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Larmor Equation
The Larmor equation is important because it is the frequency at which the nucleus will absorb energy. The absorption of that energy will cause the proton to alter its alignment and ranges from 1-100 MHz in MRI. The equation states that the frequency of precession of the nuclear magnetic moment is directly proportional to the product of the magnetic field strength (B0) and the gyromagnetic ratio (g). This is stated mathematically as w= gB0.
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Larmor Frequency
The Larmor precession frequency is the rate of precession of a spin packet under the influence of a magnetic field. The frequency of an RF signal, which will cause a change in the nucleus spin energy level, is given by the Larmor equation. The frequency is determined by the gyro magnetic ratio of atoms and the strength of the magnetic field. The gyromagnetic ratio is different for each nucleus of different atoms.
The stronger the magnetic field, the higher the precessional frequency. If an RF pulse at the Larmor frequency is applied to the nucleus of an atom, the protons will alter their alignment from the direction of the main magnetic field to the direction opposite the main magnetic field. As the proton tries to realign with the main magnetic field, it will emit energy at the Larmor frequency. By varying the magnetic field across the body with a magnetic field gradient, the corresponding variation of the Larmor frequency can be used to encode the position. For protons (hydrogen nuclei), the Larmor frequency is 42.58 MHz/Tesla.
See also Larmor Equation.

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Magnetic Resonance
(MR) Resonance phenomenon resulting in the absorption and/or emission of electromagnetic energy by nuclei (for that reason also nuclear magnetic resonance) or electrons in a static magnetic field, after excitation by a suitable RF magnetic field.
The peak resonance frequency is proportional to the magnetic field, and is given by the Larmor equation. Only unpaired electrons or nuclei with a spin exhibit magnetic resonance. The absorption or emission of energy by atomic nuclei in an external magnetic field after the application of RF excitation pulses using frequencies, which satisfy the conditions of the Larmor equation.
The magnetic resonance phenomenon may be used in one of these ways:
By manipulation of the external field (application of gradient fields), the resonance frequency can become dependent on spatial location, and hence images may be generated (MRI).
The effect of the electron cloud in any atom or molecule is to slightly shield the nucleus from the external field, thus giving any chemical species a characteristic frequency. This gives rise to ‘spectra’ where nuclei in a molecule give rise to specific signals, thus facilitating the detection of individual chemicals by means of their frequency spectra (MRS)

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Resonance Frequency
The frequency at which the resonance phenomenon occurs. The resonance frequency is given by the Larmor equation for MRI and is determined by the inductance and capacitance for RF circuits. An atom will only absorb external energy if that energy is delivered at precisely it’s resonant frequency.
The Larmor equation states that the resonance frequency of a magnetic nucleus (the radio frequency needed to excite a nucleus to the higher spin rate) is directly proportional to the magnetic environment it experiences. Atoms such as hydrogen-1 (1H) and phosporous-31 (31P) resonate at different Larmor radio frequencies because of differences in the magnetic properties of their nuclei. The resonance frequency at 1.5 T for 31P is 25.85 MHz, for 1H, 63.86 MHz.
See also Larmor Frequency.

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Nuclear Magnetic ResonanceMRI Resource Directory:
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(NMR) Nuclear Magnetic Resonance is a physical phenomenon of the magnetic property of nuclei, which have a positive nuclear spin quantum number.
Under the influence of an external static magnetic field this nuclei will precess about the direction of the magnetic field with an angular frequency (Larmor frequency). Through absorption and emission of RF energy (gradients, RF coils) at the resonance frequency (Larmor equation) and the processing of this raw data by the Fourier transformation - physical, chemical, electronic, and structural information about molecules can be obtained (NMR Magnetic Resonance Spectroscopy, Magnetic Resonance Imaging).

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