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Determination of Fermi Energy at 0 K Formula

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Fermi Energy a quantum mechanical concept that refers to the energy difference between the highest and lowest occupied states of a system of non-interacting fermions at absolute zero temperature. Check FAQs

ε F = \frac{{h p}^{2}}{2 \cdot m} \cdot {(\frac{3}{4 \cdot π \cdot g} \cdot \frac{N}{V})}^{\frac{2}{3}}

ε_F - Fermi Energy?h_p - Planck's Constant?m - Mass?g - Number of Degenerate States?N - Number of Atoms?V - Volume?π - Archimedes' constant?

Determination of Fermi Energy at 0 K Example

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Here is how the Determination of Fermi Energy at 0 K equation looks like with Values.

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Here is how the Determination of Fermi Energy at 0 K equation looks like.

8.4E-39 = \frac{{6.6E-34}^{2}}{2 \cdot 2.7E-26} \cdot {(\frac{3}{4 \cdot 3.1416 \cdot 3} \cdot \frac{8940}{0.0221})}^{\frac{2}{3}}

8.4E-39J = \frac{{6.6E-34}^{2}}{2 \cdot 2.7E-26kg} \cdot {(\frac{3}{4 \cdot 3.1416 \cdot 3} \cdot \frac{8940}{0.0221m³})}^{\frac{2}{3}}

8.4E-39 = \frac{{6.6E-34}^{2}}{2 \cdot 2.7E-26} \cdot {(\frac{3}{4 \cdot 3.1416 \cdot 3} \cdot \frac{8940}{0.0221})}^{\frac{2}{3}}

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Determination of Fermi Energy at 0 K Solution

Follow our step by step solution on how to calculate Determination of Fermi Energy at 0 K?

FIRST Step Consider the formula

ε F = \frac{{h p}^{2}}{2 \cdot m} \cdot {(\frac{3}{4 \cdot π \cdot g} \cdot \frac{N}{V})}^{\frac{2}{3}}

Next Step Substitute values of Variables

∴

ε F = \frac{{6.6E-34}^{2}}{2 \cdot 2.7E-26kg} \cdot {(\frac{3}{4 \cdot π \cdot 3} \cdot \frac{8940}{0.0221m³})}^{\frac{2}{3}}

Next Step Substitute values of Constants

∴

ε F = \frac{{6.6E-34}^{2}}{2 \cdot 2.7E-26kg} \cdot {(\frac{3}{4 \cdot 3.1416 \cdot 3} \cdot \frac{8940}{0.0221m³})}^{\frac{2}{3}}

Next Step Prepare to Evaluate

∴

ε F = \frac{{6.6E-34}^{2}}{2 \cdot 2.7E-26} \cdot {(\frac{3}{4 \cdot 3.1416 \cdot 3} \cdot \frac{8940}{0.0221})}^{\frac{2}{3}}

Next Step Evaluate

∴

ε F = 8.35368616664439E-39J

LAST Step Rounding Answer

∴

ε F = 8.4E-39J

Determination of Fermi Energy at 0 K Formula Elements

Variables

Constants

Fermi Energy

Fermi Energy a quantum mechanical concept that refers to the energy difference between the highest and lowest occupied states of a system of non-interacting fermions at absolute zero temperature.

Symbol: ε_F

Measurement: EnergyUnit: J

Note: Value can be positive or negative.

Formulas to find Fermi Energy

Planck's Constant

Planck's Constant is a fundamental constant in quantum mechanics that relates the energy of a photon to its frequency.

Symbol: h_p

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Planck's Constant

Mass

Mass is the property of a body that is a measure of its inertia and that is commonly taken as a measure of the amount of material it contains and causes it to have weight in a gravitational field.

Symbol: m

Measurement: WeightUnit: kg

Note: Value can be positive or negative.

Formulas to find Mass

Number of Degenerate States

Number of Degenerate States can be defined as the number of energy states that have the same energy.

Symbol: g

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Number of Degenerate States

Number of Atoms

Number of Atoms is the total quantity of atoms present.

Symbol: N

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Number of Atoms

Volume

Volume is the amount of space that a substance or object occupies, or that is enclosed within a container.

Symbol: V

Measurement: VolumeUnit: m³

Note: Value can be positive or negative.

Formulas to find Volume

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 in Indistinguishable Particles category

Go Mathematical Probability of Occurrence of Distribution

ρ = \frac{W}{W tot}

Go Boltzmann-Planck Equation

S = [BoltZ] \cdot \ln (W)

Go Determination of Helmholtz Free Energy using Molecular PF for Indistinguishable Particles

A = - N A \cdot [BoltZ] \cdot T \cdot (\ln (\frac{q}{N A}) + 1)

Go Determination of Gibbs Free energy using Molecular PF for Indistinguishable Particles

G = - N A \cdot [BoltZ] \cdot T \cdot \ln (\frac{q}{N A})

How to Evaluate Determination of Fermi Energy at 0 K?

Determination of Fermi Energy at 0 K evaluator uses Fermi Energy = Planck's Constant^2/(2*Mass)*(3/(4*pi*Number of Degenerate States)*Number of Atoms/Volume)^(2/3) to evaluate the Fermi Energy, The Determination of Fermi Energy at 0 K formula is defined as the energy difference between the highest and lowest occupied single-particle states in a quantum system of non-interacting fermions at absolute zero temperature. Fermi Energy is denoted by ε_F symbol.

How to evaluate Determination of Fermi Energy at 0 K using this online evaluator? To use this online evaluator for Determination of Fermi Energy at 0 K, enter Planck's Constant (h_p), Mass (m), Number of Degenerate States (g), Number of Atoms (N) & Volume (V) and hit the calculate button.

FAQs on Determination of Fermi Energy at 0 K

What is the formula to find Determination of Fermi Energy at 0 K?

The formula of Determination of Fermi Energy at 0 K is expressed as Fermi Energy = Planck's Constant^2/(2*Mass)*(3/(4*pi*Number of Degenerate States)*Number of Atoms/Volume)^(2/3). Here is an example- 8.4E-39 = 6.626E-34^2/(2*2.656E-26)*(3/(4*pi*3)*8940/0.02214)^(2/3).

How to calculate Determination of Fermi Energy at 0 K?

With Planck's Constant (h_p), Mass (m), Number of Degenerate States (g), Number of Atoms (N) & Volume (V) we can find Determination of Fermi Energy at 0 K using the formula - Fermi Energy = Planck's Constant^2/(2*Mass)*(3/(4*pi*Number of Degenerate States)*Number of Atoms/Volume)^(2/3). This formula also uses Archimedes' constant .

Can the Determination of Fermi Energy at 0 K be negative?

Yes, the Determination of Fermi Energy at 0 K, measured in Energy can be negative.

Which unit is used to measure Determination of Fermi Energy at 0 K?

Determination of Fermi Energy at 0 K is usually measured using the Joule[J] for Energy. Kilojoule[J], Gigajoule[J], Megajoule[J] are the few other units in which Determination of Fermi Energy at 0 K can be measured.

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Determination of Fermi Energy at 0 K Formula

Determination of Fermi Energy at 0 K Example

Determination of Fermi Energy at 0 K Solution

Determination of Fermi Energy at 0 K Formula Elements

Other formulas in Indistinguishable Particles category

How to Evaluate Determination of Fermi Energy at 0 K?

FAQs on Determination of Fermi Energy at 0 K

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