Nuclear Larmor Frequency Calculator

Nuclear Larmor Frequency Equation:

\[ \nu_L = \frac{\gamma \cdot B_{loc}}{2\pi} \]

Nuclear Larmor Frequency (ν_L):

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1. What is Nuclear Larmor Frequency?

Nuclear Larmor Frequency refers to the rate of precession of the magnetic moment of the proton around the external magnetic field. It is a fundamental concept in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI).

2. How Does the Calculator Work?

The calculator uses the Nuclear Larmor Frequency equation:

\[ \nu_L = \frac{\gamma \cdot B_{loc}}{2\pi} \]

Where:

\( \nu_L \) — Nuclear Larmor Frequency (Hz)
\( \gamma \) — Gyromagnetic Ratio (C/kg)
\( B_{loc} \) — Local Magnetic Field (T)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: The equation calculates the frequency at which nuclei precess in a magnetic field, which is proportional to both the gyromagnetic ratio and the strength of the local magnetic field.

3. Importance of Nuclear Larmor Frequency

Details: Accurate calculation of Nuclear Larmor Frequency is crucial for NMR spectroscopy and MRI applications, as it determines the resonance frequency for nuclear spins in a magnetic field.

4. Using the Calculator

Tips: Enter the gyromagnetic ratio in coulombs per kilogram (C/kg) and the local magnetic field in tesla (T). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the gyromagnetic ratio?
A: The gyromagnetic ratio is the ratio of the magnetic moment of a spinning charged particle to its angular momentum.

Q2: What is the local magnetic field?
A: Local Magnetic Field is the field felt by a particular nucleus, where the applied field induces currents in the electrons surrounding the nucleus giving rise to a shielding effect.

Q3: What are typical values for gyromagnetic ratios?
A: Different nuclei have different gyromagnetic ratios. For example, the proton's gyromagnetic ratio is approximately 2.675×10⁸ rad/s/T.

Q4: How does this relate to MRI?
A: In MRI, the Larmor frequency determines the radiofrequency needed to excite hydrogen nuclei in the body, which is essential for image formation.

Q5: Are there limitations to this equation?
A: The equation assumes a homogeneous magnetic field and doesn't account for chemical shift effects or other local field variations.