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

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Indistinguishable Particles Distinguishable Particles

✖Lagrange's Undetermined Multiplier 'β' is denoted by 1/kT. Where, k= Boltzmann constant, T= temperature.ⓘ Lagrange's Undetermined Multiplier 'β' [β]			+10% -10%
✖Number of Degenerate States can be defined as the number of energy states that have the same energy.ⓘ Number of Degenerate States [g]			+10% -10%
✖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%

✖Energy of i-th State is defined as the total quantity of energy present in a particular energy state.ⓘ Determination of Energy of I-th State for Fermi-Dirac Statistics [ε_i]

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

STEP 0: Pre-Calculation Summary

Formula Used

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')
ε_i = 1/β*(ln(g/n_i-1)-α)
This formula uses 1 Functions, 5 Variables

Functions Used

ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., ln(Number)

Variables Used

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.
Lagrange's Undetermined Multiplier 'β' - (Measured in Joule) - Lagrange's Undetermined Multiplier 'β' is denoted by 1/kT. Where, k= Boltzmann constant, T= temperature.
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.

STEP 1: Convert Input(s) to Base Unit

Lagrange's Undetermined Multiplier 'β': 0.00012 Joule --> 0.00012 Joule No Conversion Required
Number of Degenerate States: 3 --> No Conversion Required
Number of particles in i-th State: 0.00016 --> No Conversion Required
Lagrange's Undetermined Multiplier 'α': 5.0324 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ε_i = 1/β*(ln(g/n_i-1)-α) --> 1/0.00012*(ln(3/0.00016-1)-5.0324)

Evaluating ... ...

ε_i = 40054.1308053579

STEP 3: Convert Result to Output's Unit

40054.1308053579 Joule --> No Conversion Required

FINAL ANSWER

40054.1308053579 ≈ 40054.13 Joule <-- Energy of i-th State

(Calculation completed in 00.004 seconds)

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

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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 Energy of I-th State for Fermi-Dirac Statistics?

Determination of Energy of I-th State for Fermi-Dirac Statistics calculator 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 calculate the Energy of i-th State, The Determination of Energy of I-th State for Fermi-Dirac 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 calculate Determination of Energy of I-th State for Fermi-Dirac Statistics using this online calculator? To use this online calculator for Determination of Energy of I-th State for Fermi-Dirac 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. Here is how the Determination of Energy of I-th State for Fermi-Dirac Statistics calculation can be explained with given input values -> 40054.13 = 1/0.00012*(ln(3/0.00016-1)-5.0324).

FAQ

What is Determination of Energy of I-th State for Fermi-Dirac Statistics?

The Determination of Energy of I-th State for Fermi-Dirac Statistics formula is defined as the amount of energy present in a particular state and is represented as ε_i = 1/β*(ln(g/n_i-1)-α) or 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'). Lagrange's Undetermined Multiplier 'β' is denoted by 1/kT. Where, k= Boltzmann constant, T= temperature, 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 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.

How to calculate Determination of Energy of I-th State for Fermi-Dirac Statistics?

The Determination of Energy of I-th State for Fermi-Dirac Statistics formula is defined as the amount of energy present in a particular state is calculated using 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 calculate Determination of Energy of I-th State for Fermi-Dirac Statistics, you need 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). With our tool, you need to enter the respective value for Lagrange's Undetermined Multiplier 'β', Number of Degenerate States, Number of particles in i-th State & Lagrange's Undetermined Multiplier 'α' and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Energy of i-th State?

In this formula, Energy of i-th State uses Lagrange's Undetermined Multiplier 'β', Number of Degenerate States, Number of particles in i-th State & Lagrange's Undetermined Multiplier 'α'. We can use 1 other way(s) to calculate the same, which is/are as follows -

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')

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