One Spin in a Magnetic Field

The nucleus is viewed as a positively charged sphere that spins on its axis, producing a small magnetic field whose strength (magnetogyric ratio or gamma y) is characteristic of the particular isotope (e.g., 1H, 13C, 31P, etc.). 

Throughout this book we will treat y as the strength of the nuclear magnet, ignoring its units and its definition as a ratio. We will also assume that y is positive. 

NMR Spectroscopy Explained Simplified Theory, Applications and Examples for Organic Chemistry and Structural Biology, by Neil E Jacobsen Copyright 2007 John Wiley Sons, Inc. 

The precession frequency, also called the Larmor frequency, is represented as v0 ( new-zero, in hertz or cycles per second). The division by In is sometimes omitted because the units of y can be expressed in hertz per tesla rather than radians per seconds per tesla. When the Larmor frequency is represented in units of radians per second it is called the angular velocity or co0. These are related by a factor of In  

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