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

STEP 0: Pre-Calculation Summary
Formula Used
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)
ni = g/exp(α+β*εi)
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 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.
Number of Degenerate States - Number of Degenerate States can be defined as the number of energy states that have the same energy.
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 Degenerate States: 3 --> 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
ni = g/exp(α+β*εi) --> 3/exp(5.0324+0.00012*28786)
Evaluating ... ...
ni = 0.000618565350945962
STEP 3: Convert Result to Output's Unit
0.000618565350945962 --> No Conversion Required
FINAL ANSWER
0.000618565350945962 0.000619 <-- Number of particles in i-th State
(Calculation completed in 00.004 seconds)

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

​LaTeX ​Go
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)
ni = g/exp(α+β*εi)

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How to Calculate 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 calculator 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 calculate 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 ni symbol.

How to calculate Determination of Number of Particles in I-th State for Maxwell-Boltzmann Statistics using this online calculator? To use this online calculator 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 i) and hit the calculate button. Here is how the Determination of Number of Particles in I-th State for Maxwell-Boltzmann Statistics calculation can be explained with given input values -> 0.000619 = 3/exp(5.0324+0.00012*28786).

FAQ

What is Determination of Number of Particles in I-th State for Maxwell-Boltzmann Statistics?
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 and is represented as ni = g/exp(α+β*εi) or 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). Number of Degenerate States can be defined as the number of energy states that have the same energy, 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 Number of Particles in I-th State for Maxwell-Boltzmann Statistics?
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 is calculated using 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 calculate Determination of Number of Particles in I-th State for Maxwell-Boltzmann Statistics, you need Number of Degenerate States (g), Lagrange's Undetermined Multiplier 'α' (α), Lagrange's Undetermined Multiplier 'β' (β) & Energy of i-th State i). With our tool, you need to enter the respective value for Number of Degenerate States, 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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