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Determination of Energy of I-th State for Bose-Einstein Statistics Formula

GoDetermination of Energy of I-th State for Fermi-Dirac Statistics Formula

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

ε i = \frac{1}{β} \cdot (\ln (\frac{g}{n i} - 1) - α)

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

Determination of Energy of I-th State for Bose-Einstein Statistics Example

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Here is how the Determination of Energy of I-th State for Bose-Einstein Statistics equation looks like with Values.

Here is how the Determination of Energy of I-th State for Bose-Einstein Statistics equation looks like with Units.

Here is how the Determination of Energy of I-th State for Bose-Einstein Statistics equation looks like.

40054.1308 = \frac{1}{0.0001} \cdot (\ln (\frac{3}{0.0002} - 1) - 5.0324)

40054.1308J = \frac{1}{0.0001J} \cdot (\ln (\frac{3}{0.0002} - 1) - 5.0324)

40054.1308 = \frac{1}{0.0001} \cdot (\ln (\frac{3}{0.0002} - 1) - 5.0324)

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Determination of Energy of I-th State for Bose-Einstein Statistics Solution

Follow our step by step solution on how to calculate Determination of Energy of I-th State for Bose-Einstein Statistics?

FIRST Step Consider the formula

ε i = \frac{1}{β} \cdot (\ln (\frac{g}{n i} - 1) - α)

Next Step Substitute values of Variables

∴

ε i = \frac{1}{0.0001J} \cdot (\ln (\frac{3}{0.0002} - 1) - 5.0324)

Next Step Prepare to Evaluate

∴

ε i = \frac{1}{0.0001} \cdot (\ln (\frac{3}{0.0002} - 1) - 5.0324)

Next Step Evaluate

∴

ε i = 40054.1308053579J

LAST Step Rounding Answer

∴

ε i = 40054.1308J

Determination of Energy of I-th State for Bose-Einstein Statistics Formula Elements

Variables

Functions

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

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'

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'

The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function.

Syntax: ln(Number)

Other Formulas to find Energy of i-th State

Go Determination of Energy of I-th State for Fermi-Dirac Statistics

ε i = \frac{1}{β} \cdot (\ln (\frac{g}{n i} - 1) - α)

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 Energy of I-th State for Bose-Einstein Statistics?

Determination of Energy of I-th State for Bose-Einstein Statistics evaluator uses Energy of i-th State = 1/Lagrange's Undetermined Multiplier 'β'*(ln(Number of Degenerate States/Number of particles in i-th State-1)-Lagrange's Undetermined Multiplier 'α') to evaluate the Energy of i-th State, The Determination of Energy of I-th State for Bose-Einstein Statistics formula is defined as the amount of energy present in a particular state. Energy of i-th State is denoted by ε_i symbol.

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

FAQs on Determination of Energy of I-th State for Bose-Einstein Statistics

What is the formula to find Determination of Energy of I-th State for Bose-Einstein Statistics?

The formula of Determination of Energy of I-th State for Bose-Einstein Statistics is expressed as Energy of i-th State = 1/Lagrange's Undetermined Multiplier 'β'*(ln(Number of Degenerate States/Number of particles in i-th State-1)-Lagrange's Undetermined Multiplier 'α'). Here is an example- 40054.13 = 1/0.00012*(ln(3/0.00016-1)-5.0324).

How to calculate Determination of Energy of I-th State for Bose-Einstein Statistics?

With Lagrange's Undetermined Multiplier 'β' (β), Number of Degenerate States (g), Number of particles in i-th State (n_i) & Lagrange's Undetermined Multiplier 'α' (α) we can find Determination of Energy of I-th State for Bose-Einstein Statistics using the formula - Energy of i-th State = 1/Lagrange's Undetermined Multiplier 'β'*(ln(Number of Degenerate States/Number of particles in i-th State-1)-Lagrange's Undetermined Multiplier 'α'). This formula also uses Natural Logarithm (ln) function(s).

What are the other ways to Calculate Energy of i-th State?

Here are the different ways to Calculate Energy of i-th State-

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

Can the Determination of Energy of I-th State for Bose-Einstein Statistics be negative?

Yes, the Determination of Energy of I-th State for Bose-Einstein Statistics, measured in Energy can be negative.

Which unit is used to measure Determination of Energy of I-th State for Bose-Einstein Statistics?

Determination of Energy of I-th State for Bose-Einstein Statistics is usually measured using the Joule[J] for Energy. Kilojoule[J], Gigajoule[J], Megajoule[J] are the few other units in which Determination of Energy of I-th State for Bose-Einstein Statistics can be measured.

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Determination of Energy of I-th State for Bose-Einstein Statistics Formula

​GoDetermination of Energy of I-th State for Fermi-Dirac Statistics Formula

Determination of Energy of I-th State for Bose-Einstein Statistics Example

Determination of Energy of I-th State for Bose-Einstein Statistics Solution

Determination of Energy of I-th State for Bose-Einstein Statistics Formula Elements

Other Formulas to find Energy of i-th State

Other formulas in Indistinguishable Particles category

How to Evaluate Determination of Energy of I-th State for Bose-Einstein Statistics?

FAQs on Determination of Energy of I-th State for Bose-Einstein Statistics

Variable Name

GoDetermination of Energy of I-th State for Fermi-Dirac Statistics Formula