STEP 0: Pre-Calculation Summary
Formula Used
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)
54.2883523318981 54.28835 Nanometer <-- Radius of Cluster
(Calculation completed in 00.004 seconds)
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## Credits

Created by Abhijit gharphalia
national institute of technology meghalaya (NIT Meghalaya), Shillong
Abhijit gharphalia has created this Calculator and 50+ more calculators!
Verified by Soupayan banerjee
National University of Judicial Science (NUJS), Kolkata
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## < 8 Electronic Structure in Clusters and Nanoparticles Calculators

Energy of Liquid Drop in Neutral System
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
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
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
Energy Deficiency of Surface = Binding Energy Deficiency of Surface Atom*(Number of Atom^(2/3))
Coulomb Energy of Charged Particle using Radius of Cluster
Coulomb Energy of Charged Sphere = (Surface Electrons^2)/(2*Radius of Cluster)
Energy Deficiency of Curvature containing Cluster Surface
Energy Deficiency of Curvature = Curvature Coefficient*(Number of Atom^(1/3))
Energy per Unit Volume of Cluster
Energy per Unit Volume = Energy per Atom*Number of Atom

R0 = r0*(n^(1/3))

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.

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)).