FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

No. of Particles in Upper State using Boltzmann Distribution Formula

Fx Copy

LaTeX Copy

Upper State Particles is the number of particles present in upper state in epr spectra i.e in the excited state. Check FAQs

N upper = N lower \cdot e^{\frac{g j \cdot μ \cdot B}{[Molar-g]}}

N_upper - Upper State Particles?N_lower - Lower State Particles?g_j - Lande g Factor?μ - Bohr Magneton?B - External Magnetic Field Strength?[Molar-g] - Molar gas constant?

No. of Particles in Upper State using Boltzmann Distribution Example

With values

With units

Only example

Here is how the No. of Particles in Upper State using Boltzmann Distribution equation looks like with Values.

Here is how the No. of Particles in Upper State using Boltzmann Distribution equation looks like with Units.

Here is how the No. of Particles in Upper State using Boltzmann Distribution equation looks like.

2 = 2 \cdot e^{\frac{1.5 \cdot 0.0001 \cdot 7E-34}{8.3145}}

2 = 2 \cdot e^{\frac{1.5 \cdot 0.0001A*m² \cdot 7E-34A/m}{8.3145J/K*mol}}

2 = 2 \cdot e^{\frac{1.5 \cdot 0.0001 \cdot 7E-34}{8.3145}}

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Chemistry » Category

EPR Spectroscopy » fx No. of Particles in Upper State using Boltzmann Distribution

No. of Particles in Upper State using Boltzmann Distribution Solution

Follow our step by step solution on how to calculate No. of Particles in Upper State using Boltzmann Distribution?

FIRST Step Consider the formula

N upper = N lower \cdot e^{\frac{g j \cdot μ \cdot B}{[Molar-g]}}

Next Step Substitute values of Variables

∴

N upper = 2 \cdot e^{\frac{1.5 \cdot 0.0001A*m² \cdot 7E-34A/m}{[Molar-g]}}

Next Step Substitute values of Constants

∴

N upper = 2 \cdot e^{\frac{1.5 \cdot 0.0001A*m² \cdot 7E-34A/m}{8.3145J/K*mol}}

Next Step Prepare to Evaluate

∴

N upper = 2 \cdot e^{\frac{1.5 \cdot 0.0001 \cdot 7E-34}{8.3145}}

LAST Step Evaluate

∴

N upper = 2

No. of Particles in Upper State using Boltzmann Distribution Formula Elements

Variables

Constants

Upper State Particles

Upper State Particles is the number of particles present in upper state in epr spectra i.e in the excited state.

Symbol: N_upper

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Upper State Particles

Lower State Particles

Lower State Particles is the number of particles present in ground state in epr spectra.

Symbol: N_lower

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Lower State Particles

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.

Symbol: g_j

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Lande g Factor

Bohr Magneton

Bohr Magneton is the magnitude of the magnetic dipole moment of an electron orbiting an atom with such angular momentum.

Symbol: μ

Measurement: Magnetic MomentUnit: A*m²

Note: Value can be positive or negative.

Formulas to find Bohr Magneton

External Magnetic Field Strength

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.

Symbol: B

Measurement: Magnetic Field StrengthUnit: A/m

Note: Value can be positive or negative.

Formulas to find External Magnetic Field Strength

Molar gas constant

Molar gas constant is a fundamental physical constant that relates the energy of a mole of particles to the temperature of a system.

Symbol: [Molar-g]

Value: 8.3145 J/K*mol

Other formulas in EPR Spectroscopy category

Go Energy Difference between Two Spin States

ΔE +1/2-1/2 = (g j \cdot μ \cdot B)

Go Number of Lines Generated

N lines = (2 \cdot N nuclei \cdot I) + 1

Go Energy of Negative Spin State

E -1/2 = - (\frac{1}{2} \cdot (g j \cdot μ \cdot B))

Go Lines Generated for Spin Half

N I=1/2 = 1 + N nuclei

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

No. of Particles in Upper State using Boltzmann Distribution evaluator uses Upper State Particles = Lower State Particles*e^((Lande g Factor*Bohr Magneton*External Magnetic Field Strength)/[Molar-g]) to evaluate 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 evaluate No. of Particles in Upper State using Boltzmann Distribution using this online evaluator? To use this online evaluator 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.

FAQs on No. of Particles in Upper State using Boltzmann Distribution

What is the formula to find No. of Particles in Upper State using Boltzmann Distribution?

The formula of No. of Particles in Upper State using Boltzmann Distribution is expressed as Upper State Particles = Lower State Particles*e^((Lande g Factor*Bohr Magneton*External Magnetic Field Strength)/[Molar-g]). Here is an example- 2 = 2*e^((1.5*0.0001*7E-34)/[Molar-g]).

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

With Lower State Particles (N_lower), Lande g Factor (g_j), Bohr Magneton (μ) & External Magnetic Field Strength (B) we can find No. of Particles in Upper State using Boltzmann Distribution using the formula - Upper State Particles = Lower State Particles*e^((Lande g Factor*Bohr Magneton*External Magnetic Field Strength)/[Molar-g]). This formula also uses Molar gas constant .

Let Others Know

✖

Facebook

Twitter

Copied!

: Value
: Unit

No. of Particles in Upper State using Boltzmann Distribution Formula

No. of Particles in Upper State using Boltzmann Distribution Example

No. of Particles in Upper State using Boltzmann Distribution Solution

No. of Particles in Upper State using Boltzmann Distribution Formula Elements

Other formulas in EPR Spectroscopy category

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

FAQs on No. of Particles in Upper State using Boltzmann Distribution

Variable Name