying the rest mass of an electron & Effective Mass of Hole is the mass that it seems to have when responding to forces.
How to calculate Brus Equation?
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 is calculated using 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 calculate Brus Equation, you need Band Gap Energy (Egap), Radius of Quantum Dot (a), Effective Mass of Electron (me) & Effective Mass of Hole (mh). With our tool, you need to enter the respective value for Band Gap Energy, Radius of Quantum Dot, Effective Mass of Electron & Effective Mass of Hole and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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