Electron Density using Average Electron Density and Spill-out Amplitude Calculator

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Optical Properties of Metallic Nanoparticles

Electronic Structure in Clusters and Nanoparticles

Mechanical and Nanomechanical Properties

Size Effects on Structure and Morphology of Free or Supported Nanoparticles

✖The Average Electron Density is the average of total density of electrons present in a bulk material.ⓘ Average Electron Density [n_e-avg]			+10% -10%
✖The Spill Out Amplitude is the measure of its change in a single period where the electron wave functions extend beyond the sphere defined by the crystal lattice.ⓘ Spill Out Amplitude [d_so]			+10% -10%
✖The Nanoparticle Diameter is any straight line segment that passes through the center of the nanoparticle and whose endpoints lie on the nanoparticle boundary.ⓘ Nanoparticle Diameter [D]			+10% -10%

✖The Electron Density is the measure of the probability of an electron being present at an infinitesimal element of space surrounding any given point.ⓘ Electron Density using Average Electron Density and Spill-out Amplitude [n_e]

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Formula

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Electron Density using Average Electron Density and Spill-out Amplitude

Formula

`"n"_{"e"} = "n"_{"e-avg"}/(1-(3*"d"_{"so"}/"D"))`

Example

`"62.5"="50"/(1-(3*"20nm"/"300nm"))`

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Electron Density using Average Electron Density and Spill-out Amplitude Solution

STEP 0: Pre-Calculation Summary

Formula Used

Electron Density = Average Electron Density/(1-(3*Spill Out Amplitude/Nanoparticle Diameter))
n_e = n_e-avg/(1-(3*d_so/D))
This formula uses 4 Variables

Variables Used

Electron Density - The Electron Density is the measure of the probability of an electron being present at an infinitesimal element of space surrounding any given point.
Average Electron Density - The Average Electron Density is the average of total density of electrons present in a bulk material.
Spill Out Amplitude - (Measured in Meter) - The Spill Out Amplitude is the measure of its change in a single period where the electron wave functions extend beyond the sphere defined by the crystal lattice.
Nanoparticle Diameter - (Measured in Meter) - The Nanoparticle Diameter is any straight line segment that passes through the center of the nanoparticle and whose endpoints lie on the nanoparticle boundary.

STEP 1: Convert Input(s) to Base Unit

Average Electron Density: 50 --> No Conversion Required
Spill Out Amplitude: 20 Nanometer --> 2E-08 Meter (Check conversion here)
Nanoparticle Diameter: 300 Nanometer --> 3E-07 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

n_e = n_e-avg/(1-(3*d_so/D)) --> 50/(1-(3*2E-08/3E-07))

Evaluating ... ...

n_e = 62.5

STEP 3: Convert Result to Output's Unit

62.5 --> No Conversion Required

FINAL ANSWER

62.5 <-- Electron Density

(Calculation completed in 00.004 seconds)

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national institute of technology meghalaya (NIT Meghalaya), Shillong

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< 23 Optical Properties of Metallic Nanoparticles Calculators

Total Polarization of Composite Material using Dielectric Constants and Incident Field

Go Total polarization of Composite Material = Vacuum Dielectric Constant*(Real Dielectric Constant-1)*Incident Field+((Volume Fraction*Dipole Moment of Sphere)/Volume of Nanoparticle)

Total Collision Rate using Intrinsic Electron Collision Frequency

Go Total Collision Rate = Intrinsic Electron Collision Rate+(Proportionality Factor*Fermi Speed of Electron)/Diameter of Spheres

Intrinsic Electron Collision Frequency using Total Collision Rate

Go Intrinsic Electron Collision Rate = Total Collision Rate-(Proportionality Factor*Fermi Speed of Electron)/Diameter of Spheres

Local field using Incident Field and Polarization

Go Local Field = Incident Field+(Polarization due to Sphere/(3*Real Dielectric Constant*Vacuum Dielectric Constant))

Incident Field using Local Field and Polarization

Go Incident Field = Local Field-(Polarization due to Sphere/(3*Real Dielectric Constant*Vacuum Dielectric Constant))

Polarization due to Sphere using Local field and Incident Field

Go Polarization due to Sphere = (Local Field-Incident Field)*3*Real Dielectric Constant*Vacuum Dielectric Constant

Polarization Due to Metallic Particle using Dielectric Constants and Incident Field

Go Polarization due to Metallic Particle = Vacuum Dielectric Constant*(Real Dielectric Constant-1)*Incident Field

Average Electron Density using Nanoparticle Density and Spill-out Amplitude

Go Average Electron Density = Electron Density*(1-(3*Spill Out Amplitude/Nanoparticle Diameter))

Electron Density using Average Electron Density and Spill-out Amplitude

Go Electron Density = Average Electron Density/(1-(3*Spill Out Amplitude/Nanoparticle Diameter))

Volume Fraction using Polarization and Dipole Moment of Sphere

Go Volume Fraction = Polarization due to Sphere*Volume of Nanoparticle/Dipole Moment of Sphere

Polarization due to Sphere using Dipole moment of Sphere

Go Polarization due to Sphere = Volume Fraction*Dipole Moment of Sphere/Volume of Nanoparticle

Dipole moment of Sphere using Polarization due to Sphere

Go Dipole Moment of Sphere = Polarization due to Sphere*Volume of Nanoparticle/Volume Fraction

Average Electron Density using Electron Density and Electron diameter

Go Average Electron Density = (Electron Density*Nanoparticle Diameter^3)/Electron Diameter^3

Electron Density using Average Electron Density and Electron diameter

Go Electron Density = Average Electron Density*Electron Diameter^3/Nanoparticle Diameter^3

Number of Nanoparticles using Volume Fraction and Volume of Nanoparticle

Go Number of Nanoparticles = (Volume Fraction*Volume of Material)/Volume of Nanoparticle

Volume Fraction using Volume of Nanoparticles

Go Volume Fraction = (Number of Nanoparticles*Volume of Nanoparticle)/Volume of Material

Volume of Nanoparticles using Volume Fraction

Go Volume of Nanoparticle = (Volume Fraction*Volume of Material)/Number of Nanoparticles

Total Polarization of Composite Material using Polarization due to Metallic Particle and Sphere

Go Total polarization of Composite Material = Polarization due to Metallic Particle+Polarization due to Sphere

Polarization Due to Metallic Particle using Total Polarization and Polarization Due to Sphere

Go Polarization due to Metallic Particle = Total polarization of Composite Material-Polarization due to Sphere

Polarization Due to Sphere using Polarization Due to Metallic Particle and Total Polarization

Go Polarization due to Sphere = Total polarization of Composite Material-Polarization due to Metallic Particle

Nanoparticle Diameter using Electron Diameter and Spill-out Amplitude

Go Nanoparticle Diameter = Electron Diameter-Spill Out Amplitude

Electron Diameter using Nanoparticle Diameter and Spill-out Amplitude

Go Electron Diameter = Nanoparticle Diameter+Spill Out Amplitude

Spill-out Amplitude using Nanoparticle Diameter and Electron Diameter

Go Spill Out Amplitude = Electron Diameter-Nanoparticle Diameter

Electron Density using Average Electron Density and Spill-out Amplitude Formula

Electron Density = Average Electron Density/(1-(3*Spill Out Amplitude/Nanoparticle Diameter))
n_e = n_e-avg/(1-(3*d_so/D))

What is surface plasmon resonance?

Surface Plasmon Resonance (SPR) is an optical phenomenon that occurs when polarized light hits a metal surface at the interface of media with different refractive indices.

How to Calculate Electron Density using Average Electron Density and Spill-out Amplitude?

Electron Density using Average Electron Density and Spill-out Amplitude calculator uses Electron Density = Average Electron Density/(1-(3*Spill Out Amplitude/Nanoparticle Diameter)) to calculate the Electron Density, The Electron Density using Average Electron Density and Spill-out Amplitude formula is defined as the product of average electron density and cube of electron diameter, divided by the cube of the nanoparticle diameter, which can also be calculated using spill-out amplitude and nanoparticle diameter. Electron Density is denoted by n_e symbol.

How to calculate Electron Density using Average Electron Density and Spill-out Amplitude using this online calculator? To use this online calculator for Electron Density using Average Electron Density and Spill-out Amplitude, enter Average Electron Density (n_e-avg), Spill Out Amplitude (d_so) & Nanoparticle Diameter (D) and hit the calculate button. Here is how the Electron Density using Average Electron Density and Spill-out Amplitude calculation can be explained with given input values -> -50 = 50/(1-(3*2E-08/3E-07)).

FAQ

What is Electron Density using Average Electron Density and Spill-out Amplitude?

The Electron Density using Average Electron Density and Spill-out Amplitude formula is defined as the product of average electron density and cube of electron diameter, divided by the cube of the nanoparticle diameter, which can also be calculated using spill-out amplitude and nanoparticle diameter and is represented as n_e = n_e-avg/(1-(3*d_so/D)) or Electron Density = Average Electron Density/(1-(3*Spill Out Amplitude/Nanoparticle Diameter)). The Average Electron Density is the average of total density of electrons present in a bulk material, The Spill Out Amplitude is the measure of its change in a single period where the electron wave functions extend beyond the sphere defined by the crystal lattice & The Nanoparticle Diameter is any straight line segment that passes through the center of the nanoparticle and whose endpoints lie on the nanoparticle boundary.

How to calculate Electron Density using Average Electron Density and Spill-out Amplitude?

The Electron Density using Average Electron Density and Spill-out Amplitude formula is defined as the product of average electron density and cube of electron diameter, divided by the cube of the nanoparticle diameter, which can also be calculated using spill-out amplitude and nanoparticle diameter is calculated using Electron Density = Average Electron Density/(1-(3*Spill Out Amplitude/Nanoparticle Diameter)). To calculate Electron Density using Average Electron Density and Spill-out Amplitude, you need Average Electron Density (n_e-avg), Spill Out Amplitude (d_so) & Nanoparticle Diameter (D). With our tool, you need to enter the respective value for Average Electron Density, Spill Out Amplitude & Nanoparticle Diameter and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Electron Density?

In this formula, Electron Density uses Average Electron Density, Spill Out Amplitude & Nanoparticle Diameter. We can use 1 other way(s) to calculate the same, which is/are as follows -

Electron Density = Average Electron Density*Electron Diameter^3/Nanoparticle Diameter^3

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