No. of Particles in Upper State using Boltzmann Distribution Calculator

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✖Lower State Particles is the number of particles present in ground state in epr spectra.ⓘ Lower State Particles [N_lower]			+10% -10%
✖Lande g Factor is a multiplicative term appearing in the expression for the energy levels of an atom in a weak magnetic field.ⓘ Lande g Factor [g_j]			+10% -10%
✖Bohr Magneton is the magnitude of the magnetic dipole moment of an electron orbiting an atom with such angular momentum.ⓘ Bohr Magneton [μ]			+10% -10%
✖External Magnetic Field Strength is produced by moving electric charges and the intrinsic magnetic moments of elementary particles associated with a fundamental quantum property, their spin.ⓘ External Magnetic Field Strength [B]			+10% -10%

✖Upper State Particles is the number of particles present in upper state in epr spectra i.e in the excited state.ⓘ No. of Particles in Upper State using Boltzmann Distribution [N_upper]

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Formula

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No. of Particles in Upper State using Boltzmann Distribution

Formula

`"N"_{"upper"} = "N"_{"lower"}*e^(("g"_{"j"}*"μ"*"B"_{""})/"[Molar-g]")`

Example

`"2"="2"*e^(("1.5"*"0.0001A*m²"*"7E^-34A/m")/"[Molar-g]")`

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No. of Particles in Upper State using Boltzmann Distribution Solution

STEP 0: Pre-Calculation Summary

Formula Used

Upper State Particles = Lower State Particles*e^((Lande g Factor*Bohr Magneton*External Magnetic Field Strength)/[Molar-g])
N_upper = N_lower*e^((g_j*μ*B)/[Molar-g])
This formula uses 2 Constants, 5 Variables

Constants Used

[Molar-g] - Molar gas constant Value Taken As 8.3145
e - Napier's constant Value Taken As 2.71828182845904523536028747135266249

Variables Used

Upper State Particles - Upper State Particles is the number of particles present in upper state in epr spectra i.e in the excited state.
Lower State Particles - Lower State Particles is the number of particles present in ground state in epr spectra.
Lande g Factor - Lande g Factor is a multiplicative term appearing in the expression for the energy levels of an atom in a weak magnetic field.
Bohr Magneton - (Measured in Ampere Square Meter) - Bohr Magneton is the magnitude of the magnetic dipole moment of an electron orbiting an atom with such angular momentum.
External Magnetic Field Strength - (Measured in Ampere per Meter) - External Magnetic Field Strength is produced by moving electric charges and the intrinsic magnetic moments of elementary particles associated with a fundamental quantum property, their spin.

STEP 1: Convert Input(s) to Base Unit

Lower State Particles: 2 --> No Conversion Required
Lande g Factor: 1.5 --> No Conversion Required
Bohr Magneton: 0.0001 Ampere Square Meter --> 0.0001 Ampere Square Meter No Conversion Required
External Magnetic Field Strength: 7E-34 Ampere per Meter --> 7E-34 Ampere per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

N_upper = N_lower*e^((g_j*μ*B)/[Molar-g]) --> 2*e^((1.5*0.0001*7E-34)/[Molar-g])

Evaluating ... ...

N_upper = 2

STEP 3: Convert Result to Output's Unit

2 --> No Conversion Required

FINAL ANSWER

2 <-- Upper State Particles

(Calculation completed in 00.014 seconds)

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Lande g Factor in Electron Paramagnetic Resonance

Go Lande g Factor = 1.5-((Orbital Quantum Number*(Orbital Quantum Number+1))-(Spin Quantum Number*(Spin Quantum Number+1)))/(2*Total Angular Momentum Quantum No*(Total Angular Momentum Quantum No+1))

No. of Particles in Upper State using Boltzmann Distribution

Go Upper State Particles = Lower State Particles*e^((Lande g Factor*Bohr Magneton*External Magnetic Field Strength)/[Molar-g])

Electron Paramagnetic Resonance Frequency

Go Electron Paramagnetic Resonance Frequency = (Lande g Factor*Bohr Magneton*External Magnetic Field Strength)/[hP]

External Magnetic Field Strength

Go External Magnetic Field Strength = (sqrt(Spin Quantum Number*(Spin Quantum Number+1)))*([hP]/(2*3.14))

Energy Difference between Two Spin States

Go Energy Difference between Spin States = (Lande g Factor*Bohr Magneton*External Magnetic Field Strength)

Energy of Negative Spin State

Go Energy of Negative Spin State = -(1/2*(Lande g Factor*Bohr Magneton*External Magnetic Field Strength))

Applied Magnetic Field using External Field

Go External applied Magnetic Field = External Magnetic Field Strength*(1-Local Fields)

Number of Lines Generated

Go Number of Lines Generated = (2*Number of Equivalent Nuclei*Spin Value)+1

Lines Generated for Spin Half

Go Lines Generated for Spin Half = 1+Number of Equivalent Nuclei

No. of Particles in Upper State using Boltzmann Distribution Formula

Upper State Particles = Lower State Particles*e^((Lande g Factor*Bohr Magneton*External Magnetic Field Strength)/[Molar-g])
N_upper = N_lower*e^((g_j*μ*B)/[Molar-g])

What is Probability Distribution?

A Probability Distribution is a statistical function that describes all the possible values and likelihoods that a random variable can take within a given range.

How to Calculate No. of Particles in Upper State using Boltzmann Distribution?

No. of Particles in Upper State using Boltzmann Distribution calculator uses Upper State Particles = Lower State Particles*e^((Lande g Factor*Bohr Magneton*External Magnetic Field Strength)/[Molar-g]) to calculate the Upper State Particles, No. of Particles in Upper State using Boltzmann Distribution (also called Gibbs distribution) is a probability distribution or probability measure that gives the probability that a system will be in a upper state as a function of that state's energy and the temperature of the system. Upper State Particles is denoted by N_upper symbol.

How to calculate No. of Particles in Upper State using Boltzmann Distribution using this online calculator? To use this online calculator for No. of Particles in Upper State using Boltzmann Distribution, enter Lower State Particles (N_lower), Lande g Factor (g_j), Bohr Magneton (μ) & External Magnetic Field Strength (B) and hit the calculate button. Here is how the No. of Particles in Upper State using Boltzmann Distribution calculation can be explained with given input values -> 2 = 2*e^((1.5*0.0001*7E-34)/[Molar-g]).

FAQ

What is No. of Particles in Upper State using Boltzmann Distribution?

No. of Particles in Upper State using Boltzmann Distribution (also called Gibbs distribution) is a probability distribution or probability measure that gives the probability that a system will be in a upper state as a function of that state's energy and the temperature of the system and is represented as N_upper = N_lower*e^((g_j*μ*B)/[Molar-g]) or Upper State Particles = Lower State Particles*e^((Lande g Factor*Bohr Magneton*External Magnetic Field Strength)/[Molar-g]). Lower State Particles is the number of particles present in ground state in epr spectra, Lande g Factor is a multiplicative term appearing in the expression for the energy levels of an atom in a weak magnetic field, Bohr Magneton is the magnitude of the magnetic dipole moment of an electron orbiting an atom with such angular momentum & External Magnetic Field Strength is produced by moving electric charges and the intrinsic magnetic moments of elementary particles associated with a fundamental quantum property, their spin.

How to calculate No. of Particles in Upper State using Boltzmann Distribution?

No. of Particles in Upper State using Boltzmann Distribution (also called Gibbs distribution) is a probability distribution or probability measure that gives the probability that a system will be in a upper state as a function of that state's energy and the temperature of the system is calculated using Upper State Particles = Lower State Particles*e^((Lande g Factor*Bohr Magneton*External Magnetic Field Strength)/[Molar-g]). To calculate No. of Particles in Upper State using Boltzmann Distribution, you need Lower State Particles (N_lower), Lande g Factor (g_j), Bohr Magneton (μ) & External Magnetic Field Strength (B). With our tool, you need to enter the respective value for Lower State Particles, Lande g Factor, Bohr Magneton & External Magnetic Field Strength 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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