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Atomic Packing Factor of FCC in Terms of Particle Radius Formula

GoAtomic Packing Factor in Terms of Volume of Particle and Unit Cell Formula

GoAtomic Packing Factor of SCC Formula

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Atomic Packing Factor is the fraction of volume in a crystal structure that is occupied by constituent particles. Check FAQs

APF = \frac{4 \cdot (\frac{4}{3}) \cdot π \cdot (r^{3})}{{(2 \cdot \sqrt{2} \cdot r)}^{3}}

APF - Atomic Packing Factor?r - Radius of Particle?π - Archimedes' constant?

Atomic Packing Factor of FCC in Terms of Particle Radius Example

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Here is how the Atomic Packing Factor of FCC in Terms of Particle Radius equation looks like with Values.

Here is how the Atomic Packing Factor of FCC in Terms of Particle Radius equation looks like with Units.

Here is how the Atomic Packing Factor of FCC in Terms of Particle Radius equation looks like.

0.7405 = \frac{4 \cdot (\frac{4}{3}) \cdot 3.1416 \cdot (2^{3})}{{(2 \cdot \sqrt{2} \cdot 2)}^{3}}

0.7405 = \frac{4 \cdot (\frac{4}{3}) \cdot 3.1416 \cdot ({2m}^{3})}{{(2 \cdot \sqrt{2} \cdot 2m)}^{3}}

0.7405 = \frac{4 \cdot (\frac{4}{3}) \cdot 3.1416 \cdot (2^{3})}{{(2 \cdot \sqrt{2} \cdot 2)}^{3}}

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Atomic Packing Factor of FCC in Terms of Particle Radius Solution

Follow our step by step solution on how to calculate Atomic Packing Factor of FCC in Terms of Particle Radius?

FIRST Step Consider the formula

APF = \frac{4 \cdot (\frac{4}{3}) \cdot π \cdot (r^{3})}{{(2 \cdot \sqrt{2} \cdot r)}^{3}}

Next Step Substitute values of Variables

∴

APF = \frac{4 \cdot (\frac{4}{3}) \cdot π \cdot ({2m}^{3})}{{(2 \cdot \sqrt{2} \cdot 2m)}^{3}}

Next Step Substitute values of Constants

∴

APF = \frac{4 \cdot (\frac{4}{3}) \cdot 3.1416 \cdot ({2m}^{3})}{{(2 \cdot \sqrt{2} \cdot 2m)}^{3}}

Next Step Prepare to Evaluate

∴

APF = \frac{4 \cdot (\frac{4}{3}) \cdot 3.1416 \cdot (2^{3})}{{(2 \cdot \sqrt{2} \cdot 2)}^{3}}

Next Step Evaluate

∴

APF = 0.740480489693061

LAST Step Rounding Answer

∴

APF = 0.7405

Atomic Packing Factor of FCC in Terms of Particle Radius Formula Elements

Variables

Constants

Functions

Atomic Packing Factor

Atomic Packing Factor is the fraction of volume in a crystal structure that is occupied by constituent particles.

Symbol: APF

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Atomic Packing Factor

Radius of Particle

Radius of Particle is defined as half of the diameter of that particle.

Symbol: r

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radius of Particle

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Atomic Packing Factor

Go Atomic Packing Factor in Terms of Volume of Particle and Unit Cell

APF = \frac{z \cdot V particle}{V unit cell}

Go Atomic Packing Factor of SCC

APF = \frac{V particle}{V unit cell}

Go Atomic Packing Factor of FCC

APF = \frac{4 \cdot V particle}{V unit cell}

Go Atomic Packing Factor of BCC

APF = \frac{2 \cdot V particle}{V unit cell}

How to Evaluate Atomic Packing Factor of FCC in Terms of Particle Radius?

Atomic Packing Factor of FCC in Terms of Particle Radius evaluator uses Atomic Packing Factor = (4*(4/3)*pi*(Radius of Particle^3))/((2*sqrt(2)*Radius of Particle)^3) to evaluate the Atomic Packing Factor, The Atomic Packing Factor of FCC in terms of particle radius is the fraction of volume in a face centered crystal that is occupied by constituent particles. It is a dimensionless quantity and always less than unity. For a face-centered cubic unit cell, the number of atoms is four. Atomic Packing Factor is denoted by APF symbol.

How to evaluate Atomic Packing Factor of FCC in Terms of Particle Radius using this online evaluator? To use this online evaluator for Atomic Packing Factor of FCC in Terms of Particle Radius, enter Radius of Particle (r) and hit the calculate button.

FAQs on Atomic Packing Factor of FCC in Terms of Particle Radius

What is the formula to find Atomic Packing Factor of FCC in Terms of Particle Radius?

The formula of Atomic Packing Factor of FCC in Terms of Particle Radius is expressed as Atomic Packing Factor = (4*(4/3)*pi*(Radius of Particle^3))/((2*sqrt(2)*Radius of Particle)^3). Here is an example- 0.74048 = (4*(4/3)*pi*(2^3))/((2*sqrt(2)*2)^3).

How to calculate Atomic Packing Factor of FCC in Terms of Particle Radius?

With Radius of Particle (r) we can find Atomic Packing Factor of FCC in Terms of Particle Radius using the formula - Atomic Packing Factor = (4*(4/3)*pi*(Radius of Particle^3))/((2*sqrt(2)*Radius of Particle)^3). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

What are the other ways to Calculate Atomic Packing Factor?

Here are the different ways to Calculate Atomic Packing Factor-

Atomic Packing Factor=(Number of Atoms*Volume of Each Particle)/(Volume of Unit Cell)
Atomic Packing Factor=Volume of Each Particle/Volume of Unit Cell
Atomic Packing Factor=(4*Volume of Each Particle)/(Volume of Unit Cell)

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