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Atomic Packing Factor 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{z \cdot (\frac{4}{3}) \cdot π \cdot (r^{3})}{a^{3}}

APF - Atomic Packing Factor?z - Number of Atoms?r - Radius of Particle?a - Edge Length in APF?π - Archimedes' constant?

Atomic Packing Factor in Terms of Particle Radius Example

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

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

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

0.007 = \frac{35 \cdot (\frac{4}{3}) \cdot 3.1416 \cdot (2^{3})}{55^{3}}

0.007 = \frac{35 \cdot (\frac{4}{3}) \cdot 3.1416 \cdot ({2m}^{3})}{{55m}^{3}}

0.007 = \frac{35 \cdot (\frac{4}{3}) \cdot 3.1416 \cdot (2^{3})}{55^{3}}

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Atomic Packing Factor in Terms of Particle Radius Solution

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

FIRST Step Consider the formula

APF = \frac{z \cdot (\frac{4}{3}) \cdot π \cdot (r^{3})}{a^{3}}

Next Step Substitute values of Variables

∴

APF = \frac{35 \cdot (\frac{4}{3}) \cdot π \cdot ({2m}^{3})}{{55m}^{3}}

Next Step Substitute values of Constants

∴

APF = \frac{35 \cdot (\frac{4}{3}) \cdot 3.1416 \cdot ({2m}^{3})}{{55m}^{3}}

Next Step Prepare to Evaluate

∴

APF = \frac{35 \cdot (\frac{4}{3}) \cdot 3.1416 \cdot (2^{3})}{55^{3}}

Next Step Evaluate

∴

APF = 0.00704950417634975

LAST Step Rounding Answer

∴

APF = 0.007

Atomic Packing Factor in Terms of Particle Radius Formula Elements

Variables

Constants

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

Number of Atoms

The Number of Atoms is the the total number of constituent atoms in the unit cell.

Symbol: z

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Number of Atoms

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

Edge Length in APF

Edge Length in APF is the length of the edge of the unit cell in Atomic packing factor.

Symbol: a

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Edge Length in APF

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

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 in Terms of Particle Radius?

Atomic Packing Factor in Terms of Particle Radius evaluator uses Atomic Packing Factor = (Number of Atoms*(4/3)*pi*(Radius of Particle^3))/(Edge Length in APF^3) to evaluate the Atomic Packing Factor, The Atomic Packing Factor in terms of particle radius is the fraction of volume in a crystal structure that is occupied by constituent particles. It is a dimensionless quantity and always less than unity. Atomic Packing Factor is denoted by APF symbol.

How to evaluate Atomic Packing Factor in Terms of Particle Radius using this online evaluator? To use this online evaluator for Atomic Packing Factor in Terms of Particle Radius, enter Number of Atoms (z), Radius of Particle (r) & Edge Length in APF (a) and hit the calculate button.

FAQs on Atomic Packing Factor in Terms of Particle Radius

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

The formula of Atomic Packing Factor in Terms of Particle Radius is expressed as Atomic Packing Factor = (Number of Atoms*(4/3)*pi*(Radius of Particle^3))/(Edge Length in APF^3). Here is an example- 0.00705 = (35*(4/3)*pi*(2^3))/(55^3).

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

With Number of Atoms (z), Radius of Particle (r) & Edge Length in APF (a) we can find Atomic Packing Factor in Terms of Particle Radius using the formula - Atomic Packing Factor = (Number of Atoms*(4/3)*pi*(Radius of Particle^3))/(Edge Length in APF^3). This formula also uses Archimedes' constant .

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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Atomic Packing Factor 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

Atomic Packing Factor in Terms of Particle Radius Example

Atomic Packing Factor in Terms of Particle Radius Solution

Atomic Packing Factor in Terms of Particle Radius Formula Elements

Other Formulas to find Atomic Packing Factor

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

FAQs on Atomic Packing Factor in Terms of Particle Radius

Variable Name

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

GoAtomic Packing Factor of SCC Formula