Gyromagnetic Ratio For A Nucleus
Protons, neutrons, and many nuclei carry nuclear spin, which gives rise to a gyromagnetic ratio as above. The ratio is conventionally written in terms of the proton mass and charge, even for neutrons and for other nuclei, for the sake of simplicity and consistency. The formula is:
where is the nuclear magneton, and is the g-factor of the nucleon or nucleus in question.
The gyromagnetic ratio of a nucleus is particularly important because of the role it plays in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI). These procedures rely on the fact that nuclear spins precess in a magnetic field at a rate called the Larmor frequency, which is simply the product of the gyromagnetic ratio with the magnetic field strength.
Approximate values for some common nuclei are given in the table below.
| Nucleus | (106 rad sā1 T ā1) | (MHz T ā1) |
|---|---|---|
| 1H | 267.513 | 42.576 |
| 2H | 41.065 | 6.536 |
| 3He | -203.789 | -32.434 |
| 7Li | 103.962 | 16.546 |
| 13C | 67.262 | 10.705 |
| 14N | 19.331 | 3.077 |
| 15N | -27.116 | -4.316 |
| 17O | -36.264 | -5.772 |
| 19F | 251.662 | 40.053 |
| 23Na | 70.761 | 11.262 |
| 31P | 108.291 | 17.235 |
| 129Xe | -73.997 | -11.777 |
Read more about this topic: Gyromagnetic Ratio
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