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Determination of Degeneracy for I-th State for Fermi-Dirac Satistics Formula

GoDetermination of Degeneracy for I-th State for Bose-Eintein Satistics Formula

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

g = n i \cdot (\exp (α + β \cdot ε i) + 1)

g - Number of Degenerate States?n_i - Number of particles in i-th State?α - Lagrange's Undetermined Multiplier 'α'?β - Lagrange's Undetermined Multiplier 'β'?ε_i - Energy of i-th State?

Determination of Degeneracy for I-th State for Fermi-Dirac Satistics Example

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Here is how the Determination of Degeneracy for I-th State for Fermi-Dirac Satistics equation looks like with Values.

Here is how the Determination of Degeneracy for I-th State for Fermi-Dirac Satistics equation looks like with Units.

Here is how the Determination of Degeneracy for I-th State for Fermi-Dirac Satistics equation looks like.

0.7761 = 0.0002 \cdot (\exp (5.0324 + 0.0001 \cdot 28786) + 1)

0.7761 = 0.0002 \cdot (\exp (5.0324 + 0.0001J \cdot 28786J) + 1)

0.7761 = 0.0002 \cdot (\exp (5.0324 + 0.0001 \cdot 28786) + 1)

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Indistinguishable Particles » fx Determination of Degeneracy for I-th State for Fermi-Dirac Satistics

Determination of Degeneracy for I-th State for Fermi-Dirac Satistics Solution

Follow our step by step solution on how to calculate Determination of Degeneracy for I-th State for Fermi-Dirac Satistics?

FIRST Step Consider the formula

g = n i \cdot (\exp (α + β \cdot ε i) + 1)

Next Step Substitute values of Variables

∴

g = 0.0002 \cdot (\exp (5.0324 + 0.0001J \cdot 28786J) + 1)

Next Step Prepare to Evaluate

∴

g = 0.0002 \cdot (\exp (5.0324 + 0.0001 \cdot 28786) + 1)

Next Step Evaluate

∴

g = 0.776149148545007

LAST Step Rounding Answer

∴

g = 0.7761

Determination of Degeneracy for I-th State for Fermi-Dirac Satistics Formula Elements

Variables

Functions

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 particles in i-th State

Number of particles in i-th State can be defined as the total number of particles present in a particular energy state.

Symbol: n_i

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Number of particles in i-th State

Lagrange's Undetermined Multiplier 'α'

Lagrange's Undetermined Multiplier 'α' is denoted by μ/kT, Where μ= chemical potential; k= Boltzmann constant; T= temperature.

Symbol: α

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Lagrange's Undetermined Multiplier 'α'

Lagrange's Undetermined Multiplier 'β'

Lagrange's Undetermined Multiplier 'β' is denoted by 1/kT. Where, k= Boltzmann constant, T= temperature.

Symbol: β

Measurement: EnergyUnit: J

Note: Value can be positive or negative.

Formulas to find Lagrange's Undetermined Multiplier 'β'

Energy of i-th State

Energy of i-th State is defined as the total quantity of energy present in a particular energy state.

Symbol: ε_i

Measurement: EnergyUnit: J

Note: Value can be positive or negative.

Formulas to find Energy of i-th State

exp

n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable.

Syntax: exp(Number)

Other Formulas to find Number of Degenerate States

Go Determination of Degeneracy for I-th State for Bose-Eintein Satistics

g = n i \cdot (\exp (α + β \cdot ε i) - 1)

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 Degeneracy for I-th State for Fermi-Dirac Satistics?

Determination of Degeneracy for I-th State for Fermi-Dirac Satistics evaluator uses Number of Degenerate States = Number of particles in i-th State*(exp(Lagrange's Undetermined Multiplier 'α'+Lagrange's Undetermined Multiplier 'β'*Energy of i-th State)+1) to evaluate the Number of Degenerate States, The Determination of Degeneracy for I-th State for Fermi-Dirac Satistics formula is defined as the degree of degeneracy for a particular energy state in Fermi-Dirac Statistics. Number of Degenerate States is denoted by g symbol.

How to evaluate Determination of Degeneracy for I-th State for Fermi-Dirac Satistics using this online evaluator? To use this online evaluator for Determination of Degeneracy for I-th State for Fermi-Dirac Satistics, enter Number of particles in i-th State (n_i), Lagrange's Undetermined Multiplier 'α' (α), Lagrange's Undetermined Multiplier 'β' (β) & Energy of i-th State (ε_i) and hit the calculate button.

FAQs on Determination of Degeneracy for I-th State for Fermi-Dirac Satistics

What is the formula to find Determination of Degeneracy for I-th State for Fermi-Dirac Satistics?

The formula of Determination of Degeneracy for I-th State for Fermi-Dirac Satistics is expressed as Number of Degenerate States = Number of particles in i-th State*(exp(Lagrange's Undetermined Multiplier 'α'+Lagrange's Undetermined Multiplier 'β'*Energy of i-th State)+1). Here is an example- 0.776149 = 0.00016*(exp(5.0324+0.00012*28786)+1).

How to calculate Determination of Degeneracy for I-th State for Fermi-Dirac Satistics?

With Number of particles in i-th State (n_i), Lagrange's Undetermined Multiplier 'α' (α), Lagrange's Undetermined Multiplier 'β' (β) & Energy of i-th State (ε_i) we can find Determination of Degeneracy for I-th State for Fermi-Dirac Satistics using the formula - Number of Degenerate States = Number of particles in i-th State*(exp(Lagrange's Undetermined Multiplier 'α'+Lagrange's Undetermined Multiplier 'β'*Energy of i-th State)+1). This formula also uses Exponential Growth (exp) function(s).

What are the other ways to Calculate Number of Degenerate States?

Here are the different ways to Calculate Number of Degenerate States-

Number of Degenerate States=Number of particles in i-th State*(exp(Lagrange's Undetermined Multiplier 'α'+Lagrange's Undetermined Multiplier 'β'*Energy of i-th State)-1)

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Determination of Degeneracy for I-th State for Fermi-Dirac Satistics Formula

​GoDetermination of Degeneracy for I-th State for Bose-Eintein Satistics Formula

Determination of Degeneracy for I-th State for Fermi-Dirac Satistics Example

Determination of Degeneracy for I-th State for Fermi-Dirac Satistics Solution

Determination of Degeneracy for I-th State for Fermi-Dirac Satistics Formula Elements

Other Formulas to find Number of Degenerate States

Other formulas in Indistinguishable Particles category

How to Evaluate Determination of Degeneracy for I-th State for Fermi-Dirac Satistics?

FAQs on Determination of Degeneracy for I-th State for Fermi-Dirac Satistics

Variable Name

GoDetermination of Degeneracy for I-th State for Bose-Eintein Satistics Formula