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Gyromagnetic Ratio given Larmor Frequency Formula

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Gyromagnetic Ratio is the ratio of the magnetic moment of a spinning charged particle to its angular momentum. Check FAQs

γ = \frac{ν L \cdot 2 \cdot π}{(1 - σ) \cdot B 0}

γ - Gyromagnetic Ratio?ν_L - Nuclear Larmor Frequency?σ - Shielding Constant in NMR?B₀ - Magnitude of Magnetic Field in Z-Direction?π - Archimedes' constant?

Gyromagnetic Ratio given Larmor Frequency Example

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Here is how the Gyromagnetic Ratio given Larmor Frequency equation looks like with Values.

Here is how the Gyromagnetic Ratio given Larmor Frequency equation looks like with Units.

Here is how the Gyromagnetic Ratio given Larmor Frequency equation looks like.

5.236 = \frac{7.5 \cdot 2 \cdot 3.1416}{(1 - 0.5) \cdot 18}

5.236C/kg = \frac{7.5Hz \cdot 2 \cdot 3.1416}{(1 - 0.5) \cdot 18T}

5.236 = \frac{7.5 \cdot 2 \cdot 3.1416}{(1 - 0.5) \cdot 18}

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Gyromagnetic Ratio given Larmor Frequency Solution

Follow our step by step solution on how to calculate Gyromagnetic Ratio given Larmor Frequency?

FIRST Step Consider the formula

γ = \frac{ν L \cdot 2 \cdot π}{(1 - σ) \cdot B 0}

Next Step Substitute values of Variables

∴

γ = \frac{7.5Hz \cdot 2 \cdot π}{(1 - 0.5) \cdot 18T}

Next Step Substitute values of Constants

∴

γ = \frac{7.5Hz \cdot 2 \cdot 3.1416}{(1 - 0.5) \cdot 18T}

Next Step Prepare to Evaluate

∴

γ = \frac{7.5 \cdot 2 \cdot 3.1416}{(1 - 0.5) \cdot 18}

Next Step Evaluate

∴

γ = 5.23598775598299C/kg

LAST Step Rounding Answer

∴

γ = 5.236C/kg

Gyromagnetic Ratio given Larmor Frequency Formula Elements

Variables

Constants

Gyromagnetic Ratio

Gyromagnetic Ratio is the ratio of the magnetic moment of a spinning charged particle to its angular momentum.

Symbol: γ

Measurement: Radiation ExposureUnit: C/kg

Note: Value can be positive or negative.

Formulas to find Gyromagnetic Ratio

Nuclear Larmor Frequency

Nuclear Larmor Frequency refers to the rate of precession of the magnetic moment of the proton around the external magnetic field.

Symbol: ν_L

Measurement: FrequencyUnit: Hz

Note: Value can be positive or negative.

Formulas to find Nuclear Larmor Frequency

Shielding Constant in NMR

The Shielding Constant in NMR is a measure of the shielding of an electron from the charge of the nucleus by other inner electrons.

Symbol: σ

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Shielding Constant in NMR

Magnitude of Magnetic Field in Z-Direction

The Magnitude of Magnetic Field in Z-Direction is an area that is under the influence of a magnetic charge in the z-direction.

Symbol: B₀

Measurement: Magnetic FieldUnit: T

Note: Value can be positive or negative.

Formulas to find Magnitude of Magnetic Field in Z-Direction

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other formulas in Nuclear Magnetic Resonance Spectroscopy category

Go Chemical Shift in Nuclear Magnetic Resonance Spectroscopy

δ = (\frac{ν - ν °}{ν °}) \cdot 10^{6}

Go Nuclear Larmor Frequency given Shielding Constant

ν L = (1 - σ) \cdot (\frac{γ \cdot B 0}{2 \cdot π})

Go Local Distribution to Shielding Constant

σ local = σ d + σ p

Go Total Local Magnetic Field

B loc = (1 - σ) \cdot B 0

How to Evaluate Gyromagnetic Ratio given Larmor Frequency?

Gyromagnetic Ratio given Larmor Frequency evaluator uses Gyromagnetic Ratio = (Nuclear Larmor Frequency*2*pi)/((1-Shielding Constant in NMR)*Magnitude of Magnetic Field in Z-Direction) to evaluate the Gyromagnetic Ratio, The Gyromagnetic Ratio given Larmor Frequency formula is defined as the ratio of the magnetic momentum in a particle to its angular momentum. Gyromagnetic Ratio is denoted by γ symbol.

How to evaluate Gyromagnetic Ratio given Larmor Frequency using this online evaluator? To use this online evaluator for Gyromagnetic Ratio given Larmor Frequency, enter Nuclear Larmor Frequency (ν_L), Shielding Constant in NMR (σ) & Magnitude of Magnetic Field in Z-Direction (B₀) and hit the calculate button.

FAQs on Gyromagnetic Ratio given Larmor Frequency

What is the formula to find Gyromagnetic Ratio given Larmor Frequency?

The formula of Gyromagnetic Ratio given Larmor Frequency is expressed as Gyromagnetic Ratio = (Nuclear Larmor Frequency*2*pi)/((1-Shielding Constant in NMR)*Magnitude of Magnetic Field in Z-Direction). Here is an example- 5.235988 = (7.5*2*pi)/((1-0.5)*18).

How to calculate Gyromagnetic Ratio given Larmor Frequency?

With Nuclear Larmor Frequency (ν_L), Shielding Constant in NMR (σ) & Magnitude of Magnetic Field in Z-Direction (B₀) we can find Gyromagnetic Ratio given Larmor Frequency using the formula - Gyromagnetic Ratio = (Nuclear Larmor Frequency*2*pi)/((1-Shielding Constant in NMR)*Magnitude of Magnetic Field in Z-Direction). This formula also uses Archimedes' constant .

Can the Gyromagnetic Ratio given Larmor Frequency be negative?

Yes, the Gyromagnetic Ratio given Larmor Frequency, measured in Radiation Exposure can be negative.

Which unit is used to measure Gyromagnetic Ratio given Larmor Frequency?

Gyromagnetic Ratio given Larmor Frequency is usually measured using the Coulomb per Kilogram[C/kg] for Radiation Exposure. Millicoulomb per Kilogram[C/kg], Microcoulomb per Kilogram[C/kg] are the few other units in which Gyromagnetic Ratio given Larmor Frequency can be measured.

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Gyromagnetic Ratio given Larmor Frequency Formula

Gyromagnetic Ratio given Larmor Frequency Example

Gyromagnetic Ratio given Larmor Frequency Solution

Gyromagnetic Ratio given Larmor Frequency Formula Elements

Other formulas in Nuclear Magnetic Resonance Spectroscopy category

How to Evaluate Gyromagnetic Ratio given Larmor Frequency?

FAQs on Gyromagnetic Ratio given Larmor Frequency

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