Exciton Bohr Radius Calculator

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✖Dielectric Constant of Bulk Material is the permittivity of Bulk Material expressed as a ratio with the electric permittivity of a vacuum.ⓘ Dielectric Constant of Bulk Material [ε_r]			+10% -10%
✖Effective Mass of Electron is usually stated as a factor multiplying the rest mass of an electron.ⓘ Effective Mass of Electron [m_e]			+10% -10%
✖Effective Mass of Hole is the mass that it seems to have when responding to forces.ⓘ Effective Mass of Hole [m_h]			+10% -10%

✖Exciton Bohr Radius can be defined as the separation distance between electron and hole.ⓘ Exciton Bohr Radius [a_B]

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Formula

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Exciton Bohr Radius

Formula

`"a"_{"B"} = "ε"_{"r"}*("m"_{"e"}/(("m"_{"e"}*"m"_{"h"})/("m"_{"e"}+"m"_{"h"})))*"[Bohr-r]"`

Example

`"0.373043nm"="5.6"*("0.21"/(("0.21"*"0.81")/("0.21"+"0.81")))*"[Bohr-r]"`

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Exciton Bohr Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

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]
a_B = ε_r*(m_e/((m_e*m_h)/(m_e+m_h)))*[Bohr-r]
This formula uses 1 Constants, 4 Variables

Constants Used

[Bohr-r] - Bohr radius Value Taken As 0.529E-10 Meter

Variables Used

Exciton Bohr Radius - (Measured in Meter) - Exciton Bohr Radius can be defined as the separation distance between electron and hole.
Dielectric Constant of Bulk Material - Dielectric Constant of Bulk Material is the permittivity of Bulk Material expressed as a ratio with the electric permittivity of a vacuum.
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

Dielectric Constant of Bulk Material: 5.6 --> No Conversion Required
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

a_B = ε_r*(m_e/((m_e*m_h)/(m_e+m_h)))*[Bohr-r] --> 5.6*(0.21/((0.21*0.81)/(0.21+0.81)))*[Bohr-r]

Evaluating ... ...

a_B = 3.73042962962963E-10

STEP 3: Convert Result to Output's Unit

3.73042962962963E-10 Meter -->0.373042962962963 Nanometer (Check conversion here)

FINAL ANSWER

0.373042962962963 ≈ 0.373043 Nanometer <-- Exciton Bohr Radius

(Calculation completed in 00.004 seconds)

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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)

Exciton Bohr Radius Formula

What is Bohr Radius?

The Bohr radius (a0) is a physical constant, approximately equal to the most probable distance between the nucleus and the electron in a hydrogen atom in its ground state.

How to Calculate Exciton Bohr Radius?

Exciton Bohr Radius calculator uses 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] to calculate the Exciton Bohr Radius, The Exciton Bohr Radius formula is defined as the separation distance between electron and hole in an exciton. The charge carriers can move freely in bulk semiconductor, thus the wavefunction looks much like a hydrogen atom. Exciton Bohr Radius is denoted by a_B symbol.

How to calculate Exciton Bohr Radius using this online calculator? To use this online calculator for Exciton Bohr Radius, enter Dielectric Constant of Bulk Material (ε_r), Effective Mass of Electron (m_e) & Effective Mass of Hole (m_h) and hit the calculate button. Here is how the Exciton Bohr Radius calculation can be explained with given input values -> 3.7E+8 = 5.6*(0.21/((0.21*0.81)/(0.21+0.81)))*[Bohr-r].

FAQ

What is Exciton Bohr Radius?

The Exciton Bohr Radius formula is defined as the separation distance between electron and hole in an exciton. The charge carriers can move freely in bulk semiconductor, thus the wavefunction looks much like a hydrogen atom and is represented as a_B = ε_r*(m_e/((m_e*m_h)/(m_e+m_h)))*[Bohr-r] or 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]. Dielectric Constant of Bulk Material is the permittivity of Bulk Material expressed as a ratio with the electric permittivity of a vacuum, 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 Exciton Bohr Radius?

The Exciton Bohr Radius formula is defined as the separation distance between electron and hole in an exciton. The charge carriers can move freely in bulk semiconductor, thus the wavefunction looks much like a hydrogen atom is calculated using 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]. To calculate Exciton Bohr Radius, you need Dielectric Constant of Bulk Material (ε_r), Effective Mass of Electron (m_e) & Effective Mass of Hole (m_h). With our tool, you need to enter the respective value for Dielectric Constant of Bulk Material, 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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