Radius of Cluster using Wigner Seitz Radius Calculator

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Electronic Structure in Clusters and Nanoparticles

Mechanical and Nanomechanical Properties

Optical Properties of Metallic Nanoparticles

Size Effects on Structure and Morphology of Free or Supported Nanoparticles

✖The Wigner Seitz radius is the radius of a sphere whose volume is equal to the mean volume per atom in a solid.ⓘ Wigner Seitz radius [r₀]			+10% -10%
✖Number of Atoms is the amount of total atoms present in a macroscopic boy.ⓘ Number of Atom [n]			+10% -10%

✖The Radius of Cluster is the square root of the average distance from any point of the cluster to its centroid.ⓘ Radius of Cluster using Wigner Seitz Radius [R₀]

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Formula

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Radius of Cluster using Wigner Seitz Radius

Formula

`"R"_{"0"} = "r"_{"0"}*("n"^(1/3))`

Example

`"54.28835nm"="20nm"*(("20")^(1/3))`

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Radius of Cluster using Wigner Seitz Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radius of Cluster = Wigner Seitz radius*(Number of Atom^(1/3))
R₀ = r₀*(n^(1/3))
This formula uses 3 Variables

Variables Used

Radius of Cluster - (Measured in Meter) - The Radius of Cluster is the square root of the average distance from any point of the cluster to its centroid.
Wigner Seitz radius - (Measured in Meter) - The Wigner Seitz radius is the radius of a sphere whose volume is equal to the mean volume per atom in a solid.
Number of Atom - Number of Atoms is the amount of total atoms present in a macroscopic boy.

STEP 1: Convert Input(s) to Base Unit

Wigner Seitz radius: 20 Nanometer --> 2E-08 Meter (Check conversion here)
Number of Atom: 20 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R₀ = r₀*(n^(1/3)) --> 2E-08*(20^(1/3))

Evaluating ... ...

R₀ = 5.42883523318981E-08

STEP 3: Convert Result to Output's Unit

5.42883523318981E-08 Meter -->54.2883523318981 Nanometer (Check conversion here)

FINAL ANSWER

54.2883523318981 ≈ 54.28835 Nanometer <-- Radius of Cluster

(Calculation completed in 00.004 seconds)

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Home » Chemistry » Nanomaterials and Nanochemistry » Electronic Structure in Clusters and Nanoparticles » Radius of Cluster using Wigner Seitz Radius

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national institute of technology meghalaya (NIT Meghalaya), Shillong

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< 8 Electronic Structure in Clusters and Nanoparticles Calculators

Energy of Liquid Drop in Neutral System

Go Energy of Liquid Drop = Energy per Atom*Number of Atom+Binding Energy Deficiency of Surface Atom*(Number of Atom^(2/3))+Curvature Coefficient*(Number of Atom^(1/3))

Energy Deficiency of Plane Surface using Surface Tension

Go Energy Deficiency of Surface = Surface Tension*4*pi*(Wigner Seitz radius^2)*(Number of Atom^(2/3))

Coulomb Energy of Charged Particle using Wigner Seitz radius

Go Coulomb Energy of Charged Sphere = (Surface Electrons^2)*(Number of Atom^(1/3))/(2*Wigner Seitz radius)

Energy Deficiency of Plane Surface using Binding Energy Deficiency

Go Energy Deficiency of Surface = Binding Energy Deficiency of Surface Atom*(Number of Atom^(2/3))

Coulomb Energy of Charged Particle using Radius of Cluster

Go Coulomb Energy of Charged Sphere = (Surface Electrons^2)/(2*Radius of Cluster)

Energy Deficiency of Curvature containing Cluster Surface

Go Energy Deficiency of Curvature = Curvature Coefficient*(Number of Atom^(1/3))

Radius of Cluster using Wigner Seitz Radius

Go Radius of Cluster = Wigner Seitz radius*(Number of Atom^(1/3))

Energy per Unit Volume of Cluster

Go Energy per Unit Volume = Energy per Atom*Number of Atom

Radius of Cluster using Wigner Seitz Radius Formula

Radius of Cluster = Wigner Seitz radius*(Number of Atom^(1/3))
R₀ = r₀*(n^(1/3))

What is Wigner–Seitz radius?

The Wigner-Seitz radius is a measure of the radius of a sphere with a volume equal to the actual crystal volume per formula unit.

How to Calculate Radius of Cluster using Wigner Seitz Radius?

Radius of Cluster using Wigner Seitz Radius calculator uses Radius of Cluster = Wigner Seitz radius*(Number of Atom^(1/3)) to calculate the Radius of Cluster, The Radius of Cluster using Wigner Seitz Radius formula is defined as the square root of the average distance from any point of the cluster to its centroid. This can be calculated as the multiplication of Wigner–Seitz radius and cube root of the number of particles present in the cluster. Radius of Cluster is denoted by R₀ symbol.

How to calculate Radius of Cluster using Wigner Seitz Radius using this online calculator? To use this online calculator for Radius of Cluster using Wigner Seitz Radius, enter Wigner Seitz radius (r₀) & Number of Atom (n) and hit the calculate button. Here is how the Radius of Cluster using Wigner Seitz Radius calculation can be explained with given input values -> 5.4E+10 = 2E-08*(20^(1/3)).

FAQ

What is Radius of Cluster using Wigner Seitz Radius?

The Radius of Cluster using Wigner Seitz Radius formula is defined as the square root of the average distance from any point of the cluster to its centroid. This can be calculated as the multiplication of Wigner–Seitz radius and cube root of the number of particles present in the cluster and is represented as R₀ = r₀*(n^(1/3)) or Radius of Cluster = Wigner Seitz radius*(Number of Atom^(1/3)). The Wigner Seitz radius is the radius of a sphere whose volume is equal to the mean volume per atom in a solid & Number of Atoms is the amount of total atoms present in a macroscopic boy.

How to calculate Radius of Cluster using Wigner Seitz Radius?

The Radius of Cluster using Wigner Seitz Radius formula is defined as the square root of the average distance from any point of the cluster to its centroid. This can be calculated as the multiplication of Wigner–Seitz radius and cube root of the number of particles present in the cluster is calculated using Radius of Cluster = Wigner Seitz radius*(Number of Atom^(1/3)). To calculate Radius of Cluster using Wigner Seitz Radius, you need Wigner Seitz radius (r₀) & Number of Atom (n). With our tool, you need to enter the respective value for Wigner Seitz radius & Number of Atom 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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