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Determination of Degeneracy for I-th State for Maxwell-Boltzmann Statistics Calculator

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Distinguishable Particles Indistinguishable Particles

✖Number of particles in i-th State can be defined as the total number of particles present in a particular energy state.ⓘ Number of particles in i-th State [n_i]			+10% -10%
✖Lagrange's Undetermined Multiplier 'α' is denoted by μ/kT, Where μ= chemical potential; k= Boltzmann constant; T= temperature.ⓘ Lagrange's Undetermined Multiplier 'α' [α]			+10% -10%
✖Lagrange's Undetermined Multiplier 'β' is denoted by 1/kT. Where, k= Boltzmann constant, T= temperature.ⓘ Lagrange's Undetermined Multiplier 'β' [β]			+10% -10%
✖Energy of i-th State is defined as the total quantity of energy present in a particular energy state.ⓘ Energy of i-th State [ε_i]			+10% -10%

✖Number of Degenerate States can be defined as the number of energy states that have the same energy.ⓘ Determination of Degeneracy for I-th State for Maxwell-Boltzmann Statistics [g]

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Determination of Degeneracy for I-th State for Maxwell-Boltzmann Statistics Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
g = n_i*(exp(α+β*ε_i))
This formula uses 1 Functions, 5 Variables

Functions Used

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

Variables Used

Number of Degenerate States - Number of Degenerate States can be defined as the number of energy states that have the same energy.
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.
Lagrange's Undetermined Multiplier 'α' - Lagrange's Undetermined Multiplier 'α' is denoted by μ/kT, Where μ= chemical potential; k= Boltzmann constant; T= temperature.
Lagrange's Undetermined Multiplier 'β' - (Measured in Joule) - Lagrange's Undetermined Multiplier 'β' is denoted by 1/kT. Where, k= Boltzmann constant, T= temperature.
Energy of i-th State - (Measured in Joule) - Energy of i-th State is defined as the total quantity of energy present in a particular energy state.

STEP 1: Convert Input(s) to Base Unit

Number of particles in i-th State: 0.00016 --> No Conversion Required
Lagrange's Undetermined Multiplier 'α': 5.0324 --> No Conversion Required
Lagrange's Undetermined Multiplier 'β': 0.00012 Joule --> 0.00012 Joule No Conversion Required
Energy of i-th State: 28786 Joule --> 28786 Joule No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

g = n_i*(exp(α+β*ε_i)) --> 0.00016*(exp(5.0324+0.00012*28786))

Evaluating ... ...

g = 0.775989148545007

STEP 3: Convert Result to Output's Unit

0.775989148545007 --> No Conversion Required

FINAL ANSWER

0.775989148545007 ≈ 0.775989 <-- Number of Degenerate States

(Calculation completed in 00.020 seconds)

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Determination of Degeneracy for I-th State for Maxwell-Boltzmann Statistics 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))
g = n_i*(exp(α+β*ε_i))

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 Degeneracy for I-th State for Maxwell-Boltzmann Statistics?

Determination of Degeneracy for I-th State for Maxwell-Boltzmann Statistics calculator 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)) to calculate the Number of Degenerate States, The Determination of Degeneracy for I-th State for Maxwell-Boltzmann Statistics formula is defined as the degree of degeneracy for a particular energy state in Maxwell-Boltzmann Statistics. Number of Degenerate States is denoted by g symbol.

How to calculate Determination of Degeneracy for I-th State for Maxwell-Boltzmann Statistics using this online calculator? To use this online calculator for Determination of Degeneracy for I-th State for Maxwell-Boltzmann Statistics, 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. Here is how the Determination of Degeneracy for I-th State for Maxwell-Boltzmann Statistics calculation can be explained with given input values -> 9699.864 = 0.00016*(exp(5.0324+0.00012*28786)).

FAQ

What is Determination of Degeneracy for I-th State for Maxwell-Boltzmann Statistics?

The Determination of Degeneracy for I-th State for Maxwell-Boltzmann Statistics formula is defined as the degree of degeneracy for a particular energy state in Maxwell-Boltzmann Statistics and is represented as g = n_i*(exp(α+β*ε_i)) or 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)). Number of particles in i-th State can be defined as the total number of particles present in a particular energy state, Lagrange's Undetermined Multiplier 'α' is denoted by μ/kT, Where μ= chemical potential; k= Boltzmann constant; T= temperature, Lagrange's Undetermined Multiplier 'β' is denoted by 1/kT. Where, k= Boltzmann constant, T= temperature & Energy of i-th State is defined as the total quantity of energy present in a particular energy state.

How to calculate Determination of Degeneracy for I-th State for Maxwell-Boltzmann Statistics?

The Determination of Degeneracy for I-th State for Maxwell-Boltzmann Statistics formula is defined as the degree of degeneracy for a particular energy state in Maxwell-Boltzmann Statistics is calculated using 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)). To calculate Determination of Degeneracy for I-th State for Maxwell-Boltzmann Statistics, you need 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). With our tool, you need to enter the respective value for Number of particles in i-th State, Lagrange's Undetermined Multiplier 'α', Lagrange's Undetermined Multiplier 'β' & Energy of i-th State 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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