What is the magnitude of the magnetic field?

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SUMMARY

The discussion focuses on calculating the magnitude of the magnetic field applied to a Thallium (Tl) atom with an atomic mass of 203 and an atomic number of 81. The magnetic moment of the Tl nucleus is given as 1.611 µn, and the NMR frequency is determined to be 3.90 MHz. The relationship between torque, magnetic moment, and magnetic field is highlighted, along with the need to understand Larmor precession to solve the problem effectively.

PREREQUISITES
  • Understanding of magnetic moments and their significance in nuclear magnetic resonance (NMR).
  • Familiarity with Larmor precession and its mathematical implications.
  • Knowledge of torque and its relationship to magnetic fields.
  • Basic principles of centripetal force and motion in magnetic fields.
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  • Study the concept of Larmor precession in detail.
  • Learn how to apply the torque equation in magnetic field calculations.
  • Research the relationship between NMR frequency and magnetic field strength.
  • Explore advanced topics in magnetic moments and their applications in NMR spectroscopy.
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Homework Statement



The nucleus of a Tl atom (Atomic mass = 203, element #81) has a magnetic moment of 1.611 µn. A magnetic field is applied to it and its NMR frequency determined to be 3.90 MHz. What is the magnitude of the magnetic field?

Homework Equations



torque = magnetic moment x magnetic field
radius = mv/qB
v = rw
Fcentripetal = mv^2/r

The Attempt at a Solution


I tried (magnetic moment x magnetic field)/radius = mv^2/r but this always leaves me with r in the equation, which is unknown.
 
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You can try looking in your textbook, or do an online search, for "Larmor precession" or "precession of magnetic moment" or something along those lines.
 

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