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Determination of Number of Particles in I-th State for Maxwell-Boltzmann Statistics Formula

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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

n i = \frac{g}{\exp (α + β \cdot ε i)}

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

Determination of Number of Particles in I-th State for Maxwell-Boltzmann Statistics Example

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

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

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

0.0006 = \frac{3}{\exp (5.0324 + 0.0001 \cdot 28786)}

0.0006 = \frac{3}{\exp (5.0324 + 0.0001J \cdot 28786J)}

0.0006 = \frac{3}{\exp (5.0324 + 0.0001 \cdot 28786)}

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Determination of Number of Particles in I-th State for Maxwell-Boltzmann Statistics Solution

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

FIRST Step Consider the formula

n i = \frac{g}{\exp (α + β \cdot ε i)}

Next Step Substitute values of Variables

∴

n i = \frac{3}{\exp (5.0324 + 0.0001J \cdot 28786J)}

Next Step Prepare to Evaluate

∴

n i = \frac{3}{\exp (5.0324 + 0.0001 \cdot 28786)}

Next Step Evaluate

∴

n i = 0.000618565350945962

LAST Step Rounding Answer

∴

n i = 0.0006

Determination of Number of Particles in I-th State for Maxwell-Boltzmann 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: n_i

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Number of particles in i-th State

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

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 in Distinguishable Particles category

Go Total Number of Microstates in All Distributions

W tot = \frac{(N' + E - 1)!}{(N' - 1)! \cdot (E!)}

Go Translational Partition Function

q trans = V \cdot {(\frac{2 \cdot π \cdot m \cdot [BoltZ] \cdot T}{{[hP]}^{2}})}^{\frac{3}{2}}

Go Translational Partition Function using Thermal de Broglie Wavelength

q trans = \frac{V}{{(Λ)}^{3}}

Go Determination of Entropy using Sackur-Tetrode Equation

S° m = R \cdot (- 1.154 + (\frac{3}{2}) \cdot \ln (A r) + (\frac{5}{2}) \cdot \ln (T) - \ln (\frac{p}{p°}))

How to Evaluate Determination of Number of Particles in I-th State for Maxwell-Boltzmann Statistics?

Determination of Number of Particles in I-th State for Maxwell-Boltzmann 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) to evaluate the Number of particles in i-th State, The Determination of Number of Particles in I-th State for Maxwell-Boltzmann Statistics formula is defined as the total number of distinguishable particles that can be present in i-th energy state. Number of particles in i-th State is denoted by n_i symbol.

How to evaluate Determination of Number of Particles in I-th State for Maxwell-Boltzmann Statistics using this online evaluator? To use this online evaluator for Determination of Number of Particles in I-th State for Maxwell-Boltzmann Statistics, enter Number of Degenerate States (g), 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 Number of Particles in I-th State for Maxwell-Boltzmann Statistics

What is the formula to find Determination of Number of Particles in I-th State for Maxwell-Boltzmann Statistics?

The formula of Determination of Number of Particles in I-th State for Maxwell-Boltzmann 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). Here is an example- 0.000619 = 3/exp(5.0324+0.00012*28786).

How to calculate Determination of Number of Particles in I-th State for Maxwell-Boltzmann Statistics?

With Number of Degenerate States (g), Lagrange's Undetermined Multiplier 'α' (α), Lagrange's Undetermined Multiplier 'β' (β) & Energy of i-th State (ε_i) we can find Determination of Number of Particles in I-th State for Maxwell-Boltzmann 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). This formula also uses Exponential Growth (exp) function(s).

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Determination of Number of Particles in I-th State for Maxwell-Boltzmann Statistics Formula

Determination of Number of Particles in I-th State for Maxwell-Boltzmann Statistics Example

Determination of Number of Particles in I-th State for Maxwell-Boltzmann Statistics Solution

Determination of Number of Particles in I-th State for Maxwell-Boltzmann Statistics Formula Elements

Other formulas in Distinguishable Particles category

How to Evaluate Determination of Number of Particles in I-th State for Maxwell-Boltzmann Statistics?

FAQs on Determination of Number of Particles in I-th State for Maxwell-Boltzmann Statistics

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