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Number of particles in i-th State can be defined as the total number of particles present in a particular energy state. Check FAQs
ni=gexp(α+βεi)+1
ni - Number of particles in i-th State?g - Number of Degenerate States?α - Lagrange's Undetermined Multiplier 'α'?β - Lagrange's Undetermined Multiplier 'β'?εi - Energy of i-th State?

Determination of Number of Particles in I-th State for Fermi-Dirac Statistics Example

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Here is how the Determination of Number of Particles in I-th State for Fermi-Dirac Statistics equation looks like with Values.

Here is how the Determination of Number of Particles in I-th State for Fermi-Dirac Statistics equation looks like with Units.

Here is how the Determination of Number of Particles in I-th State for Fermi-Dirac Statistics equation looks like.

0.0006Edit=3Editexp(5.0324Edit+0.0001Edit28786Edit)+1
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Determination of Number of Particles in I-th State for Fermi-Dirac Statistics Solution

Follow our step by step solution on how to calculate Determination of Number of Particles in I-th State for Fermi-Dirac Statistics?

FIRST Step Consider the formula
ni=gexp(α+βεi)+1
Next Step Substitute values of Variables
ni=3exp(5.0324+0.0001J28786J)+1
Next Step Prepare to Evaluate
ni=3exp(5.0324+0.000128786)+1
Next Step Evaluate
ni=0.000618437836206898
LAST Step Rounding Answer
ni=0.0006

Determination of Number of Particles in I-th State for Fermi-Dirac Statistics Formula Elements

Variables
Functions
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: ni
Measurement: NAUnit: Unitless
Note: Value can be positive or negative.
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.
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.
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.
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: εi
Measurement: EnergyUnit: J
Note: Value can be positive or negative.
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 particles in i-th State

​Go Determination of Number of Particles in I-th State for Bose-Einstein Statistics
ni=gexp(α+βεi)-1

Other formulas in Indistinguishable Particles category

​Go Mathematical Probability of Occurrence of Distribution
ρ=WWtot
​Go Boltzmann-Planck Equation
S=[BoltZ]ln(W)
​Go Determination of Helmholtz Free Energy using Molecular PF for Indistinguishable Particles
A=-NA[BoltZ]T(ln(qNA)+1)
​Go Determination of Gibbs Free energy using Molecular PF for Indistinguishable Particles
G=-NA[BoltZ]Tln(qNA)

How to Evaluate Determination of Number of Particles in I-th State for Fermi-Dirac Statistics?

Determination of Number of Particles in I-th State for Fermi-Dirac Statistics evaluator uses Number of particles in i-th State = Number of Degenerate States/(exp(Lagrange's Undetermined Multiplier 'α'+Lagrange's Undetermined Multiplier 'β'*Energy of i-th State)+1) to evaluate the Number of particles in i-th State, The Determination of Number of Particles in I-th State for Fermi-Dirac Statistics formula is defined as the number of indistinguishable fermion particles that can be present in a particular energy state. Number of particles in i-th State is denoted by ni symbol.

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

FAQs on Determination of Number of Particles in I-th State for Fermi-Dirac Statistics

What is the formula to find Determination of Number of Particles in I-th State for Fermi-Dirac Statistics?
The formula of Determination of Number of Particles in I-th State for Fermi-Dirac Statistics is expressed as Number of particles in i-th State = Number of Degenerate States/(exp(Lagrange's Undetermined Multiplier 'α'+Lagrange's Undetermined Multiplier 'β'*Energy of i-th State)+1). Here is an example- 0.000618 = 3/(exp(5.0324+0.00012*28786)+1).
How to calculate Determination of Number of Particles in I-th State for Fermi-Dirac Statistics?
With Number of Degenerate States (g), Lagrange's Undetermined Multiplier 'α' (α), Lagrange's Undetermined Multiplier 'β' (β) & Energy of i-th State i) we can find Determination of Number of Particles in I-th State for Fermi-Dirac Statistics using the formula - Number of particles in i-th State = Number of Degenerate States/(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 particles in i-th State?
Here are the different ways to Calculate Number of particles in i-th State-
  • Number of particles in i-th State=Number of Degenerate States/(exp(Lagrange's Undetermined Multiplier 'α'+Lagrange's Undetermined Multiplier 'β'*Energy of i-th State)-1)OpenImg
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