Discussion
A nucleus resonates at frequency \( \nu = \gamma B_{0} / 2\pi \). What does this state?
Answer: D
The Larmor equation says the resonance frequency is directly proportional to the applied field, the constant of proportionality being the gyromagnetic ratio of the nucleus divided by two pi. Doubling the field doubles the frequency, which is exactly why instruments are named by the proton frequency they reach: a 400 MHz spectrometer holds about 9.4 tesla. Neither an inverse nor a square root dependence appears anywhere in the treatment, and a field-independent frequency would make the whole technique useless for chemistry.
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