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Determination of Fermi Energy at 0 K Calculator

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Indistinguishable Particles Distinguishable Particles

✖Planck's Constant is a fundamental constant in quantum mechanics that relates the energy of a photon to its frequency.ⓘ Planck's Constant [h_p]			+10% -10%
✖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.ⓘ Mass [m]			+10% -10%
✖Number of Degenerate States can be defined as the number of energy states that have the same energy.ⓘ Number of Degenerate States [g]			+10% -10%
✖Number of Atoms is the total quantity of atoms present.ⓘ Number of Atoms [N]			+10% -10%
✖Volume is the amount of space that a substance or object occupies, or that is enclosed within a container.ⓘ Volume [V]			+10% -10%

✖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.ⓘ Determination of Fermi Energy at 0 K [ε_F]

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Determination of Fermi Energy at 0 K Solution

STEP 0: Pre-Calculation Summary

Formula Used

Fermi Energy = Planck's Constant^2/(2*Mass)*(3/(4*pi*Number of Degenerate States)*Number of Atoms/Volume)^(2/3)
ε_F = h_p^2/(2*m)*(3/(4*pi*g)*N/V)^(2/3)
This formula uses 1 Constants, 6 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Fermi Energy - (Measured in Joule) - 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.
Planck's Constant - Planck's Constant is a fundamental constant in quantum mechanics that relates the energy of a photon to its frequency.
Mass - (Measured in Kilogram) - 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.
Number of Degenerate States - Number of Degenerate States can be defined as the number of energy states that have the same energy.
Number of Atoms - Number of Atoms is the total quantity of atoms present.
Volume - (Measured in Cubic Meter) - Volume is the amount of space that a substance or object occupies, or that is enclosed within a container.

STEP 1: Convert Input(s) to Base Unit

Planck's Constant: 6.626E-34 --> No Conversion Required
Mass: 2.656E-26 Kilogram --> 2.656E-26 Kilogram No Conversion Required
Number of Degenerate States: 3 --> No Conversion Required
Number of Atoms: 8940 --> No Conversion Required
Volume: 0.02214 Cubic Meter --> 0.02214 Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ε_F = h_p^2/(2*m)*(3/(4*pi*g)*N/V)^(2/3) --> 6.626E-34^2/(2*2.656E-26)*(3/(4*pi*3)*8940/0.02214)^(2/3)

Evaluating ... ...

ε_F = 8.35368616664439E-39

STEP 3: Convert Result to Output's Unit

8.35368616664439E-39 Joule --> No Conversion Required

FINAL ANSWER

8.35368616664439E-39 ≈ 8.4E-39 Joule <-- Fermi Energy

(Calculation completed in 00.004 seconds)

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Determination of Fermi Energy at 0 K Formula

LaTeX Go

Fermi Energy = Planck's Constant^2/(2*Mass)*(3/(4*pi*Number of Degenerate States)*Number of Atoms/Volume)^(2/3)
ε_F = h_p^2/(2*m)*(3/(4*pi*g)*N/V)^(2/3)

What is Statistical Thermodynamics?

Statistical thermodynamics is a theory that uses molecular properties to predict the behavior of macroscopic quantities of compounds. While the origins of statistical thermodynamics predate the development of quantum mechanics, the modern development of statistical thermodynamics assumes that the quantized energy levels associated with a particular system are known. From these energy-level data, a temperature-dependent quantity called the partition function can be calculated. From the partition function, all of the thermodynamic properties of the system can be calculated. Statistical thermodynamics has also been applied to the general problem of predicting reaction rates. This application is called transition state theory or the theory of absolute reaction rates.

How to Calculate Determination of Fermi Energy at 0 K?

Determination of Fermi Energy at 0 K calculator uses Fermi Energy = Planck's Constant^2/(2*Mass)*(3/(4*pi*Number of Degenerate States)*Number of Atoms/Volume)^(2/3) to calculate 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 calculate Determination of Fermi Energy at 0 K using this online calculator? To use this online calculator 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. Here is how the Determination of Fermi Energy at 0 K calculation can be explained with given input values -> 8.4E-39 = 6.626E-34^2/(2*2.656E-26)*(3/(4*pi*3)*8940/0.02214)^(2/3).

FAQ

What is Determination of Fermi Energy at 0 K?

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 and is represented as ε_F = h_p^2/(2*m)*(3/(4*pi*g)*N/V)^(2/3) or Fermi Energy = Planck's Constant^2/(2*Mass)*(3/(4*pi*Number of Degenerate States)*Number of Atoms/Volume)^(2/3). Planck's Constant is a fundamental constant in quantum mechanics that relates the energy of a photon to its frequency, 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, Number of Degenerate States can be defined as the number of energy states that have the same energy, Number of Atoms is the total quantity of atoms present & Volume is the amount of space that a substance or object occupies, or that is enclosed within a container.

How to calculate Determination of Fermi Energy at 0 K?

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 is calculated using Fermi Energy = Planck's Constant^2/(2*Mass)*(3/(4*pi*Number of Degenerate States)*Number of Atoms/Volume)^(2/3). To calculate Determination of Fermi Energy at 0 K, you need Planck's Constant (h_p), Mass (m), Number of Degenerate States (g), Number of Atoms (N) & Volume (V). With our tool, you need to enter the respective value for Planck's Constant, Mass, Number of Degenerate States, Number of Atoms & Volume 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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